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We apply physics-informed neural networks (PINNs) to first-order two-scale periodic asymptotic homogenization of the property tensor in a generic elliptic equation. The problem of lack of differentiability of property tensors at the sharp…

Materials Science · Physics 2023-01-25 Celal Soyarslan , Marc Pradas

Motivated by recent research on Physics-Informed Neural Networks (PINNs), we make the first attempt to introduce the PINNs for numerical simulation of the elliptic Partial Differential Equations (PDEs) on 3D manifolds. PINNs are one of the…

Numerical Analysis · Mathematics 2021-03-05 Zhuochao Tang , Zhuojia Fu

Physics-informed neural networks (PINNs) provide a powerful framework for learning governing equations of dynamical systems from data. Biologically-informed neural networks (BINNs) are a variant of PINNs that preserve the known differential…

Machine Learning · Computer Science 2026-04-21 William Lavery , Jodie A. Cochrane , Christian Olesen , Dagim S. Tadele , John T. Nardini , Sara Hamis

A Physics-Informed Neural Network (PINN) provides a distinct advantage by synergizing neural networks' capabilities with the problem's governing physical laws. In this study, we introduce an innovative approach for solving seepage problems…

Computational Engineering, Finance, and Science · Computer Science 2023-11-28 Tianfu Luo , Yelin Feng , Qingfu Huang , Zongliang Zhang , Mingjiao Yan , Zaihong Yang , Dawei Zheng , Yang Yang

Physics-informed neural networks (PINNs) is an emerging category of neural networks which can be trained to solve supervised learning tasks while taking into consideration given laws of physics described by general nonlinear partial…

Cryptography and Security · Computer Science 2026-04-07 Solon Falas , Charalambos Konstantinou , Maria K. Michael

Recent advancements in physics-informed neural networks (PINNs) and their variants have garnered substantial focus from researchers due to their effectiveness in solving both forward and inverse problems governed by differential equations.…

Machine Learning · Computer Science 2026-01-06 Shivani Saini , Ramesh Kumar Vats , Arup Kumar Sahoo

Physics-informed neural networks (PINNs) have demonstrated promise in solving forward and inverse problems involving partial differential equations. Despite recent progress on expanding the class of problems that can be tackled by PINNs,…

Machine Learning · Computer Science 2025-02-18 Francisco Sahli Costabal , Simone Pezzuto , Paris Perdikaris

Physics-informed neural networks (PINNs) are a versatile tool in the burgeoning field of scientific machine learning for solving partial differential equations (PDEs). However, determining suitable training strategies for them is not…

Numerical Analysis · Mathematics 2026-03-09 Saad Qadeer , Panos Stinis

Considering the growing necessity for precise modeling of power electronics amidst operational and environmental uncertainties, this paper introduces an innovative methodology that ingeniously combines model-driven and data-driven…

Systems and Control · Electrical Eng. & Systems 2024-06-25 Peifeng Hui , Chenggang Cui , Pengfeng Lin , Amer M. Y. M. Ghias , Xitong Niu , Chuanlin Zhang

Physics-Informed Neural Networks (PINN) emerged as a powerful tool for solving scientific computing problems, ranging from the solution of Partial Differential Equations to data assimilation tasks. One of the advantages of using PINN is to…

Quantum Physics · Physics 2023-01-12 Stefano Markidis

Direct observations of earthquake nucleation and propagation are few and yet the next decade will likely see an unprecedented increase in indirect, surface observations that must be integrated into modeling efforts. Machine learning (ML)…

Mathematical Physics · Physics 2024-07-25 Cody Rucker , Brittany A. Erickson

Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems for partial differential equations. This article aims to…

Numerical Analysis · Mathematics 2024-11-20 Tim De Ryck , Siddhartha Mishra

Using Physics-Informed Neural Networks (PINNs) to solve a specific boundary value problem is becoming more popular as an alternative to traditional methods. However, depending on the specific problem, they could be computationally expensive…

High Energy Astrophysical Phenomena · Physics 2023-07-06 Jorge F. Urbán , Petros Stefanou , Clara Dehman , José A. Pons

We develop improved physics-informed neural networks (PINNs) for high-order and high-dimensional power system models described by nonlinear ordinary differential equations. We propose some novel enhancements to improve PINN training and…

Machine Learning · Computer Science 2024-10-11 Vineet Jagadeesan Nair

We propose a mesh-free policy iteration framework based on physics-informed neural networks (PINNs) for solving entropy-regularized stochastic control problems. The method iteratively alternates between soft policy evaluation and…

Numerical Analysis · Mathematics 2025-11-18 Yeongjong Kim , Namkyeong Cho , Minseok Kim , Yeoneung Kim

In this paper, numerical methods using Physics-Informed Neural Networks (PINNs) are presented with the aim to solve higher-order ordinary differential equations (ODEs). Indeed, this deep-learning technique is successfully applied for…

Computational Physics · Physics 2023-07-17 Hubert Baty

With the rapid advancement of graphical processing units, Physics-Informed Neural Networks (PINNs) are emerging as a promising tool for solving partial differential equations (PDEs). However, PINNs are not well suited for solving PDEs with…

Machine Learning · Computer Science 2024-05-28 Yuxiang Gao , Soheil Kolouri , Ravindra Duddu

This paper proposes a meshless deep learning algorithm, enriched physics-informed neural networks (EPINNs), to solve dynamic Poisson-Nernst-Planck (PNP) equations with strong coupling and nonlinear characteristics. The EPINNs takes the…

Machine Learning · Computer Science 2024-02-06 Xujia Huang , Fajie Wang , Benrong Zhang , Hanqing Liu

The emergence of neural networks constrained by physical governing equations has sparked a new trend in deep learning research, which is known as Physics-Informed Neural Networks (PINNs). However, solving high-dimensional problems with…

Machine Learning · Computer Science 2025-09-26 Biao Yuan , Ana Heitor , He Wang , Xiaohui Chen

In this paper, we compute numerical approximations of the minimal surfaces, an essential type of Partial Differential Equation (PDE), in higher dimensions. Classical methods cannot handle it in this case because of the Curse of…

Analysis of PDEs · Mathematics 2023-09-08 Steven Zhou , Xiaojing Ye