Related papers: Physics-informed Discretization-independent Deep C…

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets…

We propose a novel fine-tuning method to achieve multi-operator learning through training a distributed neural operator with diverse function data and then zero-shot fine-tuning the neural network using physics-informed losses for…

Neural operators have recently grown in popularity as Partial Differential Equation (PDE) surrogate models. Learning solution functionals, rather than functions, has proven to be a powerful approach to calculate fast, accurate solutions to…

Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…

Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high…

In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (e.g., aircraft shape optimization over many design…

We propose a finite-element local basis-based operator learning framework for solving partial differential equations (PDEs). Operator learning aims to approximate mappings from input functions to output functions, where the latter are…

Physics-Informed Neural Networks (PINNs) are a class of deep learning neural networks that learn the response of a physical system without any simulation data, and only by incorporating the governing partial differential equations (PDEs) in…

This study focuses on addressing the challenges of solving analytically intractable differential equations that arise in scientific and engineering fields such as Hamilton-Jacobi-Bellman. Traditional numerical methods and neural network…

Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed…

Physics-informed neural networks (PINNs) have lately received significant attention as a representative deep learning-based technique for solving partial differential equations (PDEs). Most fully connected network-based PINNs use automatic…

The physics-informed neural operator (PINO) is a machine learning paradigm that has demonstrated promising results for learning solutions to partial differential equations (PDEs). It leverages the Fourier Neural Operator to learn solution…

In this work, we describe a novel approach to building a neural PDE solver leveraging recent advances in transformer based neural network architectures. Our model can provide solutions for different values of PDE parameters without any need…

Physics-informed neural networks (PINNs) are an emerging technique to solve partial differential equations (PDEs). In this work, we propose a simple but effective PINN approach for the phase-field model of ferroelectric microstructure…

Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use…

Physics-Informed Neural Networks (PINNs) have emerged as powerful tools for solving partial differential equations (PDEs). However, training PINNs from scratch is often computationally intensive and time-consuming. To address this problem,…

We propose a novel composite framework to find unknown fields in the context of inverse problems for partial differential equations (PDEs). We blend the high expressibility of deep neural networks as universal function estimators with the…

Physics-informed neural network (PINN) is a data-driven solver for partial and ordinary differential equations(ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the…

Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at…