Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs

29 June 2020

Papers citing "Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs"

50 / 83 papers shown

Title
PC-SRGAN: Physically Consistent Super-Resolution Generative Adversarial Network for General Transient Simulations Md Rakibul Hasan Pouria Behnoudfar Dan MacKinlay Thomas Poulet GAN 32 0 0 10 May 2025
Physics-Informed Deep B-Spline Networks for Dynamical Systems Zhuoyuan Wang Raffaele Romagnoli Jasmine Ratchford Yorie Nakahira PINN AI4CE 53 0 0 21 Mar 2025
Understanding Generalization in Physics Informed Models through Affine Variety Dimensions Takeshi Koshizuka Issei Sato AI4CE 107 0 0 31 Jan 2025
Exact and approximate error bounds for physics-informed neural networks Augusto T. Chantada Pavlos Protopapas Luca Gomez Bachar Susana J. Landau Claudia G. Scóccola PINN 59 0 0 21 Nov 2024
Long-time Integration of Nonlinear Wave Equations with Neural Operators Guanhang Lei Zhen Lei Lei Shi 28 0 0 21 Oct 2024
Physics-informed kernel learning Nathan Doumèche Francis Bach Gérard Biau Claire Boyer PINN 37 2 0 20 Sep 2024
Physics-Informed Neural Networks and Extensions Maziar Raissi P. Perdikaris Nazanin Ahmadi George Karniadakis PINN AI4CE 41 4 0 29 Aug 2024
DeepSPoC: A Deep Learning-Based PDE Solver Governed by Sequential Propagation of Chaos Kai Du Yongle Xie Tao Zhou Yuancheng Zhou 21 0 0 29 Aug 2024
Improving PINNs By Algebraic Inclusion of Boundary and Initial Conditions Mohan Ren Zhihao Fang Keren Li Anirbit Mukherjee PINN AI4CE 47 0 0 30 Jul 2024
Generalizable Physics-Informed Learning for Stochastic Safety-Critical Systems Zhuoyuan Wang Albert Chern Yorie Nakahira 25 0 0 11 Jul 2024
Magnetic Hysteresis Modeling with Neural Operators Abhishek Chandra B. Daniels M. Curti K. Tiels E. Lomonova AI4CE 43 2 0 03 Jul 2024
On the estimation rate of Bayesian PINN for inverse problems Yi Sun Debarghya Mukherjee Yves Atchadé PINN 72 1 0 21 Jun 2024
Tackling the Curse of Dimensionality in Fractional and Tempered Fractional PDEs with Physics-Informed Neural Networks Zheyuan Hu Kenji Kawaguchi Zhongqiang Zhang George Karniadakis AI4CE 55 1 0 17 Jun 2024
Error Analysis and Numerical Algorithm for PDE Approximation with Hidden-Layer Concatenated Physics Informed Neural Networks Yianxia Qian Yongchao Zhang Suchuan Dong PINN 29 0 0 10 Jun 2024
Initialization-enhanced Physics-Informed Neural Network with Domain Decomposition (IDPINN) Chenhao Si Ming Yan AI4CE PINN 35 3 0 05 Jun 2024
RoPINN: Region Optimized Physics-Informed Neural Networks Haixu Wu Huakun Luo Yuezhou Ma Jianmin Wang Mingsheng Long AI4CE 32 6 0 23 May 2024
Error analysis for finite element operator learning methods for solving parametric second-order elliptic PDEs Youngjoon Hong Seungchan Ko Jae Yong Lee 20 1 0 27 Apr 2024
PINNACLE: PINN Adaptive ColLocation and Experimental points selection Gregory Kang Ruey Lau Apivich Hemachandra See-Kiong Ng K. H. Low 3DPC 29 18 0 11 Apr 2024
Error Estimation for Physics-informed Neural Networks Approximating Semilinear Wave Equations Beatrice Lorenz Aras Bacho Gitta Kutyniok PINN 11 2 0 11 Feb 2024
Challenges in Training PINNs: A Loss Landscape Perspective Pratik Rathore Weimu Lei Zachary Frangella Lu Lu Madeleine Udell AI4CE PINN ODL 33 39 0 02 Feb 2024
Efficient Discrete Physics-informed Neural Networks for Addressing Evolutionary Partial Differential Equations Siqi Chen Bin Shan Ye Li AI4CE PINN 21 1 0 22 Dec 2023
Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks Zheyuan Hu Zekun Shi George Karniadakis Kenji Kawaguchi AI4CE PINN 44 22 0 22 Dec 2023
NVFi: Neural Velocity Fields for 3D Physics Learning from Dynamic Videos Jinxi Li Ziyang Song Bo Yang 3DH 37 11 0 11 Dec 2023
Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs Zheyuan Hu Zhouhao Yang Yezhen Wang George Karniadakis Kenji Kawaguchi 44 9 0 26 Nov 2023
An Operator Learning Framework for Spatiotemporal Super-resolution of Scientific Simulations Valentin Duruisseaux Amit Chakraborty AI4CE 16 1 0 04 Nov 2023
An operator preconditioning perspective on training in physics-informed machine learning Tim De Ryck Florent Bonnet Siddhartha Mishra Emmanuel de Bezenac AI4CE 39 14 0 09 Oct 2023
Investigating the Ability of PINNs To Solve Burgers' PDE Near Finite-Time BlowUp Dibyakanti Kumar Anirbit Mukherjee 31 2 0 08 Oct 2023
Solving Elliptic Optimal Control Problems via Neural Networks and Optimality System Yongcheng Dai Bangti Jin R. Sau Zhi Zhou 37 4 0 23 Aug 2023
Neural oscillators for generalization of physics-informed machine learning Taniya Kapoor Abhishek Chandra D. Tartakovsky Hongrui Wang Alfredo Núñez R. Dollevoet AI4CE 19 11 0 17 Aug 2023
Tackling the Curse of Dimensionality with Physics-Informed Neural Networks Zheyuan Hu K. Shukla George Karniadakis Kenji Kawaguchi PINN AI4CE 63 85 0 23 Jul 2023
Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs Elham Kiyani M. Kooshkbaghi K. Shukla R. Koneru Zhen Li L. Bravo A. Ghoshal George Karniadakis M. Karttunen AI4CE 37 4 0 18 Jul 2023
Spectral-Bias and Kernel-Task Alignment in Physically Informed Neural Networks Inbar Seroussi Asaf Miron Z. Ringel PINN 37 0 0 12 Jul 2023
$PINNs error estimates for nonlinear equations in $\mathbb{R}$-smooth Banach spaces$ PINNs error estimates for nonlinear equations in $\mathbb{R}$ -smooth Banach spaces Jiexing Gao Yurii Zakharian 20 1 0 18 May 2023
Efficient Error Certification for Physics-Informed Neural Networks Francisco Eiras Adel Bibi Rudy Bunel Krishnamurthy Dvijotham Philip H. S. Torr M. P. Kumar PINN 24 1 0 17 May 2023
Convergence and error analysis of PINNs Nathan Doumèche Gérard Biau D. Boyer PINN AI4CE 42 17 0 02 May 2023
Multilevel CNNs for Parametric PDEs Cosmas Heiß Ingo Gühring Martin Eigel AI4CE 17 8 0 01 Apr 2023
Error Analysis of Physics-Informed Neural Networks for Approximating Dynamic PDEs of Second Order in Time Y. Qian Yongchao Zhang Yuanfei Huang S. Dong PINN 13 1 0 22 Mar 2023
Physics-informed neural networks for solving forward and inverse problems in complex beam systems Taniya Kapoor Hongrui Wang A. Núñez R. Dollevoet AI4CE PINN 21 46 0 02 Mar 2023
h-analysis and data-parallel physics-informed neural networks Paul Escapil-Inchauspé G. A. Ruz PINN AI4CE 27 2 0 17 Feb 2023
Entropy-dissipation Informed Neural Network for McKean-Vlasov Type PDEs Zebang Shen Zhenfu Wang 19 4 0 11 Feb 2023
Convergence Analysis of the Deep Galerkin Method for Weak Solutions Yuling Jiao Yanming Lai Yang Wang Haizhao Yang Yunfei Yang 21 3 0 05 Feb 2023
Deep Learning and Computational Physics (Lecture Notes) Deep Ray Orazio Pinti Assad A. Oberai PINN AI4CE 19 7 0 03 Jan 2023
Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems Derick Nganyu Tanyu Jianfeng Ning Tom Freudenberg Nick Heilenkötter A. Rademacher U. Iben Peter Maass AI4CE 23 34 0 06 Dec 2022
Utilising physics-guided deep learning to overcome data scarcity Jinshuai Bai Laith Alzubaidi Qingxia Wang E. Kuhl Bennamoun Yuantong T. Gu PINN AI4CE 26 3 0 24 Nov 2022
Physics-Informed Koopman Network Yuying Liu A. Sholokhov Hassan Mansour S. Nabi AI4CE 25 3 0 17 Nov 2022
Physics-informed neural networks for operator equations with stochastic data Paul Escapil-Inchauspé G. A. Ruz 26 2 0 15 Nov 2022
Partial Differential Equations Meet Deep Neural Networks: A Survey Shudong Huang Wentao Feng Chenwei Tang Jiancheng Lv AI4CE AIMat 24 17 0 27 Oct 2022
Neural Network Approximations of PDEs Beyond Linearity: A Representational Perspective Tanya Marwah Zachary Chase Lipton Jianfeng Lu Andrej Risteski 44 10 0 21 Oct 2022
On Physics-Informed Neural Networks for Quantum Computers Stefano Markidis PINN 32 18 0 28 Sep 2022
Variationally Mimetic Operator Networks Dhruv V. Patel Deep Ray M. Abdelmalik T. Hughes Assad A. Oberai 49 23 0 26 Sep 2022