Can physics-informed neural networks beat the finite element method?
Partial differential equations play a fundamental role in the mathematical modelling of many
processes and systems in physical, biological and other sciences. To simulate such …
processes and systems in physical, biological and other sciences. To simulate such …
State-of-the-art review of design of experiments for physics-informed deep learning
S Das, S Tesfamariam - arXiv preprint arXiv:2202.06416, 2022 - arxiv.org
This paper presents a comprehensive review of the design of experiments used in the
surrogate models. In particular, this study demonstrates the necessity of the design of …
surrogate models. In particular, this study demonstrates the necessity of the design of …
Neuralpde: Automating physics-informed neural networks (pinns) with error approximations
Physics-informed neural networks (PINNs) are an increasingly powerful way to solve partial
differential equations, generate digital twins, and create neural surrogates of physical …
differential equations, generate digital twins, and create neural surrogates of physical …
On the maximum principle preserving schemes for the generalized Allen–Cahn equation
This paper is concerned with the generalized Allen–Cahn equation with a nonlinear mobility
that may be degenerate, which also includes an advection term appearing in many …
that may be degenerate, which also includes an advection term appearing in many …
[HTML][HTML] An unconditionally stable hybrid numerical method for solving the Allen–Cahn equation
We present an unconditionally stable second-order hybrid numerical method for solving the
Allen–Cahn equation representing a model for antiphase domain coarsening in a binary …
Allen–Cahn equation representing a model for antiphase domain coarsening in a binary …
Numerical analysis and applications of explicit high order maximum principle preserving integrating factor Runge-Kutta schemes for Allen-Cahn equation
Whether high order temporal integrators can preserve the maximum principle of Allen-Cahn
equation has been an open problem in recent years. This work provides a positive answer …
equation has been an open problem in recent years. This work provides a positive answer …
An unconditionally gradient stable numerical method for solving the Allen–Cahn equation
We consider an unconditionally gradient stable scheme for solving the Allen–Cahn equation
representing a model for anti-phase domain coarsening in a binary mixture. The continuous …
representing a model for anti-phase domain coarsening in a binary mixture. The continuous …
[HTML][HTML] An improved differential transform scheme implementation on the generalized Allen–Cahn equation governing oil pollution dynamics in oceanography
TK Akinfe, AC Loyinmi - Partial Differential Equations in Applied …, 2022 - Elsevier
Studies in computational mathematics have taken a fantastic aesthetics in interdisciplinary
fields as researchers in this area have resiliently adopted constructive methods, schemes …
fields as researchers in this area have resiliently adopted constructive methods, schemes …
Solution of stochastic Allen–Cahn equation in the framework of soliton theoretical approach
In this paper, the Allen–Cahn equation with time noise is under consideration. The extended
fan-sub technique is used to find the exact solutions. The solutions are successfully …
fan-sub technique is used to find the exact solutions. The solutions are successfully …
Brownian motion effects on the stabilization of stochastic solutions to fractional diffusion equations with polynomials
A class of stochastic fractional diffusion equations with polynomials is considered in this
article. This equation is used in numerous applications, such as ecology, bioengineering …
article. This equation is used in numerous applications, such as ecology, bioengineering …