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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…

Materials Science · Physics 2024-09-06 Lan Shang , Sizheng Zheng , Jin Wang , Jie Wang

We consider physics-informed neural networks (PINNs) [Raissi et al., J.~Comput. Phys. 278 (2019) 686-707] for forward physical problems. In order to find optimal PINNs configuration, we introduce a hyper-parameter optimization (HPO)…

Numerical Analysis · Mathematics 2023-02-01 Paul Escapil-Inchauspé , Gonzalo A. Ruz

This paper presents a deep learning strategy to simultaneously solve Partial Differential Equations (PDEs) and back-calculate their parameters in the context of deep tunnel excavation. A Physics-Informed Neural Network (PINN) model is…

Computational Physics · Physics 2026-05-29 Alec Tristani , Chloé Arson

We present a physics-informed neural network (PINN) approach for the discovery of slow invariant manifolds (SIMs), for the most general class of fast/slow dynamical systems of ODEs. In contrast to other machine learning (ML) approaches that…

Numerical Analysis · Mathematics 2025-06-24 Dimitrios G. Patsatzis , Lucia Russo , Constantinos Siettos

Spatiotemporal partial differential equations (PDEs) find extensive application across various scientific and engineering fields. While numerous models have emerged from both physics and machine learning (ML) communities, there is a growing…

Machine Learning · Computer Science 2024-08-21 Coşku Can Horuz , Matthias Karlbauer , Timothy Praditia , Sergey Oladyshkin , Wolfgang Nowak , Sebastian Otte

We show that the physics-informed neural networks (PINNs), in combination with some recently developed discontinuity capturing neural networks, can be applied to solve optimal control problems subject to partial differential equations…

Optimization and Control · Mathematics 2026-02-16 Ming-Chih Lai , Yongcun Song , Xiaoming Yuan , Hangrui Yue , Tianyou Zeng

Channel modeling is fundamental in advancing wireless systems and has thus attracted considerable research focus. Recent trends have seen a growing reliance on data-driven techniques to facilitate the modeling process and yield accurate…

Information Theory · Computer Science 2024-01-03 Ethan Zhu , Haijian Sun , Mingyue Ji

In recent years, the researches about solving partial differential equations (PDEs) based on artificial neural network have attracted considerable attention. In these researches, the neural network models are usually designed depend on…

Neural and Evolutionary Computing · Computer Science 2024-05-21 Bo Zhang , Chao Yang

Physics-informed neural networks (PINNs) offer a powerful framework for seismic wavefield modeling, yet they typically require time-consuming retraining when applied to different velocity models. Moreover, their training can suffer from…

Geophysics · Physics 2025-06-03 Shijun Cheng , Tariq Alkhalifah

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…

Numerical Analysis · Mathematics 2023-05-08 Nicola Rares Franco , Andrea Manzoni , Paolo Zunino

Physics-informed neural networks (PINNs), owing to their mesh-free nature, offer a powerful approach for solving high-dimensional partial differential equations (PDEs) in complex geometries, including irregular domains. This capability…

Numerical Analysis · Mathematics 2025-06-06 Hanfei Zhou , Lei Shi

Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…

Numerical Analysis · Mathematics 2020-06-16 Chengping Rao , Hao Sun , Yang Liu

Physics-informed neural networks (PINNs) are promising to replace conventional partial differential equation (PDE) solvers by offering more accurate and flexible PDE solutions. However, they are hampered by the relatively slow convergence…

Machine Learning · Computer Science 2023-05-16 Mohammad H. Taufik , Tariq Alkhalifah

Coupling physics with machine learning models has shown great potential for solving fluid dynamics problems governed by partial differential equations. However, conventional methods, such as physics-informed neural networks, often suffer…

Fluid Dynamics · Physics 2026-03-10 Yuling Han , Zhihui Li , Zhibin Yu

This work investigates the use of shallow physics-informed neural networks (PINNs) for solving forward and inverse problems of nonlinear partial differential equations (PDEs). By reformulating PINNs as nonlinear systems, the…

Numerical Analysis · Mathematics 2026-02-12 Muhammad Luthfi Shahab , Imam Mukhlash , Hadi Susanto

We propose characteristics-informed neural networks (CINN), a simple and efficient machine learning approach for solving forward and inverse problems involving hyperbolic PDEs. Like physics-informed neural networks (PINN), CINN is a…

Machine Learning · Computer Science 2023-01-16 Ulisses Braga-Neto

We introduce adaptive-basis physics-informed neural networks (AB-PINNs), a novel approach to domain decomposition for training PINNs in which existing subdomains dynamically adapt to the intrinsic features of the unknown solution. Drawing…

Machine Learning · Computer Science 2025-10-13 Jonah Botvinick-Greenhouse , Wael H. Ali , Mouhacine Benosman , Saviz Mowlavi

Inverse design arises in a variety of areas in engineering such as acoustic, mechanics, thermal/electronic transport, electromagnetism, and optics. Topology optimization is a major form of inverse design, where we optimize a designed…

Computational Physics · Physics 2022-01-19 Lu Lu , Raphael Pestourie , Wenjie Yao , Zhicheng Wang , Francesc Verdugo , Steven G. Johnson

Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…

Numerical Analysis · Mathematics 2023-05-23 Victorita Dolean , Alexander Heinlein , Siddhartha Mishra , Ben Moseley

Sparse identification of nonlinear dynamical systems is a topic of continuously increasing significance in the dynamical systems community. Here we explore it at the level of lattice nonlinear dynamical systems of many degrees of freedom.…

Pattern Formation and Solitons · Physics 2022-12-05 Sheikh Saqlain , Wei Zhu , Efstathios G. Charalampidis , Panayotis G. Kevrekidis