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Physics-informed neural networks (PINNs) were recently proposed in [1] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution while a PDE-induced NN is coupled to the solution NN,…

Computational Physics · Physics 2019-10-22 Xiaoli Chen , Jinqiao Duan , George Em Karniadakis

We introduce a method to convert Physics-Informed Neural Networks (PINNs), commonly used in scientific machine learning, to Spiking Neural Networks (SNNs), which are expected to have higher energy efficiency compared to traditional…

Neural and Evolutionary Computing · Computer Science 2023-09-01 Qian Zhang , Chenxi Wu , Adar Kahana , Youngeun Kim , Yuhang Li , George Em Karniadakis , Priyadarshini Panda

Physics-informed neural networks (PINNs) have recently emerged as promising data-driven PDE solvers showing encouraging results on various PDEs. However, there is a fundamental limitation of training PINNs to solve multi-dimensional PDEs…

Machine Learning · Computer Science 2023-11-01 Junwoo Cho , Seungtae Nam , Hyunmo Yang , Seok-Bae Yun , Youngjoon Hong , Eunbyung Park

We present a new technique for the accelerated training of physics-informed neural networks (PINNs): discretely-trained PINNs (DT-PINNs). The repeated computation of partial derivative terms in the PINN loss functions via automatic…

Machine Learning · Computer Science 2023-01-31 Ramansh Sharma , Varun Shankar

Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training…

Machine Learning · Computer Science 2024-07-18 Katsiaryna Haitsiukevich , Alexander Ilin

With growing investigations into solving partial differential equations by physics-informed neural networks (PINNs), more accurate and efficient PINNs are required to meet the practical demands of scientific computing. One bottleneck of…

Machine Learning · Computer Science 2025-10-29 Tianchi Yu , Yiming Qi , Ivan Oseledets , Shiyi Chen

Physics-informed neural networks (PINNs) have emerged as a new learning paradigm for solving partial differential equations (PDEs) by enforcing the constraints of physical equations, boundary conditions (BCs), and initial conditions (ICs)…

Machine Learning · Computer Science 2025-05-21 Chenhong Zhou , Jie Chen , Zaifeng Yang , Ching Eng Png

A physics informed neural network (PINN) incorporates the physics of a system by satisfying its boundary value problem through a neural network's loss function. The PINN approach has shown great success in approximating the map between the…

Numerical Analysis · Mathematics 2022-03-17 Revanth Mattey , Susanta Ghosh

Physics-informed neural networks (PINNs) are an influential method of solving differential equations and estimating their parameters given data. However, since they make use of neural networks, they provide only a point estimate of…

Machine Learning · Computer Science 2024-05-15 Lena Podina , Mahdi Torabi Rad , Mohammad Kohandel

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior. In this…

Machine Learning · Computer Science 2022-03-16 Sifan Wang , Shyam Sankaran , Paris Perdikaris

Physics-Informed Neural Networks (PINNs) solve physical systems by incorporating governing partial differential equations directly into neural network training. In electromagnetism, where well-established methodologies such as FDTD and FEM…

Computational Physics · Physics 2026-02-13 Nilufer K. Bulut

We propose a new semi-analytic physics informed neural network (PINN) to solve singularly perturbed boundary value problems. The PINN is a scientific machine learning framework that offers a promising perspective for finding numerical…

Numerical Analysis · Mathematics 2022-08-22 Gung-Min Gie , Youngjoon Hong , Chang-Yeol Jung

As a typical application of deep learning, physics-informed neural network (PINN) {has been} successfully used to find numerical solutions of partial differential equations (PDEs), but how to improve the limited accuracy is still a great…

Machine Learning · Computer Science 2022-08-09 Zhi-Yong Zhang , Hui Zhang , Li-Sheng Zhang , Lei-Lei Guo

Physics-informed neural networks (PINNs) have attracted significant attention for solving partial differential equations (PDEs) in recent years because they alleviate the curse of dimensionality that appears in traditional methods. However,…

Machine Learning · Computer Science 2024-03-15 Yihang Gao , Ka Chun Cheung , Michael K. Ng

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…

Machine Learning · Computer Science 2023-12-19 Rini J. Gladstone , Mohammad A. Nabian , N. Sukumar , Ankit Srivastava , Hadi Meidani

Recently, Physics-Informed Neural Networks (PINNs) have gained significant attention for their versatile interpolation capabilities in solving partial differential equations (PDEs). Despite their potential, the training can be…

Geophysics · Physics 2024-04-12 Tariq Alkhalifah , Xinquan Huang

The importance and cost of time-domain simulations when studying power systems have exponentially increased in the last decades. With the growing share of renewable energy sources, the slow and predictable responses from large turbines are…

Systems and Control · Electrical Eng. & Systems 2025-10-08 Ignasi Ventura Nadal , Rahul Nellikkath , Spyros Chatzivasileiadis

Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been…

Machine Learning · Computer Science 2022-04-06 Jeremy Yu , Lu Lu , Xuhui Meng , George Em Karniadakis

Physics-informed neural networks (PINNs) provide a deep learning framework for numerically solving partial differential equations (PDEs), and have been widely used in a variety of PDE problems. However, there still remain some challenges in…

Machine Learning · Computer Science 2022-05-19 Wensheng Li , Chao Zhang , Chuncheng Wang , Hanting Guan , Dacheng Tao

This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…

Machine Learning · Computer Science 2023-10-02 Sidney Besnard , Frédéric Jurie , Jalal M. Fadili