Related papers: Learning a Neural Solver for Parametric PDE to Enh…

Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…

We present a method that employs physics-informed deep learning techniques for parametrically solving partial differential equations. The focus is on the steady-state heat equations within heterogeneous solids exhibiting significant phase…

Since the seminal work of [9] and their Physics-Informed neural networks (PINNs), many efforts have been conducted towards solving partial differential equations (PDEs) with Deep Learning models. However, some challenges remain, for…

ADCME is a novel computational framework to solve inverse problems involving physical simulations and deep neural networks (DNNs). This paper benchmarks its capability to learn spatially-varying physical fields using DNNs. We demonstrate…

Solving partial differential equations (PDE) is an indispensable part of many branches of science as many processes can be modelled in terms of PDEs. However, recent numerical solvers require manual discretization of the underlying equation…

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We propose to represent the PDE in the form of a computational graph, facilitating the…

Deep learning-based partial differential equation(PDE) solvers have received much attention in the past few years. Methods of this category can solve a wide range of PDEs with high accuracy, typically by transforming the problems into…

Neural surrogate solvers of partial differential equations (PDEs) promise dramatic speedups over numerical methods, especially in scenarios requiring many solves. However, current accuracy-based evaluations do not fully consider two central…

In this paper, we introduce PDE-LEARN, a novel deep learning algorithm that can identify governing partial differential equations (PDEs) directly from noisy, limited measurements of a physical system of interest. PDE-LEARN uses a Rational…

Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…

Can neural networks learn to solve partial differential equations (PDEs)? We investigate this question for two (systems of) PDEs, namely, the Poisson equation and the steady Navier--Stokes equations. The contributions of this paper are…

Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. Accurately solving unbounded domain PDEs requires efficient…

Solving partial differential equations (PDEs) is a fundamental problem in science and engineering. While neural PDE solvers can be more efficient than established numerical solvers, they often require large amounts of training data that is…

This work presents a physics-informed deep learning-based super-resolution framework to enhance the spatio-temporal resolution of the solution of time-dependent partial differential equations (PDE). Prior works on deep learning-based…

Recent years have witnessed the promise of coupling machine learning methods and physical domain-specific insights for solving scientific problems based on partial differential equations (PDEs). However, being data-intensive, these methods…

Physics-informed neural networks (PINNs) are an increasingly powerful way to solve partial differential equations, generate digital twins, and create neural surrogates of physical models. In this manuscript we detail the inner workings of…

Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs),…

A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…