Related papers: Variational Physics-informed Neural Operator (VINO…

Physics-informed deep learning often faces optimization challenges due to the complexity of solving partial differential equations (PDEs), which involve exploring large solution spaces, require numerous iterations, and can lead to unstable…

Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…

This paper explores the difficulties in solving partial differential equations (PDEs) using physics-informed neural networks (PINNs). PINNs use physics as a regularization term in the objective function. However, a drawback of this approach…

The operator learning has received significant attention in recent years, with the aim of learning a mapping between function spaces. Prior works have proposed deep neural networks (DNNs) for learning such a mapping, enabling the learning…

The precise simulation of turbulent flows is of immense importance in a variety of scientific and engineering fields, including climate science, freshwater science, and the development of energy-efficient manufacturing processes. Within the…

Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…

We present the Physics-Informed Low-Rank Neural Operator (PILNO), a neural operator framework for efficiently approximating solution operators of partial differential equations (PDEs) on point cloud data. PILNO combines low-rank kernel…

Recently deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we…

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…

Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…

Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) using deep learning. However, PINNs face training difficulties for evolutionary PDEs, particularly for dynamical…

Physics-informed neural networks (PINNs) represent a significant advancement in scientific machine learning by integrating fundamental physical laws into their architecture through loss functions. PINNs have been successfully applied to…

Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accurate approximations of solutions to partial differential equations (PDEs). However, PINNs face serious difficulties and challenges when…

Solving nonlinear partial differential equations (PDEs) with multiple solutions using neural networks has found widespread applications in various fields such as physics, biology, and engineering. However, classical neural network methods…

Neural operators as novel neural architectures for fast approximating solution operators of partial differential equations (PDEs), have shown considerable promise for future scientific computing. However, the mainstream of training neural…

We propose the geometry-informed neural operator (GINO), a highly efficient approach to learning the solution operator of large-scale partial differential equations with varying geometries. GINO uses a signed distance function and…

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…

Learning the full family of solutions to parameterized partial differential equations (PDEs) is a central challenge to our ability to model the behavior of heterogeneous systems, with a variety of fundamental and application-oriented…

In this paper, we show a physics-informed neural network solver for the time-dependent surface PDEs. Unlike the traditional numerical solver, no extension of PDE and mesh on the surface is needed. We show a simplified prior estimate of the…

In this paper, we propose a way to solve partial differential equations (PDEs) by combining machine learning techniques and the finite element method called Phi-FEM. For that, we use the Fourier Neural Operator (FNO), a learning mapping…