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Anant-Net: Breaking the Curse of Dimensionality with Scalable and Interpretable Neural Surrogate for High-Dimensional PDEs

6 May 2025

Papers citing "Anant-Net: Breaking the Curse of Dimensionality with Scalable and Interpretable Neural Surrogate for High-Dimensional PDEs"

27 / 27 papers shown

Title
Challenges and Advancements in Modeling Shock Fronts with Physics-Informed Neural Networks: A Review and Benchmarking Study J. Abbasi Ameya D. Jagtap Ben Moseley Aksel Hiorth P. Andersen PINN AI4CE 75 1 0 14 Mar 2025
SPIKANs: Separable Physics-Informed Kolmogorov-Arnold Networks Bruno Jacob Amanda A. Howard P. Stinis 90 7 0 09 Nov 2024
SympGNNs: Symplectic Graph Neural Networks for identifiying high-dimensional Hamiltonian systems and node classification Alan John Varghese Zhen Zhang George Karniadakis 97 3 0 29 Aug 2024
Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networks Spyros Rigas M. Papachristou Theofilos Papadopoulos Fotios Anagnostopoulos Georgios Alexandridis AI4CE 87 24 0 24 Jul 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 81 3 0 17 Jun 2024
A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks K. Shukla Juan Diego Toscano Zhicheng Wang Zongren Zou George Karniadakis 107 83 0 05 Jun 2024
Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation SS Sidharth Keerthana AR R. Gokul Anas KP 112 87 0 12 May 2024
Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations Zheyuan Hu Zhongqiang Zhang George Karniadakis Kenji Kawaguchi 79 14 0 12 Feb 2024
RiemannONets: Interpretable Neural Operators for Riemann Problems Ahmad Peyvan Vivek Oommen Ameya Dilip Jagtap George Karniadakis AI4CE 70 26 0 16 Jan 2024
An operator preconditioning perspective on training in physics-informed machine learning Tim De Ryck Florent Bonnet Siddhartha Mishra Emmanuel de Bezenac AI4CE 103 18 0 09 Oct 2023
Tackling the Curse of Dimensionality with Physics-Informed Neural Networks Zheyuan Hu K. Shukla George Karniadakis Kenji Kawaguchi PINN AI4CE 105 100 0 23 Jul 2023
Separable Physics-Informed Neural Networks Junwoo Cho Seungtae Nam Hyunmo Yang S. Yun Youngjoon Hong Eunbyung Park PINN AI4CE 77 47 0 28 Jun 2023
Learning stiff chemical kinetics using extended deep neural operators S. Goswami Ameya Dilip Jagtap H. Babaee Bryan T. Susi George Karniadakis AI4CE 147 40 0 23 Feb 2023
How important are activation functions in regression and classification? A survey, performance comparison, and future directions Ameya Dilip Jagtap George Karniadakis AI4CE 51 74 0 06 Sep 2022
SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problems Tingwei Meng Zhen Zhang Jérome Darbon George Karniadakis 56 15 0 14 Jan 2022
Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations Benjamin Moseley Andrew Markham T. Nissen‐Meyer PINN 79 227 0 16 Jul 2021
Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions Ameya Dilip Jagtap Yeonjong Shin Kenji Kawaguchi George Karniadakis ODL 83 134 0 20 May 2021
Parallel Physics-Informed Neural Networks via Domain Decomposition K. Shukla Ameya Dilip Jagtap George Karniadakis PINN 162 284 0 20 Apr 2021
Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets Sizhuang He Hanwen Wang P. Perdikaris AI4CE 97 707 0 19 Mar 2021
Solving high-dimensional parabolic PDEs using the tensor train format Lorenz Richter Leon Sallandt Nikolas Nusken 65 50 0 23 Feb 2021
Fourier Neural Operator for Parametric Partial Differential Equations Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 500 2,448 0 18 Oct 2020
Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism L. McClenny U. Braga-Neto PINN 84 459 0 07 Sep 2020
When and why PINNs fail to train: A neural tangent kernel perspective Sizhuang He Xinling Yu P. Perdikaris 141 916 0 28 Jul 2020
Robust Training and Initialization of Deep Neural Networks: An Adaptive Basis Viewpoint E. Cyr Mamikon A. Gulian Ravi G. Patel M. Perego N. Trask 93 72 0 10 Dec 2019
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators Lu Lu Pengzhan Jin George Karniadakis 248 2,153 0 08 Oct 2019
Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations M. Raissi 104 188 0 19 Apr 2018
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 123 1,389 0 30 Sep 2017