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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

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

Physics-informed neural networks (PINNs) are trained using physical equations and can also incorporate unmodeled effects by learning from data. PINNs for control (PINCs) of dynamical systems are gaining interest due to their prediction…

Systems and Control · Electrical Eng. & Systems 2024-08-29 Henrik Krauss , Tim-Lukas Habich , Max Bartholdt , Thomas Seel , Moritz Schappler

Solving time-dependent Partial Differential Equations (PDEs) is one of the most critical problems in computational science. While Physics-Informed Neural Networks (PINNs) offer a promising framework for approximating PDE solutions, their…

Predicting motions of vessels in extreme sea states represents one of the most challenging problems in naval hydrodynamics. It involves computing complex nonlinear wave-body interactions, hence taxing heavily computational resources. Here,…

In recent years, scientific machine learning, particularly physic-informed neural networks (PINNs), has introduced new innovative methods to understanding the differential equations that describe power system dynamics, providing a more…

Systems and Control · Electrical Eng. & Systems 2024-03-12 Huynh T. T. Tran , Hieu T. Nguyen

This article introduces Perception-Informed Neural Networks (PrINNs), a framework designed to incorporate perception-based information into neural networks, addressing both systems with known and unknown physics laws or differential…

Machine Learning · Computer Science 2025-05-27 Mehran Mazandarani , Marzieh Najariyan

The numerical approximation of solutions to the compressible Euler and Navier-Stokes equations is a crucial but challenging task with relevance in various fields of science and engineering. Recently, methods from deep learning have been…

Fluid Dynamics · Physics 2024-01-30 Simon Wassing , Stefan Langer , Philipp Bekemeyer

This study investigates the potential accuracy boundaries of physics-informed neural networks, contrasting their approach with previous similar works and traditional numerical methods. We find that selecting improved optimization algorithms…

Computational Physics · Physics 2024-12-16 Jorge F. Urbán , Petros Stefanou , José A. Pons

Time-dependent partial differential equations are a significant class of equations that describe the evolution of various physical phenomena over time. One of the open problems in scientific computing is predicting the behaviour of the…

Numerical Analysis · Mathematics 2025-06-30 Zhenyi Zhu , Yuchen Huang , Liu Liu

Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, solving high-fidelity PDEs remains…

Machine Learning · Computer Science 2026-02-03 Olaf Yunus Laitinen Imanov

Physics-informed neural networks (PINNs) have been widely used to solve partial differential equations in a forward and inverse manner using deep neural networks. However, training these networks can be challenging for multiscale problems.…

Fluid Dynamics · Physics 2023-02-01 Sukirt Thakur , Maziar Raissi , Harsa Mitra , Arezoo Ardekani

This paper introduces a physics-informed machine learning approach for pathloss prediction. This is achieved by including in the training phase simultaneously (i) physical dependencies between spatial loss field and (ii) measured pathloss…

Machine Learning · Statistics 2023-12-15 Steffen Limmer , Alberto Martinez Alba , Nicola Michailow

Soft robots can revolutionize several applications with high demands on dexterity and safety. When operating these systems, real-time estimation and control require fast and accurate models. However, prediction with first-principles (FP)…

Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be…

Machine Learning · Computer Science 2023-05-08 Chandrajit Bajaj , Luke McLennan , Timothy Andeen , Avik Roy

Physics-informed neural networks (PINNs) offer a novel AI-driven framework for integrating physical laws directly into neural network models, facilitating the solution of complex multiphysics problems in materials engineering. This study…

Materials Science · Physics 2025-10-14 Mohid Farooqi , Ingmar Bösing , Conrard G. Tetsassi Feugmo

Realistic sound is essential in virtual environments, such as computer games and mixed reality. Efficient and accurate numerical methods for pre-calculating acoustics have been developed over the last decade; however, pre-calculating…

Sound · Computer Science 2023-08-11 Nikolas Borrel-Jensen , Allan P. Engsig-Karup , Cheol-Ho Jeong

Physics-informed Neural Networks (PINNs) have recently emerged as a principled way to include prior physical knowledge in form of partial differential equations (PDEs) into neural networks. Although PINNs are generally viewed as mesh-free,…

Machine Learning · Computer Science 2022-10-04 Fabricio Arend Torres , Marcello Massimo Negri , Monika Nagy-Huber , Maxim Samarin , Volker Roth

Efficient simulation of Laser Powder Bed Fusion (LPBF) is crucial for process prediction due to the lasting issue of high computational cost associated with traditional numerical methods such as finite element analysis (FEA). While a…

Machine Learning · Computer Science 2026-05-25 R. Sharma , Y. B. Guo

Physics-Informed Neural Networks (PINNs) are a class of deep learning models aiming to approximate solutions of PDEs by training neural networks to minimize the residual of the equation. Focusing on non-equilibrium fluctuating systems, we…

Machine Learning · Computer Science 2025-09-25 Javier Castro , Benjamin Gess