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A generalised framework for phase field-based modelling of coupled problems: application to thermo-mechanical fracture, hydraulic fracture, hydrogen embrittlement and corrosion
Y. Navidtehrani, C. Beteg\'on, E. Mart\'inez-Pa\~neda
https://arxiv.org/abs/2506.20763

A generalised framework for phase field-based modelling of coupled problems: application to thermo-mechanical fracture, hydraulic fracture, hydrogen embrittlement and corrosion
We present a novel, generalised formulation to treat coupled structural integrity problems by combining phase field and multi-physics modelling. The approach exploits the versatility of the heat transfer equation and is therefore well suited to be adopted in commercial finite element packages, requiring only integration point-level implementation. This aspect is demonstrated here by implementing coupled, multi-variable phenomena through simple \texttt{UMAT} and \texttt{UMATHT} subroutines in th…

This https://arxiv.org/abs/2406.09189 has been replaced.
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Lie Symmetry Net: Preserving Conservation Laws in Modelling Financial Market Dynamics via Differential Equations
This paper employs a novel Lie symmetries-based framework to model the intrinsic symmetries within financial market. Specifically, we introduce Lie symmetry net (LSN), which characterises the Lie symmetries of the differential equations (DE) estimating financial market dynamics, such as the Black-Scholes equation. To simulate these differential equations in a symmetry-aware manner, LSN incorporates a Lie symmetry risk derived from the conservation laws associated with the Lie symmetry operators…