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Discovering interpretable piecewise nonlinear model predictive control laws via symbolic decision trees
Ilias Mitrai
https://arxiv.org/abs/2510.10411 https://

Discovering interpretable piecewise nonlinear model predictive control laws via symbolic decision trees
In this paper, we propose symbolic decision trees as surrogate models for approximating model predictive control laws. The proposed approach learns simultaneously the partition of the input domain (splitting logic) as well as local nonlinear expressions for predicting the control action leading to interpretable piecewise nonlinear control laws. The local nonlinear expressions are determined by the learning problem and are modeled using a set of basis functions. The learning task is posed as a m…

Optical-field-induced dips and splits in nonlinear spectra of selective reflection from high-density atomic vapor
V. A. Sautenkov, S. A. Saakyan, A. A. Bobrov, B. B. Zelener
https://arxiv.org/abs/2510.15100

Non-conformally Einstein instantons in Conformal Gravity with and without nonlinear matter fields
Crist\'obal Corral, Borja Diez, Eleftherios Papantonopoulos
https://arxiv.org/abs/2510.11854

Non-conformally Einstein instantons in Conformal Gravity with and without nonlinear matter fields
In this work, we study non-conformally Einstein gravitational instantons in four-dimensional Conformal Gravity, both in vacuum and in the presence of nonlinear conformal matter. First, the one-parameter extension of the Kerr-NUT-AdS metric is analyzed. We obtain their conserved charges by using the Noether-Wald formalism. It turns out that they receive corrections from the linear modes present in Conformal Gravity, which are properly identified. Then, we perform the analytic continuation into t…

Adaptive Nonlinear Model Predictive Control of Monoclonal Antibody Glycosylation in CHO Cell Culture
Yingjie Ma, Jing Guo, Alexis B. Dubs, Krystian K. Ganko, Richard D. Braatz
https://arxiv.org/abs/2510.12333

Adaptive Nonlinear Model Predictive Control of Monoclonal Antibody Glycosylation in CHO Cell Culture
N-glycosylation is a critical quality attribute of monoclonal antibodies (mAbs), the dominant class of biopharmaceuticals. Controlling glycosylation remains difficult due to intrinsic pathway complexity, limited online measurements, and a lack of tailored control strategies. This work applies an adaptive nonlinear model predictive control (ANMPC) framework to a fed-batch mAb production process, using a multiscale model that links extracellular conditions to intracellular Golgi reactions to pred…

Spatial two-grid compact difference scheme for two-dimensional nonlinear diffusion-wave equations with variable exponent
Hao Zhang, Kexin Li, Wenlin Qiu
https://arxiv.org/abs/2510.12188

Spatial two-grid compact difference scheme for two-dimensional nonlinear diffusion-wave equations with variable exponent
This paper presents a spatial two-grid (STG) compact difference scheme for a two-dimensional (2D) nonlinear diffusion-wave equation with variable exponent, which describes, e.g., the propagation of mechanical diffusive waves in viscoelastic media with varying material properties. Following the idea of the convolution approach, the diffusion-wave model is first transformed into an equivalent formulation. A fully discrete scheme is then developed by applying a compact difference approximation in …

Nonlinear instability for the 3D MHD equations around the Taylor-Couette flow
V\'ictor Navarro-Fern\'andez, David Villringer
https://arxiv.org/abs/2510.12707 https://

Nonlinear instability for the 3D MHD equations around the Taylor-Couette flow
We study the 3D magnetohydrodynamics (MHD) equations in an annular cylinder, perturbed around the explicit steady state given by the 3D Taylor-Couette velocity field and zero magnetic field. Combining a recent linear instability result for the magnetic field with the framework of Friedlander, Pavlović and Shvydkoy [Comm. Math. Phys. 264 (2006), no. 2, 335-347], we prove nonlinear instability of the solution around this steady state in $L^p$, for any $p>1$. In particular, our results are, to th…

A microscopic approach to nonlinear theory of spin-charge separation
Oleksandr Tsyplyatyev, Yiqing Jin, Mar\'ia Moreno, Wooi Kiat Tan, Christopher J. B. Ford
https://arxiv.org/abs/2510.09515

A microscopic approach to nonlinear theory of spin-charge separation
The fate of spin-charge separation beyond the low energy remains elusive up to now. Here we develop a microscopic theory of the correlation functions using the strong coupling expansion of the Hubbard model and demonstrate its validity down to the experimentally relevant $r_{\rm s}>1$. Evaluating the spectral function, we show the general stability of the nonlinear spin-charge modes in whole energy band and investigate all the nonlinear features systematically. We confirm the general prediction…

Nonlinear Heisenberg Limit via Uncertainty Principle in Quantum Metrology
Binke Xia, Jingzheng Huang, Yuxiang Yang, Guihua Zeng
https://arxiv.org/abs/2510.09216 https://

Nonlinear Heisenberg Limit via Uncertainty Principle in Quantum Metrology
The Heisenberg limit is acknowledged as the ultimate precision limit in quantum metrology, traditionally implying that root mean square errors of parameter estimation decrease linearly with the time T of evolution and the number N of quantum gates or probes. However, this conventional perspective fails to interpret recent studies of "super-Heisenberg" scaling, where precision improves faster than linearly with T and N. In this work, we revisit the Heisenberg scaling by leveraging the position-m…

Scalable Causal Discovery from Recursive Nonlinear Data via Truncated Basis Function Scores and Tests
Joseph Ramsey, Bryan Andrews
https://arxiv.org/abs/2510.04276 https://

Scalable Causal Discovery from Recursive Nonlinear Data via Truncated Basis Function Scores and Tests
Learning graphical conditional independence structures from nonlinear, continuous or mixed data is a central challenge in machine learning and the sciences, and many existing methods struggle to scale to thousands of samples or hundreds of variables. We introduce two basis-expansion tools for scalable causal discovery. First, the Basis Function BIC (BF-BIC) score uses truncated additive expansions to approximate nonlinear dependencies. BF-BIC is theoretically consistent under additive models an…

Weakly turbulent saturation of the nonlinear scalar ergoregion instability
Nils Siemonsen
https://arxiv.org/abs/2510.07467 https://arxiv.org/pdf/2510.07467…

Weakly turbulent saturation of the nonlinear scalar ergoregion instability
We perform time-domain evolutions of the ergoregion instability on a horizonless spinning ultracompact spacetime in scalar theories with potential-type and derivative self-interactions mimicking the nonlinear structure of the Einstein equations. We find that the instability saturates by triggering a weakly turbulent direct cascade, which transfers energy from the most unstable and large-scale modes to small scales. The cascade's nonlinear timescales of each mode are orders of magnitude shorter …

Emergence of advection-diffusion transport structure and nonlinear amplitude evolution of strongly driven instabilities
Emma G. Devin, Vin\'icius N. Duarte
https://arxiv.org/abs/2510.08735

Emergence of advection-diffusion transport structure and nonlinear amplitude evolution of strongly driven instabilities
Instabilities driven by strong gradients appear in a wide variety of physical systems, including plasmas, neutral fluids, and self-gravitating systems. This work develops an analytic formulation to describe the transport structure and nonlinear amplitude evolution of a discrete, strongly driven instability in the presence of energy sources and sinks. Initially, the mode is found to evolve linearly until the gradient in the distribution has been exhausted. It then transitions to a nonlinear phas…

Revealing signals of higher-order nonlinear showers in particle-laser collisions
T. G. Blackburn, B. King, M. Samuelsson
https://arxiv.org/abs/2510.08679 https://

Revealing signals of higher-order nonlinear showers in particle-laser collisions
Several high power laser facilities are reaching field strengths where leading order strong-field quantum electrodynamical (QED) processes can be measured in the non-perturbative regime for the first time. At very high, as yet unobtainable in the laboratory, field strengths, the contribution of higher-order processes is predicted to dominate, implying a breakdown of current calculational methods. Focusing on nonlinear showers and considering currently available experimental parameters, we find …

Nonlinear Dynamics and Fermi-Pasta-Ulam-Tsingou Recurrences in Macroscopic Ultra-low Loss Levitation
Mehrdad M. Sourki, Wisdom Boinde, Ali N. Amiri, Mahdi Hosseini
https://arxiv.org/abs/2510.09490

Nonlinear Dynamics and Fermi-Pasta-Ulam-Tsingou Recurrences in Macroscopic Ultra-low Loss Levitation
Macroscopic systems, when governed by nonlinear interactions, can display rich behavior from persistent oscillations to signatures of ergodicity breaking. Nonlinearity, long regarded as a nuisance in precision systems, is increasingly recognized as a gateway to new physical regimes. While such dynamics have been extensively studied in optics and atomic physics, macroscopic systems are rarely associated with long-lived coherence and nonlinear control and remain an untapped platform for probing t…

Ultrafast optical gating in a nonlinear lithium niobate microcavity
Ouri Karni, Chirag Vaswani, Thibault Chervy
https://arxiv.org/abs/2510.11965 https://ar…

Ultrafast optical gating in a nonlinear lithium niobate microcavity
Recent advances in optical simulation and computational techniques have renewed interest in high-finesse optical cavities for applications such as enhancing light-matter interactions, engineering complex photonic band structures, and storing quantum information. However, the extended interaction times enabled by these cavities often come at the cost of slow optical read-out protocols and limited control over system transients. To address this challenge, we demonstrate an ultrafast intra-cavity …

Weak localization and antilocalization corrections to nonlinear transport: a semiclassical Boltzmann treatment
Dmitry V. Chichinadze
https://arxiv.org/abs/2510.02684 https://

Weak localization and antilocalization corrections to nonlinear transport: a semiclassical Boltzmann treatment
The nonlinear transport regime is manifested in the nonlinear current-voltage characteristic of the system. An example of such a nonlinear regime is a setup in which current is injected into the sample and the measured voltage drop is quadratic in the injected current. Such a quadratic nonlinear regime requires inversion symmetry to be broken. This is the same symmetry condition as one needs to observe weak antilocalization, which can be prominent in two-dimensional systems. Here, we study the …

Nonlinear Evolution of the Matter Trispectrum with Primordial Parity Violation
Sha Azyzy, Drew Jamieson, Eiichiro Komatsu, Toshiki Kurita
https://arxiv.org/abs/2510.06164 https:…

Nonlinear Evolution of the Matter Trispectrum with Primordial Parity Violation
Parity-odd four-point correlation functions, or trispectra, of cosmic matter density fields provide a unique probe of fundamental symmetries in cosmology. Trispectra of primordial matter density fluctuations produced in the early universe are modified by the subsequent nonlinear structure formation. In this paper, we compute the nonlinear evolution of the parity-odd matter trispectrum to one-loop order, i.e., to third order in density fluctuations, within the framework of effective field theory…

Stochastic nonlinear wave equation with rougher than white noise
Xue-Mei Li, Xianfeng Ren
https://arxiv.org/abs/2510.12221 https://arxiv.org/pdf/2510.12221…

Stochastic nonlinear wave equation with rougher than white noise
We study the singular stochastic wave equation on $\mathbb T^2$, with a cubic nonlinearity and Gaussian rough Matérn forcing (a Fourier multiplier of order $α>0$ applied to space-time white noise) and establish local well-posedness for $α< \tfrac{3}{8}$. This extends [GKO18] beyond white noise and strengthens the quadratic-case result [OO21] ($α<\tfrac 12$). Our argument develops new trilinear estimates in Bourgain spaces together with sharp, case-specific cubic counting estimates.

Nonlinear Hodge correspondence in positive characteristic
Mao Sheng
https://arxiv.org/abs/2510.05578 https://arxiv.org/pdf/2510.05578

Nonlinear Hodge correspondence in positive characteristic
In this article, we extend the nonabelian Hodge correspondence in positive characteristic to the nonlinear setting.

Who Said Neural Networks Aren't Linear?
Nimrod Berman, Assaf Hallak, Assaf Shocher
https://arxiv.org/abs/2510.08570 https://arxiv.org/pdf/2510.08570

Who Said Neural Networks Aren't Linear?
Neural networks are famously nonlinear. However, linearity is defined relative to a pair of vector spaces, $f$$:$$X$$\to$$Y$. Is it possible to identify a pair of non-standard vector spaces for which a conventionally nonlinear function is, in fact, linear? This paper introduces a method that makes such vector spaces explicit by construction. We find that if we sandwich a linear operator $A$ between two invertible neural networks, $f(x)=g_y^{-1}(A g_x(x))$, then the corresponding vector spaces $…

Real-Time Nonlinear Model Predictive Control of Heavy-Duty Skid-Steered Mobile Platform for Trajectory Tracking Tasks
Alvaro Paz, Pauli Mustalahti, Mohammad Dastranj, Jouni Mattila
https://arxiv.org/abs/2510.02976

Real-Time Nonlinear Model Predictive Control of Heavy-Duty Skid-Steered Mobile Platform for Trajectory Tracking Tasks
This paper presents a framework for real-time optimal controlling of a heavy-duty skid-steered mobile platform for trajectory tracking. The importance of accurate real-time performance of the controller lies in safety considerations of situations where the dynamic system under control is affected by uncertainties and disturbances, and the controller should compensate for such phenomena in order to provide stable performance. A multiple-shooting nonlinear model-predictive control framework is pr…

Quantum thermodynamics of Gross-Pitaevskii qubits
Sebastian Deffner
https://arxiv.org/abs/2510.12599 https://arxiv.org/pdf/2510.12599

Quantum thermodynamics of Gross-Pitaevskii qubits
What are the resources that can be leveraged for a thermodynamic device to exhibit genuine quantum advantage? Typically, the answer to this question is sought in quantum correlations. In the present work, we show that quantum Otto engines that operate with nonlinear qubits significantly outperform linear engines. To this end, we develop a comprehensive thermodynamic description of nonlinear qubits starting with identifying the proper thermodynamic equilibrium state. We then show that for ideal …

Magnetotransport in Topological Materials and Nonlinear Hall Effect via First-Principles Electronic Interactions and Band Topology
Dhruv C. Desai, Lauren A. Tan, Jin-Jian Zhou, Shiyu Peng, Jinsoo Park, Marco Bernardi
https://arxiv.org/abs/2510.07585

Magnetotransport in Topological Materials and Nonlinear Hall Effect via First-Principles Electronic Interactions and Band Topology
Topological effects arising from the Berry curvature lead to intriguing transport signatures in quantum materials. Two such phenomena are the chiral anomaly and nonlinear Hall effect (NLHE). A unified description of these transport regimes requires a quantitative treatment of both band topology and electron scattering. Here, we show accurate predictions of the magnetoresistance in topological semimetals and NLHE in noncentrosymmetric materials by solving the Boltzmann transport equation (BTE) w…

Local Rigidity of Quasi--Lie Brackets on Quaternionic Banach Modules and Applications to Nonlinear PDEs
Nassim Athmouni
https://arxiv.org/abs/2510.10124 https://

Local Rigidity of Quasi--Lie Brackets on Quaternionic Banach Modules and Applications to Nonlinear PDEs
We establish a local rigidity theorem for quasi--Lie brackets on quaternionic Banach right modules. Under quantitative control of antisymmetry and Jacobi defects, we construct an explicit bilinear correction that preserves right $\mathbb{H}$--linearity and restores the exact Lie property. The approach combines a radial homotopy operator, a controlled Neumann-series inversion, and a finite-rank adjustment, all with explicit operator estimates. This constructive framework bridges quaternionic fun…

Classification and qualitative properties of positive solutions to double-power nonlinear stationary Schr\"{o}dinger equations
Takafumi Akahori, Slim Ibrahim, Hiroaki Kikuchi, Masataka Shibata, Juncheng Wei
https://arxiv.org/abs/2510.12484

Classification and qualitative properties of positive solutions to double-power nonlinear stationary Schrödinger equations
In this paper, we investigate positive radial solutions to double-power nonlinear stationary Schrodinger equations in three space dimensions. It is now known that the non-uniqueness of H^{1}-positive solutions can occur in three dimensions when the frequency is sufficiently small. Under suitable conditions, in addition to the ground state solution (whose L^{\infty} norm vanishes as the frequency tends to zero), there exists another positive solution that minimizes a different constrained variat…

Study of the stability of the fractional Stokes system from nonlinear optics around the zero equlibrium state
Mihai Ivan
https://arxiv.org/abs/2510.10130 https://

Study of the stability of the fractional Stokes system from nonlinear optics around the zero equlibrium state
The main purpose of this paper is to study the fractional-order system with Caputo derivative associated to single Stokes pulse. The dynamic behavior for this fractional model (called the fractional Stokes system) is investigated, including: the asymptotic stability around zero equilibrium state, the stabilization problem using appropriate linear controls and the numerical integration based on fractional Euler method.

Strong exceptional parameters for the dimension of nonlinear slices
Ryan E. G. Bushling
https://arxiv.org/abs/2510.10844 https://arxiv.org/pdf/2510.10844…

Strong exceptional parameters for the dimension of nonlinear slices
Let $1 \leq m < s \leq n$ and let $A \subseteq \mathbb{R}^n$ be a Borel set of with $s$-dimensional Hausdorff measure $\mathcal{H}^s(A) > 0$. The classical Marstrand slicing theorem states that, for almost every $m$-dimensional subspace $V \subset \mathbb{R}^n$, there is a positive-measure set of $x \in V$ such that $x + V^\perp$ intersects $A$ in a set of Hausdorff dimension $s-m$. We prove a strong and quantitative version of Marstrand's slicing theorem in the Peres-Schlag framework. In parti…

Robust Closed-Form Control for MIMO Nonlinear Systems under Conflicting Time-Varying Hard and Soft Constraints
Farhad Mehdifar, Charalampos P. Bechlioulis, Dimos V. Dimarogonas
https://arxiv.org/abs/2510.11393

Robust Closed-Form Control for MIMO Nonlinear Systems under Conflicting Time-Varying Hard and Soft Constraints
This paper introduces a novel robust closed-form control law to handle time-varying hard and soft constraints in uncertain high-relative-degree nonlinear MIMO systems. These constraints represent spatiotemporal specifications in mechanical systems' operational space, with hard constraints ensuring safety-critical requirements and soft constraints encoding performance or task objectives. Initially, all constraints are consolidated into two separate scalar time-varying hard and soft constraint fu…

Finite element analysis of a nonlinear heat Equation with damping and pumping effects
Rishabh Shukla, Wasim Akram, Manil T. Mohan
https://arxiv.org/abs/2510.10210 https://

Finite element analysis of a nonlinear heat Equation with damping and pumping effects
We study the following nonlinear heat equation with damping and pumping effects (a reaction-diffusion equation) posed on a bounded simply connected convex domain $Ω\subset \mathbb{R}^d$, $d \geq 1$ with Lipschitz boundary $\partialΩ$: $$ \frac{\partial u(t)}{\partial t} - νΔu(t) + α|u(t)|^{p-2}u(t) - \sum_{\ell=1}^M β_{\ell} |u(t)|^{q_{\ell}-2}u(t) = f(t), \quad t>0, $$ subject to homogeneous Dirichlet boundary conditions and the initial condition $u(0)=u_0$, where $2 …

Nonlinear stability of vector multi-solitons in coupled NLS and modified KdV equations
Liming Ling, Huajie Su
https://arxiv.org/abs/2510.12129 https://arxi…

Nonlinear stability of vector multi-solitons in coupled NLS and modified KdV equations
We prove that the $N$-solitons, including breathers and multi-hump solitons, of the coupled nonlinear Schrödinger (CNLS) equations are nonlinearly stable in the Sobolev space $H^{N}$. Moreover, $(N_{1},N_{2})$-solitons of the coupled modified Korteweg--de Vries (CmKdV) equations are shown to be nonlinearly stable in the Sobolev space $H^{2N_{1}+N_{2}}$. The number of negative eigenvalues of the second variation of the Lyapunov functional is $N$ for $N$-solitons of the CNLS equations, and $N_{1…

Total Robustness in Bayesian Nonlinear Regression for Measurement Error Problems under Model Misspecification
Mengqi Chen, Charita Dellaporta, Thomas B. Berrett, Theodoros Damoulas
https://arxiv.org/abs/2510.03131

Total Robustness in Bayesian Nonlinear Regression for Measurement Error Problems under Model Misspecification
Modern regression analyses are often undermined by covariate measurement error, misspecification of the regression model, and misspecification of the measurement error distribution. We present, to the best of our knowledge, the first Bayesian nonparametric framework targeting total robustness that tackles all three challenges in general nonlinear regression. The framework assigns a Dirichlet process prior to the latent covariate-response distribution and updates it with posterior pseudo-samples…

Nonlinear Public Goods Game in Dynamical Environments
Yishen Jiang, Xin Wang, Wenqiang Zhu, Ming Wei, Longzhao Liu, Shaoting Tang, Hongwei Zheng
https://arxiv.org/abs/2510.10259

Nonlinear Public Goods Game in Dynamical Environments
The evolutionary mechanisms of cooperative behavior represent a fundamental topic in complex systems and evolutionary dynamics. Although recent advances have introduced real-world stochasticity in nonlinear public goods game (PGG), such stochasticity remains static, neglecting its origin in the external environment as well as the coevolution of system stochasticity and cooperative behavior driven by environmental dynamics. In this work, we introduce a dynamic environment feedback mechanism into…

The Weakly-Nonlinear Admittance at Open Ends of Two- and Three-Dimensional Acoustic Waveguides
Freddie Jensen, Harry Turnbull, Edward James Brambley
https://arxiv.org/abs/2509.21615

The Weakly-Nonlinear Admittance at Open Ends of Two- and Three-Dimensional Acoustic Waveguides
We formulate a weakly-nonlinear exit condition for open ends of acoustic waveguides without mean flow; to our knowledge this is the first time an acoustic open end has been analysed outside the linear regime. The resulting admittance boundary condition, and its weakly-nonlinear counterpart, extends recent weakly-nonlinear modelling of curved ducts (Jensen & Brambley 2025, arXiv:2503.11536) to include open ends. We approximate free space by considering the open-ended duct to be enclosed within a…

Self-Consistent Fourier-Tschebyshev Representations of the First Normal Stress Difference in Large Amplitude Oscillatory Shear
Nicholas King, Eugene Pashkovski, Reid Patterson, Paige Rockwell, Gareth H. McKinley
https://arxiv.org/abs/2510.09453

Self-Consistent Fourier-Tschebyshev Representations of the First Normal Stress Difference in Large Amplitude Oscillatory Shear
Large Amplitude Oscillatory Shear (LAOS) is a key technique for characterizing nonlinear viscoelasticity in a wide range of materials. Most research to date has focused on the shear stress response to an oscillatory strain input. However, for highly elastic materials such as polymer melts, the time-varying first normal stress difference $N_1(t;ω,γ_0)$ can become much larger than the shear stress at sufficiently large strains, serving as a sensitive probe of the material's nonlinear characteri…

An Efficient Transient Nonlinear Circuit Simulator Using Exponential Integration and Block-Jacobi Precondition
Zijian Zhang, Yuanmiao Lin, Xuesong Chen, Shuting Cai
https://arxiv.org/abs/2509.16219

An Efficient Transient Nonlinear Circuit Simulator Using Exponential Integration and Block-Jacobi Precondition
Transient simulation of linear and nonlinear circuits remains an important task in modern EDA tools. At present, SPICE-like simulators face challenges in parallelization, nonlinear convergence and linear efficiency, especially when applied to large-scale circuits. To address the limitations of simulators in handling various nonlinear circuits, we adopt a generalized row-echelon regularization approach, which extends the applicability of exponential integrators to a broader class of differential…

Simplification of nonlinear equations for a field operator
V. I. Lapushkin
https://arxiv.org/abs/2510.06129 https://arxiv.org/pdf/2510.06129

Simplification of nonlinear equations for a field operator
In this paper, we study different properties of the motion equations of interacting fields. In the second section, we prove that "Wightman's" fields (we use only a subset of Wightman's axioms) are unitarily equivalent to some operators on the vector space ${\cal F}$ (with one mathematical assumption). In the third section, we introduce $L^{\infty}$ and $DL$ Hilbert spaces, which are convenient for analyzing field equations, particularly the equations for $ϕ^3$ theory. Remarkably, we have manag…

A Quantum Generative Framework for Modeling Single-Cell Transcriptomes with Gene-Gene and Cell-Cell Interactions
Selim Romero, Vignesh Kumar, Robert S. Chapkin, James J. Cai
https://arxiv.org/abs/2510.12776

A Quantum Generative Framework for Modeling Single-Cell Transcriptomes with Gene-Gene and Cell-Cell Interactions
Single-cell RNA sequencing (scRNA-seq) data simulation is limited by classical methods that rely on linear correlations, failing to capture the intrinsic, nonlinear dependencies and the simultaneous gene-gene and cell-cell interactions. We introduce qSimCells, a novel hybrid quantum-classical simulator that leverages quantum entanglement to model single-cell transcriptomes. The core innovation is a quantum kernel that uses a parameterized quantum circuit with CNOT gates to encode complex, nonli…

A Closed-form Expression of the Gaussian Noise Model Supporting O-Band Transmission
Zelin Gan, Henrique Buglia, Romulo Aparecido, Mindaugas Jarmolovi\v{c}ius, Eric Sillekens, Jiaqian Yang, Ronit Sohanpal, Robert I. Killey, Polina Bayvel
https://arxiv.org/abs/2510.11867

A Closed-form Expression of the Gaussian Noise Model Supporting O-Band Transmission
We present a novel closed-form model for nonlinear interference (NLI) estimation in low-dispersion O-band transmission systems. The formulation incorporates the four-wave mixing (FWM) efficiency term as well as the coherent contributions of self- and cross-phase modulation (SPM/XPM) across multiple identical spans. This extension enables accurate evaluation of the NLI in scenarios where conventional closed-form Gaussian Noise (GN) models are limited. The proposed model is validated against spli…

Nonlinear seismic amplitude versus offset inversion using the exact Zoeppritz equation
Wiktor Waldemar Weibull, Nisar Ahmed
https://arxiv.org/abs/2512.13172 https://

A Backstepping-KKL observer for a cascade of a nonlinear ODE with a heat equation
Adam Braun (L2S), Lucas Brivadis (L2S), Jean Auriol (L2S)
https://arxiv.org/abs/2510.04941 http…

A Backstepping-KKL observer for a cascade of a nonlinear ODE with a heat equation
We propose an observer design for a cascaded system composed of an arbitrary nonlinear ordinary differential equation (ODE) with a 1D heat equation. The nonlinear output of the ODE imposes a boundary condition on one side of the heat equation, while the measured output is on the other side. The observer design combines an infinitedimensional Kazantzis-Kravaris/Luenberger (KKL) observer for the ODE with a backstepping observer for the heat equation. This construction is the first extension of th…

An adaptive time-stepping strategy for the modified phase field crystal model with a strong nonlinear vacancy potential
Wanrong Hao, Yunqing Huang
https://arxiv.org/abs/2510.11475

An adaptive time-stepping strategy for the modified phase field crystal model with a strong nonlinear vacancy potential
This paper develops three linear and energy-stable schemes for a modified phase field crystal model with a strong nonlinear vacancy potential (VMPFC model). This sixth-order phase-field model enables realistic crystal growth simulation. Starting from a Crank-Nicolson scheme based on the stabilized-SAV (S-SAV) method, we optimize it via the generalized positive auxiliary variable (GPAV) and modified exponential scalar auxiliary variable (ESAV) methods, thereby reducing computational complexity o…

Nonlinear Optical Response in Pseudo-Hermitian Systems at Steady State
S. Sajad Dabiri, Reza Asgari
https://arxiv.org/abs/2510.06580 https://arxiv.org/pdf/…

Nonlinear Optical Response in Pseudo-Hermitian Systems at Steady State
We establish a steady-state theory for nonlinear optical conductivity in pseudo-Hermitian systems. We derive compact formulas for the first and second order conductivity tensors in both the velocity and length gauges and prove their exact equivalence through generalized sum rules and Berry connection identities by formulating the nonlinear response in terms of a biorthogonal density matrix. Utilizing the formalism on parity-time symmetric two-level systems reveals nonlinear phenomena that are n…

Determining nonlinear balance laws in product-type domains by a single local passive boundary observation
Chaohua Duan, Hongyu Liu, Qingle Meng, Li Wang
https://arxiv.org/abs/2510.10571

Determining nonlinear balance laws in product-type domains by a single local passive boundary observation
This paper introduces an operator-theoretic paradigm for solving inverse problems in nonlinear balance laws, shifting the focus from identifying specific functional forms to recovering the input-output actions of the associated flux and source operators. It is established that a single local passive boundary observation suffices to uniquely determine realizations of these operators for systems posed on product-type domains. This framework, which encompasses dynamical regimes, reveals a holograp…

Supercontinuum Generation in 1-decanol
Nathan G. Drouillard, TJ Hammond
https://arxiv.org/abs/2510.12683 https://arxiv.org/pdf/2510.12683

Supercontinuum Generation in 1-decanol
Although solids have been recently used in ultrafast experiments for spectral broadening due to their relatively high nonlinearity, their sensitivity to damage limits their long-term stability. Liquids are a possible alternative to solids as a nonlinear medium because of their comparable nonlinearity and resistance to permanent damage. We generate a supercontinuum in 1-decanol that spans more than an octave from the visible to the near-infrared regime. We measure the nonlinear index of refracti…

Large deviation principle for a stochastic nonlinear damped Schrodinger equation
Sandip Roy, Debopriya Mukherjee, Manil Thankamani Mohan
https://arxiv.org/abs/2510.06110 https:/…

Large deviation principle for a stochastic nonlinear damped Schrodinger equation
The present paper focuses on the stochastic nonlinear Schrodinger equation with polynomial nonlinearity, and a zero-order (no derivatives involved) linear damping. Here, the random forcing term appears as a mix of a nonlinear noise in the Ito sense and a linear multiplicative noise in the Stratonovich sense. We prove the Laplace principle for the family of solutions to the stochastic system in a suitable Polish space, using the weak convergence framework of Budhiraja and Dupuis. This analysis i…

Topology optimization of nonlinear forced response curves via reduction on spectral submanifolds
Hongming Liang, Matteo Pozzi, Jacopo Marconi, Shobhit Jain, Mingwu Li
https://arxiv.org/abs/2510.07900

Topology optimization of nonlinear forced response curves via reduction on spectral submanifolds
Forced response curves (FRCs) of nonlinear systems can exhibit complex behaviors, including hardening/softening behavior and bifurcations. Although topology optimization holds great potential for tuning these nonlinear dynamic responses, its use in high-dimensional systems is limited by the high cost of repeated response and sensitivity analyses. To address this challenge, we employ the spectral submanifolds (SSMs) reduction theory, which reformulates the periodic response as the equilibria of …

Self-Sustained Oscillations of a Nonlinear Optomechanical System in the Low-Excitation Regime
Shivangi Dhiman, K. Rubenbauer, T. Luschmann, A. Marx, A. Metelmann, H. Huebl
https://arxiv.org/abs/2510.01775

Self-Sustained Oscillations of a Nonlinear Optomechanical System in the Low-Excitation Regime
Manifesting across all time, mass and length scales, nonlinearities lie at the core of numerous physical phenomena. Next-generation quantum applications, such as quantum sensing, require the combination of nonlinearity with non-classical correlations. This necessitates the search for an experimental platform which enables a nonlinear response at ultra-low excitation levels in a system with practical sensing potential and quantum compatibility. Here, we report the observation and theoretical mod…

Optimization Outperforms Unscented Techniques for Nonlinear Smoothing
Payton Howell, Aleksandr Aravkin
https://arxiv.org/abs/2510.03846 https://arxiv.org/p…

Optimization Outperforms Unscented Techniques for Nonlinear Smoothing
We review optimization-based approaches to smoothing nonlinear dynamical systems. These approaches leverage the fact that the Extended Kalman Filter and corresponding smoother can be framed as the Gauss-Newton method for a nonlinear least squares maximum a posteriori loss, and stabilized with standard globalization techniques. We compare the performance of the Optimized Kalman Smoother (OKS) to Unscented Kalman smoothing techniques, and show that they achieve significant improvement for highly …

Statistical Guarantees for High-Dimensional Stochastic Gradient Descent
Jiaqi Li, Zhipeng Lou, Johannes Schmidt-Hieber, Wei Biao Wu
https://arxiv.org/abs/2510.12013 https://

Statistical Guarantees for High-Dimensional Stochastic Gradient Descent
Stochastic Gradient Descent (SGD) and its Ruppert-Polyak averaged variant (ASGD) lie at the heart of modern large-scale learning, yet their theoretical properties in high-dimensional settings are rarely understood. In this paper, we provide rigorous statistical guarantees for constant learning-rate SGD and ASGD in high-dimensional regimes. Our key innovation is to transfer powerful tools from high-dimensional time series to online learning. Specifically, by viewing SGD as a nonlinear autoregres…

Generalized $(C, \lambda)$-structure for nonlinear diffeomorphisms of Banach spaces
Sergey Tikhomirov
https://arxiv.org/abs/2510.05499 https://arxiv.org/pd…

Generalized $(C, λ)$-structure for nonlinear diffeomorphisms of Banach spaces
We introduce a notion of generalized $(C, λ)$-structure for nonlinear diffeomorphisms in Banach spaces. It combines generalized hyperbolicity for linear operators in Banach spaces with $(C, λ)$-structure for diffeomorphisms on compact manifolds. The main differencies are that we allow the hyperbolic splitting to be discontinuous and in invariance condition assume only inclusions instead of equalities for both stable and unstable subspace, which allows us to cover Morse-Smale systems and gener…

Crosslisted article(s) found for hep-th. https://arxiv.org/list/hep-th/new
[1/1]:
- The Effective Radius of an Electric Point Charge in Nonlinear Electrodynamics
Tengyang Liu, Yisong Yang

Sliding-Window Signatures for Time Series: Application to Electricity Demand Forecasting
Nina Drobac (LPSM), Margaux Br\'eg\`ere (LPSM), Joseph de Vilmarest (LPSM), Olivier Wintenberger (LPSM)
https://arxiv.org/abs/2510.12337

Sliding-Window Signatures for Time Series: Application to Electricity Demand Forecasting
Nonlinear and delayed effects of covariates often render time series forecasting challenging. To this end, we propose a novel forecasting framework based on ridge regression with signature features calculated on sliding windows. These features capture complex temporal dynamics without relying on learned or hand-crafted representations. Focusing on the discrete-time setting, we establish theoretical guarantees, namely universality of approximation and stationarity of signatures. We introduce an …

A posteriori analysis for nonlinear convection-diffusion systems
Andreas Dedner, Jan Giesselmann, Kiwoong Kwon, Tristan Pryer
https://arxiv.org/abs/2510.09449 https://

A posteriori analysis for nonlinear convection-diffusion systems
This work provides reliable a posteriori error estimates for Runge-Kutta discontinuous Galerkin approximations of nonlinear convection-diffusion systems. The classes of systems we study are quite general with a focus on convection-dominated and degenerate parabolic problems. Our a posteriori error bounds are valid for a family of discontinuous Galerkin spatial discretizations and various temporal discretizations that include explicit and implicit-explicit time-stepping schemes, popular tools fo…

Nonlinear Response Relations and Fluctuation-Response Inequalities for Nonequilibrium Stochastic Systems
Jiming Zheng, Zhiyue Lu
https://arxiv.org/abs/2509.19606 https://…

Nonlinear Response Relations and Fluctuation-Response Inequalities for Nonequilibrium Stochastic Systems
Predicting how systems respond to external perturbations far from equilibrium remains a fundamental challenge across physics, chemistry, and biology. We present a unified response framework for stochastic Markov dynamics that integrates linear and nonlinear perturbations. Our formalism expresses nonlinear responses of observables in terms of the covariance between the observable and a nonlinear conjugate variable. The nonlinear conjugate variable is subject to the complete Bell polynomial form …

Nonlinear Strain-Mediated Magnetoelectric Coupling in Sub-Microscale Ni/BPZT Thin-Film Devices
Fanfan Meng, Emma Van Meirvenne, Federica Luciano, Xiangyu Wu, Yves Deblock, Kaustuv Banerjee, Peter Rickhaus, Florin Ciubotaru, Christoph Adelmann
https://arxiv.org/abs/2510.09795

Nonlinear Strain-Mediated Magnetoelectric Coupling in Sub-Microscale Ni/BPZT Thin-Film Devices
Strain-mediated magnetoelectric (ME) heterostructures enable electric-field control of magnetism and are promising for ultra-low-power spintronic logic. Yet achieving spatially selective, low-voltage control in thin films and quantifying ME coupling across the full ferroelastic loop remains challenging. Here, we investigate sub-micrometer Ni/BPZT thin-film devices with laterally patterned gates that localize in-plane strain beneath the Ni stripe and modulate its magnetization. We use anisotropi…

Ergoregion instability in bosonic stars: scalar mode structure, universality, and weakly nonlinear effects
Nils Siemonsen
https://arxiv.org/abs/2510.07468 https://

Ergoregion instability in bosonic stars: scalar mode structure, universality, and weakly nonlinear effects
Ultracompact spinning horizonless spacetimes with ergoregions are subject to the ergoregion instability. We systematically investigate the instability of a massless scalar field in a variety of rapidly spinning Proca stars and boson stars using WKB-, frequency-, and time-domain methods. We find universal features in the mode structure: the onset of the instability is signaled by a zero-mode, the mode frequencies and growth rates are related by a simple scaling relation in the small-frequency li…

Nonlinear Model Predictive Control with Single-Shooting Method for Autonomous Personal Mobility Vehicle
Rakha Rahmadani Pratama, Catur Hilman A. H. B. Baskoro, Joga Dharma Setiawan, Dyah Kusuma Dewi, P Paryanto, Mochammad Ariyanto, Roni Permana Saputra
https://arxiv.org/abs/2509.22694

Nonlinear Model Predictive Control with Single-Shooting Method for Autonomous Personal Mobility Vehicle
This paper introduces a proposed control method for autonomous personal mobility vehicles, specifically the Single-passenger Electric Autonomous Transporter (SEATER), using Nonlinear Model Predictive Control (NMPC). The proposed method leverages a single-shooting approach to solve the optimal control problem (OCP) via non-linear programming (NLP). The proposed NMPC is implemented to a non-holonomic vehicle with a differential drive system, using odometry data as localization feedback to guide t…

Crosslisted article(s) found for hep-ph. https://arxiv.org/list/hep-ph/new
[1/1]:
- The Effective Radius of an Electric Point Charge in Nonlinear Electrodynamics
Tengyang Liu, Yisong Yang

Nonlinear System Identification for Model-Based Control of Waked Wind Turbines
Sebastiano Randino, Lorenzo Schena, Nicolas Coudou, Emanuele Garone, Miguel Alfonso Mendez
https://arxiv.org/abs/2510.07336

Nonlinear System Identification for Model-Based Control of Waked Wind Turbines
This work presents a nonlinear system identification framework for modeling the power extraction dynamics of wind turbines, including both freestream and waked conditions. The approach models turbine dynamics using data-driven power coefficient maps expressed as combinations of compact radial basis functions and polynomial bases, parameterized in terms of tip-speed ratio and upstream conditions. These surrogate models are embedded in a first-order dynamic system suitable for model-based control…

Gaussian beam interactions and inverse source problems for nonlinear wave equations
Matti Lassas, Tony Liimatainen, Valter Pohjola, Teemu Tyni
https://arxiv.org/abs/2510.11494 h…

Gaussian beam interactions and inverse source problems for nonlinear wave equations
We study the inverse source problem for the semilinear wave equation \[ (\Box_g + q_1)u + q_2 u^2 = F, \] on a globally hyperbolic Lorentzian manifold. We demonstrate that the coefficients $q_1$ and $q_2$, as well as the source term $F$, can be recovered up to a natural gauge symmetry inherent in the problem from local measurements. Furthermore, if $q_1$ is known, we establish the unique recovery of the source $F$, which is in a striking contrast to inverse source problems for linear equations …

Optimal Control with Lyapunov Stability Guarantees for Space Applications
Abhijeet, Mohamed Naveed Gul Mohamed, Aayushman Sharma, Suman Chakravorty
https://arxiv.org/abs/2510.08854

Optimal Control with Lyapunov Stability Guarantees for Space Applications
This paper investigates the infinite horizon optimal control problem (OCP) for space applications characterized by nonlinear dynamics. The proposed approach divides the problem into a finite horizon OCP with a regularized terminal cost, guiding the system towards a terminal set, and an infinite horizon linear regulation phase within this set. This strategy guarantees global asymptotic stability under specific assumptions. Our method maintains the system's fully nonlinear dynamics until it reach…

Test time training enhances in-context learning of nonlinear functions
Kento Kuwataka, Taiji Suzuki
https://arxiv.org/abs/2509.25741 https://arxiv.org/pdf/…

Test time training enhances in-context learning of nonlinear functions
Test-time training (TTT) enhances model performance by explicitly updating designated parameters prior to each prediction to adapt to the test data. While TTT has demonstrated considerable empirical success, its theoretical underpinnings remain limited, particularly for nonlinear models. In this paper, we investigate the combination of TTT with in-context learning (ICL), where the model is given a few examples from the target distribution at inference time. We analyze this framework in the sett…

Holographic Turbulence and the Fractal Dimension of the Turbulent Horizon
Jia Du, Yu Tian, Hongbao Zhang
https://arxiv.org/abs/2510.12198 https://arxiv.org…

Holographic Turbulence and the Fractal Dimension of the Turbulent Horizon
We study two-dimensional turbulence driven by a scalar operator within the framework of the AdS/CFT correspondence, where the external driving source is used to sustain a quasi-steady turbulent state. We numerically construct dynamical and spatially inhomogeneous turbulent black holes in the asymptotically $\mathrm{AdS}_4$ spacetime by solving the full nonlinear equations of motion in the Bondi-Sachs formalism. The inverse energy cascade and the corresponding energy spectrum of both decaying an…

Non-linear causal bulk viscosity in Unified Dark Matter Cosmologies
Guillermo Palma, Gabriel Gomez
https://arxiv.org/abs/2510.11900 https://arxiv.org/pdf/2…

Non-linear causal bulk viscosity in Unified Dark Matter Cosmologies
We propose a bulk viscous unified dark matter scenario based on a nonlinear extension of the full causal Israel-Stewart theory. This framework allows the viscous fluid to remain far from equilibrium, an essential feature for a physically consistent description of viscosity-driven accelerated expansion. We adopt the standard parametrization for the bulk viscosity, $ξ= ξ_{0} ρ_{m}^{s}$, treating $s$ as a free parameter, and study the model in a spatially flat Friedmann-Robertson-Walker backgro…

Quantum reservoir computing using Jaynes-Cummings model
Sreetama Das, Gian Luca Giorgi, Roberta Zambrini
https://arxiv.org/abs/2510.00171 https://arxiv.org…

Quantum reservoir computing using Jaynes-Cummings model
We investigate quantum reservoir computing (QRC) using a hybrid qubit-boson system described by the Jaynes-Cummings (JC) Hamiltonian and its dispersive limit (DJC). These models provide high-dimensional Hilbert spaces and intrinsic nonlinear dynamics, making them powerful substrates for temporal information processing. We systematically benchmark both reservoirs through linear and nonlinear memory tasks, demonstrating that they exhibit an unusual superior nonlinear over linear memory capacity. …

Reachable Predictive Control: A Novel Control Algorithm for Nonlinear Systems with Unknown Dynamics and its Practical Applications
Taha Shafa, Yiming Meng, Melkior Ornik
https://arxiv.org/abs/2510.02623

Reachable Predictive Control: A Novel Control Algorithm for Nonlinear Systems with Unknown Dynamics and its Practical Applications
This paper proposes an algorithm capable of driving a system to follow a piecewise linear trajectory without prior knowledge of the system dynamics. Motivated by a critical failure scenario in which a system can experience an abrupt change in its dynamics, we demonstrate that it is possible to follow a set of waypoints comprised of states analytically proven to be reachable despite not knowing the system dynamics. The proposed algorithm first applies small perturbations to locally learn the sys…

All-optical nonlinear phase modulation in open semiconductor microcavities
Fedor A. Benimetskiy, Paul M. Walker, Anthony Ellul, Oleksandr Kyriienko, Martina Morassi, Aristide Lema\^itre, Tommi Isoniemi, Maurice S. Skolnick, Jacqueline Bloch, Sylvain Ravets, Dmitry N. Krizhanovskii
https://arxiv.org/abs/2510.04789

All-optical nonlinear phase modulation in open semiconductor microcavities
We report a significant advancement in ultra low power light-by-light phase modulation using open semiconductor microcavities in the strong light-matter coupling regime. We achieve cross-phase modulation of up to 247$\pm$17 mrad per particle between laser beams attenuated to single-photon average intensities. This breakthrough extends the potential for quantum information processing and nonlinear quantum optics in strongly coupled light-matter systems, setting a new benchmark in the field witho…

Robust stability of event-triggered nonlinear moving horizon estimation
Isabelle Krauss, Victor G. Lopez, Matthias A. M\"uller
https://arxiv.org/abs/2510.04814 https://

Robust stability of event-triggered nonlinear moving horizon estimation
In this work, we propose an event-triggered moving horizon estimation (ET-MHE) scheme for the remote state estimation of general nonlinear systems. In the presented method, whenever an event is triggered, a single measurement is transmitted and the nonlinear MHE optimization problem is subsequently solved. If no event is triggered, the current state estimate is updated using an open-loop prediction based on the system dynamics. Moreover, we introduce a novel event-triggering rule under which we…

Robust and efficient solvers for nonlinear partial differential equations based on random feature method
Longze Tan
https://arxiv.org/abs/2510.04170 https://

Robust and efficient solvers for nonlinear partial differential equations based on random feature method
The random feature method (RFM), a mesh-free machine learning-based framework, has emerged as a promising alternative for solving PDEs on complex domains. However, for large three-dimensional nonlinear problems, attaining high accuracy typically requires domain partitioning with many collocation points and random features per subdomain, which leads to extremely large and ill-conditioned nonlinear least-squares systems. To overcome these challenges, we propose two randomized Newton-type solvers.…

Rapid boundary stabilization of 1D nonlinear parabolic equations
Yu Xiao, Can Zhang
https://arxiv.org/abs/2510.03740 https://arxiv.org/pdf/2510.03740

Rapid boundary stabilization of 1D nonlinear parabolic equations
In this paper, we focus on the rapid boundary stabilization of 1D nonlinear parabolic equations via the modal decomposition method. The nonlinear term is assumed to satisfy certain local Lipschitz continuity and global growth conditions. Through the modal decomposition, we construct a feedback control that modifies only the unstable eigenvalues to achieve spectral reduction. Under this control, we establish locally rapid stabilization by estimating the nonlinearity in Lyapunov stability analysi…

Can One Model Gravitational Nonlinear Memory with Fractional Derivative Operators?
Sercan Kaya, Bayram Tekin
https://arxiv.org/abs/2510.07232 https://arxiv…

Can One Model Gravitational Nonlinear Memory with Fractional Derivative Operators?
We investigate whether fractional calculus, with its intrinsic long-tailed memory and nonlocal features, can provide a viable model for gravitational-wave memory effects. We consider two toy constructions: ($i$) a fractional modification of the linearized Einstein field equations using a sequential Caputo operator, and ($ii$) a fractionalized quadrupole formula where the source moment is acted upon by the same operator. Both constructions yield history-dependent responses with small memory-like…

Teleoperator-Aware and Safety-Critical Adaptive Nonlinear MPC for Shared Autonomy in Obstacle Avoidance of Legged Robots
Ruturaj Sambhus, Muneeb Ahmad, Basit Muhammad Imran, Sujith Vijayan, Dylan P. Losey, Kaveh Akbari Hamed
https://arxiv.org/abs/2509.22815

Teleoperator-Aware and Safety-Critical Adaptive Nonlinear MPC for Shared Autonomy in Obstacle Avoidance of Legged Robots
Ensuring safe and effective collaboration between humans and autonomous legged robots is a fundamental challenge in shared autonomy, particularly for teleoperated systems navigating cluttered environments. Conventional shared-control approaches often rely on fixed blending strategies that fail to capture the dynamics of legged locomotion and may compromise safety. This paper presents a teleoperator-aware, safety-critical, adaptive nonlinear model predictive control (ANMPC) framework for shared …

Control of photoionization by resonant phase-locked pulse pairs
Edvin Olofsson, Evan Lovelle Fulton, Rezvan Tahouri, Mattias Bertolino, Jean Marcel Ngoko Djiokap, Jan Marcus Dahlstr\"om
https://arxiv.org/abs/2510.09441

Control of photoionization by resonant phase-locked pulse pairs
We study the nonlinear and resonant process of two-photon ionization of atoms (He and H) in a pump-probe scheme. The pump pulse prepares the quantum system in a superposition of the ground state and an excited bound state. By varying the phase difference between the pulses, we show how it is possible to coherently control the dressed-state population during the probe pulse. Our main result is that for certain laser parameters, the control over the dressed state population leads to strong contro…

Annealed Ensemble Kalman Inversion for Constrained Nonlinear Model Predictive Control: An ADMM Approach
Ahmed Khalil, Mohamed Safwat, Efstathios Bakolas
https://arxiv.org/abs/2510.00559

Annealed Ensemble Kalman Inversion for Constrained Nonlinear Model Predictive Control: An ADMM Approach
This work proposes a novel Alternating Direction Method of Multipliers (ADMM)-based Ensemble Kalman Inversion (EKI) algorithm for solving constrained nonlinear model predictive control (NMPC) problems. First, the stage-wise nonlinear inequality constraints in the NMPC problem are embedded via an augmented Lagrangian with nonnegative slack variables. We then show that the unconstrained augmented Lagrangian formulation of the NMPC admits a Bayesian interpretation: under a Gaussian observation mod…

On the Cahn-Hilliard equation with nonlinear diffusion: the non-convex case
Monica Conti, Stefania Gatti, Andrea Giorgini, Giulio Schimperna
https://arxiv.org/abs/2510.08287 htt…

On the Cahn-Hilliard equation with nonlinear diffusion: the non-convex case
We investigate the Cahn-Hilliard equation with nonlinear diffusion and non-degenerate mobility modeling phase separation phenomena in complex systems (e.g., crystals and polymers). Previous results in the literature on this model relied on the strong convexity assumption of the gradient part of the energy, which excludes relevant cases. In this work, we remove the convexity condition and establish new qualitative properties of solutions under general assumptions on the diffusion and mobility fu…

Impact of nonlinear spectral broadening on the phase noise properties of electro-optic frequency comb
Aleksandr Razumov, Yijia Cai, Jasper Riebesehl, Eric Sillekens, Ronit Sohanpal, Francesco Da Ros, Zhixin Liu, Darko Zibar
https://arxiv.org/abs/2510.02868

Impact of nonlinear spectral broadening on the phase noise properties of electro-optic frequency comb
Electro-optic modulation is an attractive approach for generating flat, stable, and low-noise optical frequency combs with relatively high power per comb line. However, a key limitation of electro-optic combs is the restricted number of comb lines imposed by the available RF source power. To overcome this limitation, a nonlinear spectral broadening stage is typically employed. The phase noise characteristics of an electro-optic comb are well described by the standard phase noise model, which de…

Linearizing a nonlinear eigenvalue problem with quadratic rational eigenvector nonlinearities
Victor Janssens, Karl Meerbergen, Wim Michiels
https://arxiv.org/abs/2510.02900 htt…

Linearizing a nonlinear eigenvalue problem with quadratic rational eigenvector nonlinearities
Nonlinear eigenvalue problems with eigenvector nonlinearities (NEPv) are algebraic eigenvalue problems whose matrix depends on the eigenvector. Applications range from computational quantum mechanics to machine learning. Due to its nonlinear behavior, existing methods almost exclusively rely on fixed-point iterations, the global convergence properties of which are only understood in specific cases. Recently, a certain class of NEPv with linear rational eigenvector nonlinearities has been linear…

Long-time behaviour of sphalerons in $\phi^4$ models with a false vacuum
Stephen C. Anco, Danial Saadatmand
https://arxiv.org/abs/2510.04283 https://arxiv.…

Long-time behaviour of sphalerons in $ϕ^4$ models with a false vacuum
Sphalerons in nonlinear Klein-Gordon models are unstable lump-like solutions that arise from a saddle point between true and false vacua in the energy functional. Numerical simulations are presented which show the sphaleron evolving into an accelerating kink-antikink pair whose separation approaches the speed of light asymptotically at large times. Utilizing a nonlinear collective coordinate method, an approximate analytical solution is derived for this evolution. These results indicate that an…

The Age-Structured Chemostat with Substrate Dynamics as a Control System
Iasson Karafyllis, Dionysis Theodosis, Miroslav Krstic
https://arxiv.org/abs/2511.09963 https://arxiv.org/pdf/2511.09963 https://arxiv.org/html/2511.09963
arXiv:2511.09963v1 Announce Type: new
Abstract: In this work we study an age-structured chemostat model with a renewal boundary condition and a coupled substrate equation. The model is nonlinear and consists of a hyperbolic partial differential equation and an ordinary differential equation with nonlinear, nonlocal terms appearing both in the ordinary differential equation and the boundary condition. Both differential equations contain a non-negative control input, while the states of the model are required to be positive. Under an appropriate weak solution framework, we determine the state space and the input space for this model. We prove global existence and uniqueness of solutions for all admissible initial conditions and all allowable control inputs. To this purpose we employ a combination of Banach's fixed-point theorem with implicit solution formulas and useful solution estimates. Finally, we show that the age-structured chemostat model gives a well-defined control system on a metric space.
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Data-driven Practical Stabilization of Nonlinear Systems via Chain Policies: Sample Complexity and Incremental Learning
Roy Siegelmann, Enrique Mallada
https://arxiv.org/abs/2510.03982

Data-driven Practical Stabilization of Nonlinear Systems via Chain Policies: Sample Complexity and Incremental Learning
We propose a method for data-driven practical stabilization of nonlinear systems with provable guarantees, based on the concept of Nonparametric Chain Policies (NCPs). The approach employs a normalized nearest-neighbor rule to assign, at each state, a finite-duration control signal derived from stored data, after which the process repeats. Unlike recent works that model the system as linear, polynomial, or polynomial fraction, we only assume the system to be locally Lipschitz. Our analysis buil…

A Quantum Algorithm for Nonlinear Electromagnetic Fluid Dynamics via Koopman-von Neumann Linearization
Hayato Higuchi, Yuki Ito, Kazuki Sakamoto, Keisuke Fujii, Akimasa Yoshikawa
https://arxiv.org/abs/2509.22503

A Quantum Algorithm for Nonlinear Electromagnetic Fluid Dynamics via Koopman-von Neumann Linearization
To simulate plasma phenomena, large-scale computational resources have been employed in developing high-precision and high-resolution plasma simulations. One of the main obstacles in plasma simulations is the requirement of computational resources that scale polynomially with the number of spatial grids, which poses a significant challenge for large-scale modeling. To address this issue, this study presents a quantum algorithm for simulating the nonlinear electromagnetic fluid dynamics that gov…

Stable determination of the nonlinear parameter in the non-diffusive Westervelt equation from the Dirichlet-to-Neumann map
Mike Wendels
https://arxiv.org/abs/2510.02553 https://…

Stable determination of the nonlinear parameter in the non-diffusive Westervelt equation from the Dirichlet-to-Neumann map
The Westervelt equation models the propagation of nonlinear acoustic waves in a regime well-suited for applications such as medical ultrasound imaging. In this work, we prove that the nonlinear parameter, as well as the sound speed, can be stably recovered from the Dirichlet-to-Neumann map associated with the non-diffusive Westervelt equation in (1+3)-dimensions. This result is essential for the feasibility of reconstruction methods. The Dirichlet-to-Neumann map encodes boundary measurements by…

Quasinormal modes from numerical relativity with Bayesian inference
Richard Dyer, Christopher J. Moore
https://arxiv.org/abs/2510.11783 https://arxiv.org/p…

Quasinormal modes from numerical relativity with Bayesian inference
Numerical relativity (NR) enables the study of physics in strong and dynamical gravitational fields and provides predictions for the gravitational-wave signals produced by merging black holes. Despite the impressive accuracy of modern codes, the resulting waveforms inevitably contain numerical uncertainties. Quantifying these uncertainties is important, especially for studies probing subdominant or nonlinear effects around the merger and ringdown. This paper describes a flexible Gaussian-proces…

Direct Data-Driven Predictive Control for a Three-dimensional Cable-Driven Soft Robotic Arm
Cheng Ouyang, Moeen Ul Islam, Dong Chen, Kaixiang Zhang, Zhaojian Li, Xiaobo Tan
https://arxiv.org/abs/2510.08953

Direct Data-Driven Predictive Control for a Three-dimensional Cable-Driven Soft Robotic Arm
Soft robots offer significant advantages in safety and adaptability, yet achieving precise and dynamic control remains a major challenge due to their inherently complex and nonlinear dynamics. Recently, Data-enabled Predictive Control (DeePC) has emerged as a promising model-free approach that bypasses explicit system identification by directly leveraging input-output data. While DeePC has shown success in other domains, its application to soft robots remains underexplored, particularly for thr…

Global Optimization Algorithm for Mixed-Integer Nonlinear Programs with Trigonometric Functions
Christopher Montez, Sujeevraja Sanjeevi, Kaarthik Sundar
https://arxiv.org/abs/2509.26516

Global Optimization Algorithm for Mixed-Integer Nonlinear Programs with Trigonometric Functions
This article presents the first mixed-integer linear programming (MILP)-based iterative algorithm to solve factorable mixed-integer nonlinear programs (MINLPs) with bounded, differentiable periodic functions to global optimality with an emphasis on trigonometric functions. At each iteration, the algorithm solves a MILP relaxation of the original MINLP to obtain a bound on the optimal objective value. The relaxations are constructed using partitions of variables involved in each nonlinear term a…

Nonlinear Stability of the Rayleigh-Taylor Problem in Quantum Navier-Stokes Equations
Fei Jiang, Yajie Zhang, Zhipeng Zhang, Youyi Zhao
https://arxiv.org/abs/2510.07695 https://…

Nonlinear Stability of the Rayleigh-Taylor Problem in Quantum Navier-Stokes Equations
It is well-known that the Rayleigh--Taylor (abbr. RT) instability can be completely inhibited by the quantum effect stabilization in proper circumstances leading to a cutoff wavelength in the \emph{linear} motion equations. Motivated by the linear theory, we further investigate the {stability} for the \emph{nonlinear} RT problem of quantum Navier--Stokes equations in a slab with Navier boundary condition, and rigorously prove the inhibition of RT instability by the quantum effect under a proper…

Mass-Centered GCM Framework in Perturbations of Kerr(-Newman)
Allen Juntao Fang, Elena Giorgi, Jingbo Wan
https://arxiv.org/abs/2510.10811 https://arxiv.or…

Mass-Centered GCM Framework in Perturbations of Kerr(-Newman)
The nonlinear stability problem for black hole solutions of the Einstein equations critically depends on choosing an appropriate geometric gauge. In the vacuum setting, the use of Generally Covariant Modulated (GCM) spheres and hypersurfaces has played a central role in the proof of stability for slowly rotating Kerr spacetime. In this work, we develop an alternative GCM framework, that we call mass-centered, designed to overcome the breakdown of the standard GCM construction in the charged cas…

Time-relaxation structure-preserving explicit low-regularity integrators for the nonlinear Schr\"odinger equation
Hang Li, Xicui Li, Katharina Schratz, Bin Wang
https://arxiv.org/abs/2510.02963

Time-relaxation structure-preserving explicit low-regularity integrators for the nonlinear Schrödinger equation
We propose and rigorously analyze a novel family of explicit low-regularity exponential integrators for the nonlinear Schrödinger (NLS) equation, based on a time-relaxation framework. The methods combine a resonance-based scheme for the twisted variable with a dynamically adjusted relaxation parameter that guarantees exact mass conservation. Unlike existing symmetric or structure-preserving low-regularity integrators, which are typically implicit and computationally expensive, the proposed met…

Robustly Constrained Dynamic Games for Uncertain Nonlinear Dynamics
Shuyu Zhan, Chih-Yuan Chiu, Antoine P. Leeman, Glen Chou
https://arxiv.org/abs/2509.16826 https://

Robustly Constrained Dynamic Games for Uncertain Nonlinear Dynamics
We propose a novel framework for robust dynamic games with nonlinear dynamics corrupted by state-dependent additive noise, and nonlinear agent-specific and shared constraints. Leveraging system-level synthesis (SLS), each agent designs a nominal trajectory and a causal affine error feedback law to minimize their own cost while ensuring that its own constraints and the shared constraints are satisfied, even under worst-case noise realizations. Building on these nonlinear safety certificates, we …

Global weak solutions to nonlinear kinetic Fokker--Planck equations in bounded domains under physical initial data
Young-Pil Choi, Sihyun Song
https://arxiv.org/abs/2510.06656 h…

Global weak solutions to nonlinear kinetic Fokker--Planck equations in bounded domains under physical initial data
We establish the global existence of weak solutions to a nonlinear kinetic Fokker--Planck equation with degenerate diffusion, under either inflow or partial absorption-reflection boundary conditions. The novelty of our approach lies in constructing solutions under solely the physical assumptions on the initial and boundary data, namely finite mass, kinetic energy, and entropy, with no additional regularity imposed. To overcome the lack of uniform ellipticity, we develop a new compactness princi…

Einstein-Maxwell Equations on Mass-Centered GCM Hypersurfaces
Allen Juntao Fang, Elena Giorgi, Jingbo Wan
https://arxiv.org/abs/2510.10814 https://arxiv.or…

Einstein-Maxwell Equations on Mass-Centered GCM Hypersurfaces
The resolution of the nonlinear stability of black holes as solutions to the Einstein equations relies crucially on imposing the right geometric gauge conditions. In the vacuum case, the use of Generally Covariant Modulated (GCM) spheres and hypersurfaces has been successful in the proof of stability for slowly rotating Kerr spacetime. For the charged setting, our companion paper introduced an alternative mass-centered GCM framework, adapted to the additional difficulties of the Einstein-Maxwel…

Mathematical Modeling of Networks in Strength of Materials
Ioannis Dassios
https://arxiv.org/abs/2510.10132 https://arxiv.org/pdf/2510.10132

Mathematical Modeling of Networks in Strength of Materials
We study a material modeled as a network of nodes connected by edges. Using a discrete approach, we build a nonlinear algebraic system that connects applied forces to internal forces and node positions. The model can describe elasticity, plasticity, and possibly cracking. The goal is to solve this system and understand how the material responds. Students are asked to start with a simple triangle example and then apply the method to larger structures. The final aim is to solve the full system an…

A Fundamental Study for Multiobjective Optimization Problems in Nonlinear Dynamical Systems
Ryunosuke Numata, Toshimichi Saito
https://arxiv.org/abs/2509.17434 https://

A Fundamental Study for Multiobjective Optimization Problems in Nonlinear Dynamical Systems
Multiobjective optimization problems are important in analysis and application of nonlinear dynamical systems. As a first step, this paper studies a biobjective optimization problem in a simple nonlinear switched dynamical system: a piecewise linear system based on a boost converter with photovoltaic input. The piecewise linearity enables us to analyze the nonlinear dynamics exactly. In the biobjective optimization problem, the first objective evaluates stability of circuit operation and the se…

Mean-square and linear convergence of a stochastic proximal point algorithm in metric spaces of nonpositive curvature
Nicholas Pischke
https://arxiv.org/abs/2510.10697 https://

Mean-square and linear convergence of a stochastic proximal point algorithm in metric spaces of nonpositive curvature
We define a stochastic variant of the proximal point algorithm in the general setting of nonlinear (separable) Hadamard spaces for approximating zeros of the mean of a stochastically perturbed monotone vector field and prove its convergence under a suitable strong monotonicity assumption, together with a probabilistic independence assumption and a separability assumption on the tangent spaces. As a particular case, our results transfer previous work by P. Bianchi on that method in Hilbert space…

High-Parallel FPGA-Based Discrete Simulated Bifurcation for Large-Scale Optimization
Fabrizio Orlando, Deborah Volpe, Giacomo Orlandi, Mariagrazia Graziano, Fabrizio Riente, Marco Vacca
https://arxiv.org/abs/2510.12407

High-Parallel FPGA-Based Discrete Simulated Bifurcation for Large-Scale Optimization
Combinatorial Optimization (CO) problems exhibit exponential complexity, making their resolution challenging. Simulated Adiabatic Bifurcation (aSB) is a quantum-inspired algorithm to obtain approximate solutions to largescale CO problems written in the Ising form. It explores the solution space by emulating the adiabatic evolution of a network of Kerr-nonlinear parametric oscillators (KPOs), where each oscillator represents a variable in the problem. The optimal solution corresponds to the grou…

Well-posedness for the periodic Hyperbolic nonlinear Schr\"odinger equations
Engin Ba\c{s}ako\u{g}lu, Yuzhao Wang
https://arxiv.org/abs/2510.03211 https://

Well-posedness for the periodic Hyperbolic nonlinear Schrödinger equations
We establish local well-posedness for the hyperbolic nonlinear Schrodinger equation (HNLS) in the critical spaces. Following the approach of Killip and Visan, we derive scale-invariant Strichartz estimates for HNLS on both rational and irrational tori, thereby removing the epsilon-loss of derivative present in the hyperbolic Strichartz estimates of Bourgain and Demeter.

CPU- and GPU-Based Parallelization of the Robust Reference Governor
Hamid R. Ossareh, William Shayne, Samuel Chevalier
https://arxiv.org/abs/2510.08288 https://

CPU- and GPU-Based Parallelization of the Robust Reference Governor
Constraint management is a central challenge in modern control systems. A solution is the Reference Governor (RG), which is an add-on strategy to pre-stabilized feedback control systems to enforce state and input constraints by shaping the reference command. While robust formulations of RG exist for linear systems, their extension to nonlinear systems is often computationally intractable. This paper develops a scenario-based robust RG formulation for nonlinear systems and investigates its paral…

Strichartz estimates and its application to the well-posedness of the nonlinear Schr\"odinger equations on H-type groups
Hiroyuki Hirayama, Yasuyuki Oka
https://arxiv.org/abs/2510.00709

Strichartz estimates and its application to the well-posedness of the nonlinear Schrödinger equations on H-type groups
The aim of this article is to give the well-posedness results for the Cauchy problem of the nonlinear Schrödinger equation with power type nonlinearities on H-type groups. To do this, we prove the dispersive estimate and Strichartz estimate. Although these estimates are given by Hierro (2005), its complete proofs cannot be find. We correct the statement of these estimates, give the proofs, and apply to the nonlinear problem. Our well-posedness results are an improvement of the previous result …

Gain-Scheduled Data-Enabled Predictive Control: A DeePC Approach for Nonlinear Systems
Margarita A. Guerrero, Braghadeesh Lakshminarayanan, Cristian R. Rojas
https://arxiv.org/abs/2509.26334

Gain-Scheduled Data-Enabled Predictive Control: A DeePC Approach for Nonlinear Systems
Model predictive control is a well established control technology for trajectory tracking. Its use requires the availability of an accurate model of the plant, but obtaining such a model is often time consuming and costly. Data-Enabled Predictive Control (DeePC) addresses this shortcoming in the linear time-invariant setting, by skipping the model building step and instead relying directly on input-output data. Unfortunately, many real systems are nonlinear and exhibit strong operating-point de…

Robust Data-Driven Control for Nonlinear Systems Using their Digital Twins and Quadratic Funnels
Shiva Shakeri, Mehran Mesbahi
https://arxiv.org/abs/2510.01406 https://

Robust Data-Driven Control for Nonlinear Systems Using their Digital Twins and Quadratic Funnels
This paper examines a robust data-driven approach for the safe deployment of systems with nonlinear dynamics using their imperfect digital twins. Our contribution involves proposing a method that fuses the digital twin's nominal trajectory with online, data-driven uncertainty quantification to synthesize robust tracking controllers. Specifically, we derive data-driven bounds to capture the deviations of the actual system from its prescribed nominal trajectory informed via its digital twin. Subs…