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Surjective and closed range differentiation operator
Tesfa Mengestie
https://arxiv.org/abs/2506.14410 https://arxiv.org/pdf/2506.1441…

Surjective and closed range differentiation operator
We identify Fock-type spaces $\mathcal{F}_{(m,p)}$ on which the differentiation operator $D$ has closed range. We prove that $D$ has closed range only if it is surjective, and this happens if and only if $m=1$. Moreover, since the operator is unbounded on the classical Fock spaces, we consider the modified or the weighted composition--differentiation operator, $D_{(u,ψ,n)} f= u\cdot\big( f^{(n)}\circ ψ\big)$, on these spaces and describe conditions under which the operator admits closed ran…

A modified Newmark/Newton-Raphson method with automatic differentiation for general nonlinear dynamics analysis
Yifan Jiang, Yuhong Jin, Lei Hou, Yi Chen, Andong Cong
https://arxiv.org/abs/2506.13226

A modified Newmark/Newton-Raphson method with automatic differentiation for general nonlinear dynamics analysis
The Newmark/Newton-Raphson (NNR) method is widely employed for solving nonlinear dynamic systems. However, the current NNR method exhibits limited applicability in complex nonlinear dynamic systems, as the acquisition of the Jacobian matrix required for Newton iterations incurs substantial computational costs and may even prove intractable in certain cases. To address these limitations, we integrate automatic differentiation (AD) into the NNR method, proposing a modified NNR method with AD (NNR…

Fast automated adjoints for spectral PDE solvers
Calum S. Skene, Keaton J. Burns
https://arxiv.org/abs/2506.14792 https://arxiv.org/p…

Fast automated adjoints for spectral PDE solvers
We present a general and automated approach for computing model gradients for PDE solvers built on sparse spectral methods, and implement this capability in the widely used open-source Dedalus framework. We apply reverse-mode automatic differentiation to symbolic graph representations of PDEs, efficiently constructing adjoint solvers that retain the speed and memory efficiency of this important class of modern numerical methods. This approach enables users to compute gradients and perform optim…

Growth of entire functions: from frequent hypercyclicity to hypercyclicity for the differentiation operator
Augustin Mouze
https://arxiv.org/abs/2506.12763

Growth of entire functions: from frequent hypercyclicity to hypercyclicity for the differentiation operator
We study the rate of growth of entire functions that are frequently hypercyclic with respect to some upper weighted densities for the differentiation operator. The statements obtained show the link between the minimal growth of frequently hypercyclic entire functions and that of hypercyclic entire functions. The results are optimal.

Backsolution: A Framework for Solving Inverse Problems via Automatic Differentiation
Koji Kobayashi, Tomi Ohtsuki
https://arxiv.org/abs/2506.13210 https://…

Backsolution: A Framework for Solving Inverse Problems via Automatic Differentiation
We present a simple yet powerful framework for solving inverse problems by leveraging automatic differentiation. Our method is broadly applicable whenever a smooth cost function can be defined near the true solution, and a numerical simulator is available. As a concrete example, we demonstrate that our method can accurately reconstruct the spatial profiles in a conductor from magnetotransport measurements. Even if the given data are insufficient to uniquely determine the profiles, the same fram…

Hard Contacts with Soft Gradients: Refining Differentiable Simulators for Learning and Control
Anselm Paulus, A. Ren\'e Geist, Pierre Schumacher, V\'it Musil, Georg Martius
https://arxiv.org/abs/2506.14186

Hard Contacts with Soft Gradients: Refining Differentiable Simulators for Learning and Control
Contact forces pose a major challenge for gradient-based optimization of robot dynamics as they introduce jumps in the system's velocities. Penalty-based simulators, such as MuJoCo, simplify gradient computation by softening the contact forces. However, realistically simulating hard contacts requires very stiff contact settings, which leads to incorrect gradients when using automatic differentiation. On the other hand, using non-stiff settings strongly increases the sim-to-real gap. We analyze …

Quantum-Inspired Differentiable Integral Neural Networks (QIDINNs): A Feynman-Based Architecture for Continuous Learning Over Streaming Data
Oscar Boullosa Dapena
https://arxiv.org/abs/2506.12111

Quantum-Inspired Differentiable Integral Neural Networks (QIDINNs): A Feynman-Based Architecture for Continuous Learning Over Streaming Data
Real-time continuous learning over streaming data remains a central challenge in deep learning and AI systems. Traditional gradient-based models such as backpropagation through time (BPTT) face computational and stability limitations when dealing with temporally unbounded data. In this paper, we introduce a novel architecture, Quantum-Inspired Differentiable Integral Neural Networks (QIDINNs), which leverages the Feynman technique of differentiation under the integral sign to formulate neural u…

Automatic differentiation for Lax-Wendroff-type discretizations
Arpit Babbar, Valentin Churavy, Michael Schlottke Lakemper, Hendrik Ranocha
https://arxiv.org/abs/2506.11719

Automatic differentiation for Lax-Wendroff-type discretizations
Lax-Wendroff methods combined with discontinuous Galerkin/flux reconstruction spatial discretization provide a high-order, single-stage, quadrature-free method for solving hyperbolic conservation laws. In this work, we introduce automatic differentiation (AD) in the element-local time average flux computation step (the predictor step) of Lax-Wendroff methods. The application of AD is similar for methods of any order and does not need positivity corrections during the predictor step. This contra…

Restarted contractive operators to learn at equilibrium
Leo Davy (Phys-ENS), Luis M. Briceno-Arias (UTFSM), N. Pustelnik (Phys-ENS)
https://arxiv.org/abs/2506.13239

Restarted contractive operators to learn at equilibrium
Bilevel optimization offers a methodology to learn hyperparameters in imaging inverse problems, yet its integration with automatic differentiation techniques remains challenging. On the one hand, inverse problems are typically solved by iterating arbitrarily many times some elementary scheme which maps any point to the minimizer of an energy functional, known as equilibrium point. On the other hand, introducing parameters to be learned in the energy functional yield architectures very reminisce…

A Common Interface for Automatic Differentiation
Guillaume Dalle, Adrian Hill
https://arxiv.org/abs/2505.05542 https://arxiv.org/pdf/…

A Common Interface for Automatic Differentiation
For scientific machine learning tasks with a lot of custom code, picking the right Automatic Differentiation (AD) system matters. Our Julia package DifferentiationInterface.jl provides a common frontend to a dozen AD backends, unlocking easy comparison and modular development. In particular, its built-in preparation mechanism leverages the strengths of each backend by amortizing one-time computations. This is key to enabling sophisticated features like sparsity handling without putting addition…

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation
He Zhang
https://arxiv.org/abs/2506.00796

Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation
In scientific computation, it is often necessary to calculate higher-order derivatives of a function. Currently, two primary methods for higher-order automatic differentiation exist: symbolic differentiation and algorithmic automatic differentiation (AD). Differential Algebra (DA) is a mathematical technique widely used in beam dynamics analysis and simulations of particle accelerators, and it also functions as an algorithmic automatic differentiation method. DA automatically computes the Taylo…

Error Analysis of Truncation Legendre Method for Solving Numerical Differentiation
Maksym Kyselov
https://arxiv.org/abs/2506.11529 https://

Error Analysis of Truncation Legendre Method for Solving Numerical Differentiation
We study the problem of numerical differentiation of functions from weighted Wiener classes. We construct and analyze a truncation Legendre method to recover arbitrary order derivatives. The main focus is on obtaining error estimates in integral and uniform metrics. Unlike previous studies, which predominantly focused on first-order derivatives and specific functional spaces, we conduct a comprehensive analysis across a wide spectrum of function regularity parameters and various metrics for mea…

This https://arxiv.org/abs/2504.09748 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Level-set topology optimisation with unfitted finite elements and automatic shape differentiation
In this paper we develop automatic shape differentiation techniques for unfitted discretisations and link these to recent advances in shape calculus for unfitted methods. We extend existing analytic shape calculus results to the case where the domain boundary intersects with the boundary of the background domain. We further show that we can recover these analytic derivatives to machine precision regardless of the mesh size using the developed automatic shape differentiation techniques, drastica…

Exploring Integration by Differentiation
R. D. George, C. Vignat
https://arxiv.org/abs/2505.22896 https://arxiv.org/pdf/2505.22896

Exploring Integration by Differentiation
This work validates and extends the method of integration by differentiation, initially introduced by A. Kempf et al., and demonstrates its compatibility with classical rules of integration. It provides applications to classical integrals, including one by Ramanujan, and extends the method to the multivariate setting. Volumes of simplexes are computed by acting with indicator functions on elementary kernels, and a rotationally invariant formulation is derived. Finally, the method is extended to…

Replaced article(s) found for stat.CO. https://arxiv.org/list/stat.CO/new
[1/1]:
Simplifying debiased inference via automatic differentiation and probabilistic programming

The program of the 25th Swiss Transport Research Conference (#STRC25) is now online. There will be 3 papers/presentations by employees of the Swiss Federal Railways (SBB):
👉 Quantifying Future Mobility: Scenario-Based Analysis with Agent-Based Modeling
👉 Integrating Machine Learning and MATSim for High-Granularity Passenger Load Predictions at SBB
👉 Differentiation of Modal Preferen…

Antibody Consumption-Driven Dynamic Competition: A Systems Hypothesis for the Transition from Acute Immune Response to Post-Infection Sequelae
Shi Qiru
https://arxiv.org/abs/2506.06413

Antibody Consumption-Driven Dynamic Competition: A Systems Hypothesis for the Transition from Acute Immune Response to Post-Infection Sequelae
The mechanisms underlying the formation of post-infection sequelae are complex and remain controversial. This hypothesis integrates Bystryn's antibody feedback phenomenon and Imbiakha's immune cost theory, proposing for the first time a "Consumption-Driven Dynamic Competition of Antibody Clones" mechanism. This mechanism posits that the immune system may regulate the proliferation and differentiation of corresponding B cell clones by sensing and responding to the consumption rate of specific an…

Comparative analysis of financial data differentiation techniques using LSTM neural network
Dominik Stempie\'n, Janusz Gajda
https://arxiv.org/abs/2505.19243

Comparative analysis of financial data differentiation techniques using LSTM neural network
We compare traditional approach of computing logarithmic returns with the fractional differencing method and its tempered extension as methods of data preparation before their usage in advanced machine learning models. Differencing parameters are estimated using multiple techniques. The empirical investigation is conducted on data from four major stock indices covering the most recent 10-year period. The set of explanatory variables is additionally extended with technical indicators. The effect…

Replaced article(s) found for cs.MS. https://arxiv.org/list/cs.MS/new/
[1/1]:
Sparser, Better, Faster, Stronger: Sparsity Detection for Efficient Automatic Differentiation
…

Scalable Analysis and Design Using Automatic Differentiation
Julian Andrej, Tzanio Kolev, Boyan Lazarov
https://arxiv.org/abs/2506.00746 https://

Scalable Analysis and Design Using Automatic Differentiation
This article aims to demonstrate and discuss the applications of automatic differentiation (AD) for finding derivatives in PDE-constrained optimization problems and Jacobians in non-linear finite element analysis. The main idea is to localize the application of AD at the integration point level by combining it with the so-called Finite Element Operator Decomposition. The proposed methods are computationally effective, scalable, automatic, and non-intrusive, making them ideal for existing serial…

This https://arxiv.org/abs/2308.13614 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

The role of interior dynamics and differentiation on the surface and atmosphere of lava planets
Lava planets are rocky exoplanets that orbit so close to their host star that their day-side is hot enough to melt silicate rock. Their short orbital periods ensure that lava planets are tidally locked into synchronous rotation, with permanent day and night hemispheres. Such asymmetric magma oceans have no analogs in the Solar System and will exhibit novel fluid dynamics. Here we report numerical simulations of lava planet interiors showing that solid-liquid fractionation in the planetary int…

This https://arxiv.org/abs/2412.06436 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An Adaptively Inexact Method for Bilevel Learning Using Primal-Dual Style Differentiation
We consider a bilevel learning framework for learning linear operators. In this framework, the learnable parameters are optimized via a loss function that also depends on the minimizer of a convex optimization problem (denoted lower-level problem). We utilize an iterative algorithm called `piggyback' to compute the gradient of the loss and minimizer of the lower-level problem. Given that the lower-level problem is solved numerically, the loss function and thus its gradient can only be computed …

Some results on generalized Hukuhara diamond-{\alpha} derivative and integral of fuzzy valued functions and on time scales
Selami Baye\u{g}, Funda Raziye Mert, Billur Kaymak\c{c}alan
https://arxiv.org/abs/2506.00016

Some results on generalized Hukuhara diamond-α derivative and integral of fuzzy valued functions and on time scales
In this paper, we define generalized Hukuhara diamond-alpha integral for fuzzy functions on time scales and obtain some of its fundamental properties and also we establish the relationship between diamond-alpha differentiation and integration.

A note on metapopulation models
Diepreye Ayabina, Hasan Sevil, Adam Kleczkowski, M. Gabriela M. Gomes
https://arxiv.org/abs/2506.04284 https://

A note on metapopulation models
Metapopulation models are commonly used in ecology, evolution, and epidemiology. These models usually entail homogeneity assumptions within patches and study networks of migration between patches to generate insights into conservation of species, differentiation of populations, and persistence of infectious diseases. Here, focusing on infectious disease epidemiology, we take a complementary approach and study the effects of individual variation within patches while neglecting any form of diseas…

This https://arxiv.org/abs/2409.03567 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Meshless moment-free quadrature formulas arising from numerical differentiation
We suggest a method for simultaneously generating high order quadrature weights for integrals over Lipschitz domains and their boundaries that requires neither meshing nor moment computation. The weights are determined on pre-defined scattered nodes as a minimum norm solution of a sparse underdetermined linear system arising from a discretization of a suitable boundary value problem by either collocation or meshless finite differences. The method is easy to implement independently of the domain…

Antenna Q-Factor Topology Optimization with Auxiliary Edge Resistivities
Stepan Bosak, Miloslav Capek, Jiri Matas
https://arxiv.org/abs/2506.00595 https://…

Antenna Q-Factor Topology Optimization with Auxiliary Edge Resistivities
This paper presents a novel bi-level topology optimization strategy within the method-of-moments paradigm. The proposed approach utilizes an auxiliary variables called edge resistivities related to the Rao-Wilton-Glisson method-of-moments basis functions, for a definition of a fast local optimization algorithm. The local algorithm combines automatic differentiation with adaptive gradient descent. A Bayesian optimization scheme is applied on top of the local algorithm to search for an optimum po…

Multi-omic Causal Discovery using Genotypes and Gene Expression
Stephen Asiedu, David Watson
https://arxiv.org/abs/2505.15866 https://

Multi-omic Causal Discovery using Genotypes and Gene Expression
Causal discovery in multi-omic datasets is crucial for understanding the bigger picture of gene regulatory mechanisms, but remains challenging due to high dimensionality, differentiation of direct from indirect relationships, and hidden confounders. We introduce GENESIS (GEne Network inference from Expression SIgnals and SNPs), a constraint-based algorithm that leverages the natural causal precedence of genotypes to infer ancestral relationships in transcriptomic data. Unlike traditional causal…

A General Version of Carath\'{e}odory's Existence and Uniqueness Theorem
Paulo M. de Carvalho-Neto, C\'icero L. Frota, Pedro G. P. Torelli
https://arxiv.org/abs/2505.24516

A General Version of Carathéodory's Existence and Uniqueness Theorem
In this paper, we establish a general version of Carathéodory's existence and uniqueness theorem for a semilinear system of integro-differential equations arising from differential equations with distinct orders of Caputo fractional derivative. The main result of our work demonstrates that the integrability order of the Carathéodory function $f$ must be at least greater than the maximum of the reciprocals of all differentiation orders in the system; otherwise, even the existence of a solution…

A primal-dual price-optimization method for computing equilibrium prices in mean-field games models
Xu Wang, Samy Wu Fung, Levon Nurbekyan
https://arxiv.org/abs/2506.04169

A primal-dual price-optimization method for computing equilibrium prices in mean-field games models
We develop a simple yet efficient Lagrangian method for computing equilibrium prices in a mean-field game price-formation model. We prove that equilibrium prices are optimal in terms of a suitable criterion and derive a primal-dual gradient-based algorithm for computing them. One of the highlights of our computational framework is the efficient, simple, and flexible implementation of the algorithm using modern automatic differentiation techniques. Our implementation is modular and admits a seam…

Numerical solution of the wave equation outside a sphere
Michael J. Carley
https://arxiv.org/abs/2506.04809 https://arxiv.org/pdf/250…

Numerical solution of the wave equation outside a sphere
A method is presented for the fast evaluation of the transient acoustic field generated outside a spherical surface by sources inside the surface. The method employs Lebedev quadratures, which are the optimal method for spatial integration, and Lagrange interpolation and differentiation in an advanced time algorithm for the evaluation of the transient field. Numerical testing demonstrates that the approach gives near machine-precision accuracy and a speed-up in evaluation time which depends on …

A fast and memoryless numerical method for solving fractional differential equations
Nicola Guglielmi, Ernst Hairer
https://arxiv.org/abs/2506.04188 https:…

A fast and memoryless numerical method for solving fractional differential equations
The numerical solution of implicit and stiff differential equations by implicit numerical integrators has been largely investigated and there exist many excellent efficient codes available in the scientific community, as Radau5 (based on a Runge-Kutta collocation method at Radau points) and Dassl, based on backward differentiation formulas, among the others. When solving fractional ordinary differential equations (ODEs), the derivative operator is replaced by a non-local one and the fractional …