Gpt-pinn: Generative pre-trained physics-informed neural networks toward non-intrusive meta-learning of parametric pdes
Abstract Physics-Informed Neural Network (PINN) has proven itself a powerful tool to obtain
the numerical solutions of nonlinear partial differential equations (PDEs) leveraging the …
the numerical solutions of nonlinear partial differential equations (PDEs) leveraging the …
A multi-level procedure for enhancing accuracy of machine learning algorithms
We propose a multi-level method to increase the accuracy of machine learning algorithms
for approximating observables in scientific computing, particularly those that arise in systems …
for approximating observables in scientific computing, particularly those that arise in systems …
Error analysis for deep neural network approximations of parametric hyperbolic conservation laws
We derive rigorous bounds on the error resulting from the approximation of the solution of
parametric hyperbolic scalar conservation laws with ReLU neural networks. We show that …
parametric hyperbolic scalar conservation laws with ReLU neural networks. We show that …
On the stability and convergence of physics informed neural networks
D Gazoulis, I Gkanis, CG Makridakis - arXiv preprint arXiv:2308.05423, 2023 - arxiv.org
Physics Informed Neural Networks is a numerical method which uses neural networks to
approximate solutions of partial differential equations. It has received a lot of attention and is …
approximate solutions of partial differential equations. It has received a lot of attention and is …
On the learning of high order polynomial reconstructions for essentially non-oscillatory schemes
VK Jayswal, RK Dubey - Physica Scripta, 2024 - iopscience.iop.org
Approximation accuracy and convergence behavior are essential required properties for the
computed numerical solution of differential equations. These requirements restrict the …
computed numerical solution of differential equations. These requirements restrict the …
Learning WENO for entropy stable schemes to solve conservation laws
P Charles, D Ray - arXiv preprint arXiv:2403.14848, 2024 - arxiv.org
Entropy conditions play a crucial role in the extraction of a physically relevant solution for a
system of conservation laws, thus motivating the construction of entropy stable schemes that …
system of conservation laws, thus motivating the construction of entropy stable schemes that …
Eno classification and regression neural networks for numerical approximation of discontinuous flow problems
Learning high order non-oscillatory polynomial approximation procedures which form the
backbone of high order numerical solution of partial differential equations is challenging …
backbone of high order numerical solution of partial differential equations is challenging …
A new approach to generalisation error of machine learning algorithms: Estimates and convergence
M Loulakis, CG Makridakis - arXiv preprint arXiv:2306.13784, 2023 - arxiv.org
In this work we consider a model problem of deep neural learning, namely the learning of a
given function when it is assumed that we have access to its point values on a finite set of …
given function when it is assumed that we have access to its point values on a finite set of …
Runge-Kutta Physics Informed Neural Networks: Formulation and Analysis
G Akrivis, CG Makridakis, C Smaragdakis - arXiv preprint arXiv …, 2024 - arxiv.org
In this paper we consider time-dependent PDEs discretized by a special class of Physics
Informed Neural Networks whose design is based on the framework of Runge--Kutta and …
Informed Neural Networks whose design is based on the framework of Runge--Kutta and …
On the approximation of rough functions with artificial neural networks
T De Ryck - 2020 - research-collection.ethz.ch
Deep neural networks and the ENO procedure are both efficient frameworks for
approximating rough functions. We prove that at any order, the stencil shifts of the ENO and …
approximating rough functions. We prove that at any order, the stencil shifts of the ENO and …