PINN_Paper_List

Paper List of Physics-Informed Neural Network (PINN)

• Continues to update based on [PINNpapers] contributed by IDRL lab.

Survey and Review

• Physics-Informed Neural Networks and Extensions, Maziar Raissi, Paris Perdikaris, Nazanin Ahmadi, George Em Karniadakis, Frontiers of Science Awards 2024, [Paper]

• [Survey] Wang, Yizheng, et al. "Artificial intelligence for partial differential equations in computational mechanics: A review." Applied Mechanics Reviews (2024): 1-81. [Paper]

• [Survey] A Mathematical Guide to Operator Learning, Nicolas Boullé, Alex Townsend [Paper]

• Guo, Jiangtao, et al. "Advances in physics-informed neural networks for solving complex partial differential equations and their engineering applications: A systematic review." Engineering Applications of Artificial Intelligence 161 (2025): 112044. [Paper]

• [e-book] 【入门必备】物理信息神经网络入门-简明教程(1).pdf [PDF]

• Yu, Xianglong, et al. "Review of physics-informed neural networks in hemodynamics." Engineering Applications of Artificial Intelligence 163 (2026): 112834. [Paper]

• [e-book]《基于物理的深度学习书籍》 [Paper]

• "Neural Networks Meet Physics: A Survey of Physics-Informed Approaches to Modeling and Simulation." Nasir, Karthika, Rahul Menon, and Sneha Iyer. (2025). [Paper]

• Torres, Edgar, and Mathias Niepert. "Survey: Adaptive Physics-informed Neural Networks." Neurips 2024 Workshop Foundation Models for Science: Progress, Opportunities, and Challenges. [Paper]

• PINNs for Medical Image Analysis: A Survey, Chayan Banerjee, Kien Nguyen, Olivier Salvado, Truyen Tran, Clinton Fookes [Paper]

• [arXiv:2410.13228] From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning, Juan Diego Toscano, Vivek Oommen, Alan John Varghese, Zongren Zou, Nazanin Ahmadi Daryakenari, Chenxi Wu, George Em Karniadakis [Paper]

• Physics-Informed Computer Vision: A Review and Perspectives, [Paper]

• Scientific Machine Learning Through Physics–Informed Neural Networks: Where We Are and What’s Next? Journal of Scientific Computing (2022) 92:88, [Paper]

• Deep Learning and Computational Physics (Lecture Notes) Deep Ray, Orazio Pinti, Assad A. Oberai [https://arxiv.org/abs/2301.00942]

Nature and Science

• Raissi, Maziar, Alireza Yazdani, and George Em Karniadakis. "Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations." Science 367.6481 (2020): 1026-1030. [Paper]

Video Tutorials

• Physics-Informed Machine Learning for Modeling, Planning, Control and Estimation of Physical Systems (Youtube)

• [Jonas Buchli & Federico Felici: Magnetic control of tokamak plasmas with deep reinforcement learning (Youtube)]

• Introduction to Physics Informed Neural Networks | A hands on, project based course, [Youtube]

• Physics Informed Neural Networks (PINNs) || Ordinary Differential Equations || Step-by-Step Tutorial, [Youtube]

• Physics Informed Machine Learning: High Level Overview of AI and ML in Science and Engineering, [Youtube]

• Physics Informed Neural Networks, [Youtube]

• Learning Physics Informed Machine Learning Part 1 - Physics Informed Neural Networks (PINNs) [Youtube]

• Learning Physics Informed Machine Learning Part 2 - Inverse Physics Informed Neural Networks (PINNs) [Youtube]

• Learning Physics Informed Machine Learning Part 3 - Physics Informed DeepONets [Youtube]

• Physics-Informed Neural Networks for Soft Matter Problems (Paper Review) [Youtube]

• Physics-Informed Machine Learning (PIML) and Kolmogorov-Arnold Networks (KANs)- Caltech's CMX 2025 [Youtube]

---------------------- ETH Zürich AI in the Sciences and Engineering 2024 ----------------------

• ETH Zürich AISE: Physics-Informed Neural Networks – Introduction [Youtube]
• ETH Zürich AISE: Physics-Informed Neural Networks – Limitations and Extensions Part 1 [Youtube]
• ETH Zürich AISE: Physics-Informed Neural Networks – Limitations and Extensions Part 2 [Youtube]
• ETH Zürich AISE: Physics-Informed Neural Networks – Theory Part 1 [Youtube]
• ETH Zürich AISE: Physics-Informed Neural Networks – Theory Part 2 [Youtube]
• ETH Zürich AISE: Importance of PDEs in Science [Youtube]

Simple Tutorial

• https://github.com/zhaoxiaoyu1995/PINN-Task
• 物理AI论文精读1：PINN的基本原理介绍 [Wechat URL]
• 物理AI论文精读2：PINN的训练难题与自适应策略 [Wechat URL]
• 物理AI论文精读3：PINN的架构进化 [Wechat URL]
• 物理AI论文精读4：PINN基准测试与对比 [Wechat URL]

Newly Updated Papers & Toolkit

• [https://github.com/nanditadoloi/PINN]

• [https://github.com/maziarraissi/PINNs]

• [Project page] [Physics Informed Deep Learning---Data-driven solutions and discovery of Nonlinear Partial Differential Equations]

• [arXiv:1711.10561] Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations, Maziar Raissi, Paris Perdikaris, George Em Karniadakis [Paper]

• [arXiv:1711.10566] Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations, Maziar Raissi, Paris Perdikaris, George Em Karniadakis [Paper]

• SC21 Tutorial on Scientific Machine Learning (GitHub)

• Scientific Machine Learning Tutorial at SuperComputing Conference 2021 (Youtube Video List)

Software

1. DeepXDE: A Deep Learning Library for Solving Differential Equations, Lu Lu, Xuhui Meng, Zhiping Mao, George Em Karniadakis, SIAM Review, 2021. [paper][code]
2. NVIDIA SimNet™: An AI-Accelerated Multi-Physics Simulation Framework, Oliver Hennigh, Susheela Narasimhan, Mohammad Amin Nabian, Akshay Subramaniam, Kaustubh Tangsali, Zhiwei Fang, Max Rietmann, Wonmin Byeon, Sanjay Choudhry, ICCS, 2021. [paper]
3. SciANN: A Keras wrapper for scientific computations and physics-informed deep learning using artificial neural networks, Ehsan Haghighat, Ruben Juanes, arXiv preprint arXiv:2005.08803, 2020. [paper][code]
4. Elvet -- a neural network-based differential equation and variational problem solver, Jack Y. Araz, Juan Carlos Criado, Michael Spannowsky, arXiv:2103.14575 [hep-lat, physics:hep-ph, physics:hep-th, stat], 2021. [paper][code]
5. TensorDiffEq: Scalable Multi-GPU Forward and Inverse Solvers for Physics Informed Neural Networks, Levi D. McClenny, Mulugeta A. Haile, Ulisses M. Braga-Neto, arXiv:2103.16034 [physics], 2021. [paper][code]
6. PyDEns: a Python Framework for Solving Differential Equations with Neural Networks, Alex Koryagin, er, Roman Khudorozkov, Sergey Tsimfer, arXiv:1909.11544 [cs, stat], 2019. [paper]
7. NeuroDiffEq: A Python package for solving differential equations with neural networks, Feiyu Chen, David Sondak, Pavlos Protopapas, Marios Mattheakis, Shuheng Liu, Devansh Agarwal, Marco Di Giovanni, Journal of Open Source Software, 2020. [paper][code]
8. Universal Differential Equations for Scientific Machine Learning, Christopher Rackauckas, Yingbo Ma, Julius Martensen, Collin Warner, Kirill Zubov, Rohit Supekar, Dominic Skinner, Ali Ramadhan, Alan Edelman, arXiv:2001.04385 [cs, math, q-bio, stat], 2020. [paper][code]
9. NeuralPDE: Automating Physics-Informed Neural Networks (PINNs) with Error Approximations, Kirill Zubov, Zoe McCarthy, Yingbo Ma, Francesco Calisto, Valerio Pagliarino, Simone Azeglio, Luca Bottero, Emmanuel Luján, Valentin Sulzer, Ashutosh Bharambe, N Vinchhi, , Kaushik Balakrishnan, Devesh Upadhyay, Chris Rackauckas, arXiv:2107.09443 [cs], 2021. [paper][code]
10. IDRLnet: A Physics-Informed Neural Network Library, Wei Peng, Jun Zhang, Weien Zhou, Xiaoyu Zhao, Wen Yao, Xiaoqian Chen, arXiv:2107.04320 [cs, math], 2021. [paper][code]
11. NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operators, Zongren Zou, Xuhui Meng, Apostolos F. Psaros, George Em Karniadakis, UNKNOWN_JOURNAL, 2022. [paper][code]

Year 2026

• [KDD 2026] Divide and Conquer: Region Self-Paced Physics-Informed Neural Networks, Ruixuan Meng, Wenyuan Wu, Zhenwen Ren, Dezhong Peng, Yuan Sun, Xiaogang Deng, KDD '26: Proceedings of the 32nd ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.2, Pages 3727 - 3738, [DOI] [Paper]

• [IEEE TPAMI 2026] H. Viswanath et al., "Neural Operator: Is Data All You Need to Model the World? An Insight Into the Paradigm of Data-Driven Scientific ML," in IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 48, no. 8, pp. 10097-10111, Aug. 2026, doi: 10.1109/TPAMI.2026.3682604. [Paper]

• G-RANS: Generalizable Residual-Aware Neural Solvers for Sparse Systems, Weixin Liao * 1 2 Mingquan Feng * 1 2 Zhizhou Zhang 2 Youjia Wu 2 Yifan Fu 1 Junchi Yan 1 [Paper]

• [arXiv:1710.00211] Yu, Bing. "The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems." Communications in Mathematics and Statistics 6.1 (2018): 1-12. [arXiv]

• Li, Wei; Zhang, Wei; Xie, Yi; Wen, Yonggang; Yan, Qingyu (2026). Operando Thermal Reconstruction for Lithium-Ion Batteries via Physics-Informed Generative Diffusion Models. Singapore Institute of Technology. Journal contribution. https://doi.org/10.25447/sit.31986780.v1 [Paper]

• Physical Regularization Loss: Integrating Physical Knowledge to Image Segmentation, International Journal of Computer Vision 2026 [Paper]

• Pixel2Phys: Distilling Governing Laws from Visual Dynamics, Ruikun Li, Jun Yao, Yingfan Hua, Shixiang Tang, Biqing Qi, Bin Liu, Wanli Ouyang, Yan Lu [Paper]

• FovEx: Human-Inspired Explanations for Vision Transformers and Convolutional Neural Networks, Mahadev Prasad Panda, Matteo Tiezzi, Martina Vilas, Gemma Roig, Bjoern M. Eskofier & Dario Zanca, [Paper]

Year 2025

• The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning, Ruben Ohana, Michael McCabe, Lucas Meyer, Rudy Morel, Fruzsina J. Agocs, Miguel Beneitez, Marsha Berger, Blakesley Burkhart, Keaton Burns, Stuart B. Dalziel, Drummond B. Fielding, Daniel Fortunato, Jared A. Goldberg, Keiya Hirashima, Yan-Fei Jiang, Rich R. Kerswell, Suryanarayana Maddu, Jonah Miller, Payel Mukhopadhyay, Stefan S. Nixon, Jeff Shen, Romain Watteaux, Bruno Régaldo-Saint Blancard, François Rozet, Liam H. Parker, Miles Cranmer, Shirley Ho [Paper]

• AION-1: Omnimodal Foundation Model for Astronomical Sciences, Liam Parker, Francois Lanusse, Jeff Shen, Ollie Liu, Tom Hehir, Leopoldo Sarra, Lucas Meyer, Micah Bowles, Sebastian Wagner-Carena, Helen Qu, Siavash Golkar, Alberto Bietti, Hatim Bourfoune, Nathan Casserau, Pierre Cornette, Keiya Hirashima, Geraud Krawezik, Ruben Ohana, Nicholas Lourie, Michael McCabe, Rudy Morel, Payel Mukhopadhyay, Mariel Pettee, Bruno Regaldo-Saint Blancard, Kyunghyun Cho, Miles Cranmer, Shirley Ho [Paper]

• Physics Steering: Causal Control of Cross-Domain Concepts in a Physics Foundation Model, Rio Alexa Fear, Payel Mukhopadhyay, Michael McCabe, Alberto Bietti, Miles Cranmer [Paper]

• PDE-Agent: A toolchain-augmented multi-agent framework for PDE solving, Jianming Liu, Ren Zhu, Jian Xu, Kun Ding, Xu-Yao Zhang, Gaofeng Meng, Cheng-Lin Liu [Paper]

• PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems, Bocheng Zeng, Qi Wang, Mengtao Yan, Yang Liu, Ruizhi Chengze, Yi Zhang, Hongsheng Liu, Zidong Wang, Hao Sun [Paper]

• Physics-Informed Neuro-Evolution (PINE): A Survey and Prospects, Jian Cheng Wong, Abhishek Gupta, Chin Chun Ooi, Pao-Hsiung Chiu, Jiao Liu, Yew-Soon Ong [Paper]

Year 2024

• CryoGEM: Physics-Informed Generative Cryo-Electron Microscopy [Paper]

• Physics-Informed Variational State-Space Gaussian Processes [Paper]

• Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators, [Paper]

• Physics-Regularized Multi-Modal Image Assimilation for Brain Tumor Localization, [Paper]

• Dual Cone Gradient Descent for Training Physics-Informed Neural Networks, Youngsik Hwang, Dong-Young Lim [Paper]

• Musgrave, Jonathan, and Shu-Wei Huang. "Fourier Domain Physics Informed Neural Network." arXiv preprint arXiv:2409.19895 (2024). [Paper]

• Cooley, Madison, et al. "Fourier PINNs: From Strong Boundary Conditions to Adaptive Fourier Bases." arXiv preprint arXiv:2410.03496 (2024). [Paper]

• Song, Yuchen, et al. "SRS-Net: a universal framework for solving stimulated Raman scattering in nonlinear fiber-optic systems by physics-informed deep learning." Communications Engineering 3.1 (2024): 109. [Paper]

• Robust Variational Physics-Informed Neural Networks, [Paper]

• [NeurIPS 2023] Separable Physics-Informed Neural Networks, [Paper] [Code]

• Kamtue, Kawisorn, et al. "PhyOT: Physics-informed object tracking in surveillance cameras." ICASSP 2024-2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2024. [Paper]

Year 2023

• Borate, Prabhav, et al. "Using a physics-informed neural network and fault zone acoustic monitoring to predict lab earthquakes." Nature communications 14.1 (2023): 3693. [Paper]

Year 2022

• -PINNs: physics-informed neural networks on complex geometries, [Paper]

Year 2020

• Physics-informed deep learning for incompressible laminar flows, Chengping Rao, Hao Sun, Yang Liu, Theoretical and Applied Mechanics Letters, 2020 [Paper]

Papers on PINN Models

1. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, M. Raissi, P. Perdikaris, G. E. Karniadakis, Journal of Computational Physics, 2019. [paper]
2. The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems, E Weinan, Bing Yu, Communications in Mathematics and Statistics, 2018. [paper]
3. DGM: A deep learning algorithm for solving partial differential equations, Justin Sirignano, Konstantinos Spiliopoulos, Journal of Computational Physics, 2018. [paper]
4. SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEs, Amuthan A. Ramabathiran, Ramach, Prabhu ran, Journal of Computational Physics, 2021. [paper][code]
5. Deep neural network methods for solving forward and inverse problems of time fractional diffusion equations with conformable derivative, Yinlin Ye, Yajing Li, Hongtao Fan, Xinyi Liu, Hongbing Zhang, arXiv:2108.07490 [cs, math], 2021. [paper]
6. NH-PINN: Neural homogenization based physics-informed neural network for multiscale problems, Wing Tat Leung, Guang Lin, Zecheng Zhang, arXiv:2108.12942 [cs, math], 2021. [paper]
7. Physics-Augmented Learning: A New Paradigm Beyond Physics-Informed Learning, Ziming Liu, Yunyue Chen, Yuanqi Du, Max Tegmark, arXiv:2109.13901 [physics], 2021. [paper]
8. Theory-guided hard constraint projection (HCP): A knowledge-based data-driven scientific machine learning method, Yuntian Chen, Dou Huang, Dongxiao Zhang, Junsheng Zeng, Nanzhe Wang, Haoran Zhang, Jinyue Yan, Journal of Computational Physics, 2021. [paper]
9. Learning in Sinusoidal Spaces with Physics-Informed Neural Networks, Jian Cheng Wong, Chinchun Ooi, Abhishek Gupta, Yew-Soon Ong, arXiv:2109.09338 [physics], 2021. [paper]
10. HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks, Filipe de Avila Belbute-Peres, Yi-fan Chen, Fei Sha, NIPS, 2021. [paper]
11. Physics-informed PointNet: A deep learning solver for steady-state incompressible flows and thermal fields on multiple sets of irregular geometries, AliKashefi, TapanMukerji, Journal of Computational Physics, 2022. [paper]
12. Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems, HanGao, Matthew J.Zahr, Jian-XunWang, Computer Methods in Applied Mechanics and Engineering, 2022. [paper]
13. PhyGNNet: Solving spatiotemporal PDEs with Physics-informed Graph Neural Network, Longxiang Jiang, Liyuan Wang, Xinkun Chu, Yonghao Xiao and Hao Zhang, arXiv:2208.04319 [cs.NE], 2022. [paper]
14. ModalPINN : an extension of Physics-Informed Neural Networks with enforced truncated Fourier decomposition for periodic flow reconstruction using a limited number of imperfect sensors, * Ga´etan Raynaud , S´ebastien Houde, Fr´ed´erick P Gosselin*, Journal of Computational Physics, 2022. [paper]
15. ∆-PINNs: physics-informed neural networks on complex geometries, Francisco Sahli Costabal, Simone Pezzuto, Paris Perdikaris, Arxiv, 2022. [paper]
16. Robust Regression with Highly Corrupted Data via Physics Informed Neural Networks, Wei Peng, Wen Yao, Weien Zhou, Xiaoya Zhang, Weijie Yao, ArXiv, 2022. [paper][code]
17. PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks,Zhiyuan Zhao,Xueying Ding,B. Aditya Prakash, ICLR,2024. [paper] [code]
18. Scaling physics-informed hard constraints with mixture-of-experts,Nithin Chalapathi,Yiheng Du,Aditi Krishnapriyan,ICLR,2024. [paper] [code]
19. Space and time continuous physics simulation from partial observations,Steeven Janny,Madiha Nadri,Julie Digne,Christian Wolf, ICLR,2024. [paper] [code]
20. PIG: Physics-Informed Gaussians as Adaptive Parametric Mesh Representations,Zeyu Li,Hongkun Dou,Shen Fang,Wang Han,Yue Deng,Lijun Yang,ICLR,2025. [paper] [code]
21. MeshMask: Physics-Based Simulations with Masked Graph Neural Networks,Paul Garnier,Vincent Lannelongue, Jonathan Viquerat,Elie Hachem,ICLR,2025. [paper]
22. PARCv2: Physics-aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics Modeling, Phong C.H. Nguyen, Xinlun Cheng, Shahab Azarfar, Pradeep Seshadri, Yen T. Nguyen, Munho Kim, Sanghun Choi, H.S. Udaykumar, Stephen Baek.ICML,2024. [paper] [code]
23. Transolver: A Fast Transformer Solver for PDEs on General Geometries,Haixu Wu, Huakun Luo, Haowen Wang, Jianmin Wang, Mingsheng Long,ICML,2024. [paper] [code]
24. Phase2vec: dynamical systems embedding with a physics-informed convolutional network,Matthew Ricci,Noa Moriel, Zoe Piran, MorNitzan,ICLR,2023. [paper] [code]

Papers on Parallel PINN

1. Parallel Physics-Informed Neural Networks via Domain Decomposition, Khemraj Shukla, Ameya D. Jagtap, George Em Karniadakis, arXiv:2104.10013 [cs], 2021. [paper]
2. Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations, Ben Moseley, Andrew Markham, Tarje Nissen-Meyer, arXiv:2107.07871 [physics], 2021. [paper]
3. PPINN: Parareal physics-informed neural network for time-dependent PDEs, Xuhui Meng, Zhen Li, Dongkun Zhang, George Em Karniadakis, Computer Methods in Applied Mechanics and Engineering, 2020. [paper]
4. When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?, Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis, Kenji Kawaguchi, arXiv:2109.09444 [cs, math, stat], 2021. [paper]
5. Scaling physics-informed neural networks to large domains by using domain decomposition, Ben Moseley, Andrew Markham, Tarje Nissen-Meyer, NIPS, 2021. [paper]
6. Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations, Ben Moseley, Andrew Markham, Tarje Nissen-Meyer, arXiv:2107.07871 [physics], 2021. [paper]
7. Improved Deep Neural Networks with Domain Decomposition in Solving Partial Differential Equations, Wei Wu, Xinlong Feng, Hui Xu, Journal of Scientific Computing, 2022. [paper]
8. INN: Interfaced neural networks as an accessible meshless approach for solving interface PDE problems, Sidi Wu, Benzhuo Lu, Journal of Computational Physics, 2022. [paper][code]
9. Physics and Lie symmetry informed Gaussian processes,David Dalton, Dirk Husmeier, Hao Gao,ICML,2024. [paper] [code]

Papers on PINN Accerleration

1. Self-adaptive loss balanced Physics-informed neural networks for the incompressible Navier-Stokes equations, Zixue Xiang, Wei Peng, Xiaohu Zheng, Xiaoyu Zhao, Wen Yao, arXiv:2104.06217 [physics], 2021. [paper]
2. A Dual-Dimer method for training physics-constrained neural networks with minimax architecture, Dehao Liu, Yan Wang, Neural Networks, 2021. [paper]
3. Adversarial Multi-task Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations, Pongpisit Thanasutives, Masayuki Numao, Ken-ichi Fukui, arXiv:2104.14320 [cs, math], 2021. [paper]
4. DPM: A Novel Training Method for Physics-Informed Neural Networks in Extrapolation, Jungeun Kim, Kookjin Lee, Dongeun Lee, Sheo Yon Jin, Noseong Park, AAAI, 2021. [paper]
5. Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems, Jeremy Yu, Lu Lu, Xuhui Meng, George Em Karniadakis, Arxiv, 2021. [paper]
6. CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method, Pao-Hsiung Chiu, Jian Cheng Wong, Chinchun Ooi, My Ha Dao, Yew-Soon Ong, Arxiv, 2021. [paper]
7. A hybrid physics-informed neural network for nonlinear partial differential equation, Chunyue Lv, Lei Wang, Chenming Xie, Arxiv, 2021. [paper]
8. Multi-Objective Loss Balancing for Physics-Informed Deep Learning, Rafael Bischof, Michael Kraus, Arxiv, 2021. [paper]
9. A High-Efficient Hybrid Physics-Informed Neural Networks Based on Convolutional Neural Network, Zhiwei Fang, IEEE Transactions on Neural Networks and Learning Systems, 2021. [paper]
10. RPINNs: Rectified-physics informed neural networks for solving stationary partial differential equations, Pai Peng, Jiangong Pan, Hui Xu, Xinlong Feng, Computers & Fluids, 2022. [paper]
11. A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks, Chenxi Wu,Min Zhu,Qinyang Tan,Yadhu Kartha,Lu Lu, arXiv:2207.10289 [cs], 2022. [paper]
12. A Novel Adaptive Causal Sampling Method for Physics-Informed Neural Networks, Jia Guo, Haifeng Wang, Chenping Hou, arXiv:2210.12914 [cs], 2022. [paper]
13. Accelerated Training of Physics-Informed Neural Networks (PINNs) using Meshless Discretizations, Ramansh Sharma, Varun Shankar, NeurIPS, 2022. [paper]
14. Is L2 Physics-Informed Loss Always Suitable for Training Physics-Informed Neural Network, Chuwei Wang, Shanda Li, Di He, Liwei Wang, NeurIPS, 2022. [paper]
15. PINNACLE: PINN Adaptive ColLocation and Experimental points selection,Gregory Kang Ruey Lau,Apivich Hemachandra,See-Kiong Ng,Bryan Kian Hsiang Low,ICLR,2024. [paper] [code]
16. Adversarial Adaptive Sampling: Unify PINN and Optimal Transport for the Approximation of PDEs,Kejun Tang,Jiayu Zhai,Xiaoliang Wan,Chao Yang,ICLR,2024. [paper]
17. Learning a Neural Solver for Parametric PDEs to Enhance Physics-Informed Methods，Lise Le Boudec, Emmanuel de Bézenac, Louis Serrano,Ramon Daniel Regueiro-Espino,Yuan Yin,patrick Gallinari,ICLR,2025. [paper] [code]
18. Metamizer: A Versatile Neural Optimizer for Fast and Accurate Physics Simulations，Nils Wandel,Stefan Schulz,Reinhard Klein,ICLR,2025. [paper] [code]
19. Physics-aligned field reconstruction with diffusion bridge,Zeyu Li,Hongkun Dou,Shen Fang,Wang Han,Yue Deng,Lijun Yang,ICLR,2025. [paper] [code]
20. PINP: Physics-Informed Neural Predictor with latent estimation of fluid flows,Huaguan Chen,Yang Liu,Hao Sun,ICLR,2025. [paper]
21. ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks,Qiang Liu,Mengyu Chu,Nils Thuerey,ICLR,2025. [paper] [code]
22. ANaGRAM: A Natural Gradient Relative to Adapted Model for efficient PINNs learning,Nilo Schwencke,Cyril Furtlehner,ICLR,2025. [paper] [code]
23. Predicting the Energy Landscape of Stochastic Dynamical System via Physics-informed Self-supervised Learning, Wenhan Gao,Ruichen Xu,Yuefan Deng,Yi Liu,ICLR,2025. [paper] [code]
24. TENG: Time-Evolving Natural Gradient for Solving PDEs With Deep Neural Nets Toward Machine Precision, Zhuo Chen, Jacob Mccarran, Esteban Vizcaino, Marin Soljacic, Di Luo ,ICML,2024. [paper] [code]
25. Dual Cone Gradient Descent for Training Physics-Informed Neural Networks，Youngsik Hwang, Dong-Young Lim，NeurIPS,2024. [paper] [code]
26. Physics-informed Neural Networks for Functional Differential Equations: Cylindrical Approximation and Its Convergence Guarantees，Taiki Miyagawa, Takeru Yokota,NeurIPS,2024. [paper] [code]
27. Kronecker-Factored Approximate Curvature for Physics-Informed Neural Networks，Felix Dangel, Johannes Müller, Marius Zeinhofer，NeurIPS,2024. [paper]
28. Bi-level Physics-Informed Neural Networks for PDE Constrained Optimization using Broyden's Hypergradients,Zhongkai Hao, Chengyang Ying, Hang Su, Jun Zhu ,Jian Song, Ze Cheng,ICLR,2023. [paper]
29. CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representations, Peter Yichen Chen, Jinxu Xiang,Dong Heon Cho,Yue Chang,G A Pershing,Henrique Teles Maia,Maurizio M. Chiaramonte,Kevin Carlberg,Eitan Grinspun,ICLR,2023. [paper] [code]
30. A Stable and Scalable Method for Solving Initial Value PDEs with Neural Networks,Marc Finzi, Andres Potapczynski, Matthew Choptuik, Andrew Gordon Wilson,ICLR,2023. [paper] [code]

Papers on Model Transfer & Meta-Learning

1. A physics-aware learning architecture with input transfer networks for predictive modeling, Amir Behjat, Chen Zeng, Rahul Rai, Ion Matei, David Doermann, Souma Chowdhury, Applied Soft Computing, 2020. [paper]
2. Transfer learning based multi-fidelity physics informed deep neural network, Souvik Chakraborty, Journal of Computational Physics, 2021. [paper]
3. Transfer learning enhanced physics informed neural network for phase-field modeling of fracture, Somdatta Goswami, Cosmin Anitescu, Souvik Chakraborty, Timon Rabczuk, Theoretical and Applied Fracture Mechanics, 2020. [paper]
4. Meta-learning PINN loss functions, Apostolos F. Psaros, Kenji Kawaguchi, George Em Karniadakis, arXiv:2107.05544 [cs], 2021. [paper]
5. Meta-PDE: Learning to Solve PDEs Quickly Without a Mesh, Tian Qin,Alex Beatson,Deniz Oktay,Nick McGreivy,Ryan P. Adams, arXiv:2211.01604 [cs], 2022. [paper]
6. Physics-Informed Neural Networks (PINNs) for Parameterized PDEs: A Metalearning Approach, Michael Penwarden, Sh Zhe, ian, Akil Narayan, Robert M. Kirby, Arxiv, 2021. [paper]
7. MetaPhysiCa: Improving OOD Robustness in Physics-informed Machine Learning,S Chandra Mouli , Muhammad Alam,Bruno Ribeiro,ICLR,2024. [paper] [code]
8. DATS: Difficulty-Aware Task Sampler for Meta-Learning Physics-Informed Neural Networks,Maryam Toloubidokhti,Yubo Ye,Ryan Missel,Xiajun Jiang,Nilesh Kumar,Ruby Shrestha,Linwei Wang,ICLR,2024.[paper] [code]
9. PIED: Physics-Informed Experimental Design for Inverse Problems,Apivich Hemachandra,Gregory Kang Ruey Lau,See-Kiong Ng,Bryan Kian Hsiang Low,ICLR,2025. [paper] [code]

Papers on Probabilistic PINNs and Uncertainty Quantification

1. A physics-aware, probabilistic machine learning framework for coarse-graining high-dimensional systems in the Small Data regime, Constantin Grigo, Phaedon-Stelios Koutsourelakis, Journal of Computational Physics, 2019. [paper]
2. Adversarial uncertainty quantification in physics-informed neural networks, Yibo Yang, Paris Perdikaris, Journal of Computational Physics, 2019. [paper]
3. B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data, Liu Yang, Xuhui Meng, George Em Karniadakis, Journal of Computational Physics, 2021. [paper]
4. PID-GAN: A GAN Framework based on a Physics-informed Discriminator for Uncertainty Quantification with Physics, Arka Daw, M. Maruf, Anuj Karpatne, arXiv:2106.02993 [cs, stat], 2021. [paper]
5. Quantifying Uncertainty in Physics-Informed Variational Autoencoders for Anomaly Detection, Marcus J. Neuer, ESTEP, 2020. [paper]
6. A Physics-Data-Driven Bayesian Method for Heat Conduction Problems, Xinchao Jiang, Hu Wang, Yu li, arXiv:2109.00996 [cs, math], 2021. [paper]
7. Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural Networks, Yihang Gao, Michael K. Ng, arXiv:2108.13054 [cs, math], 2021. [paper]
8. Flow Field Tomography with Uncertainty Quantification using a Bayesian Physics-Informed Neural Network, Joseph P. Molnar, Samuel J. Grauer, arXiv:2108.09247 [physics], 2021. [paper]
9. Stochastic Physics-Informed Neural Networks (SPINN): A Moment-Matching Framework for Learning Hidden Physics within Stochastic Differential Equations, Jared O'Leary, Joel A. Paulson, Ali Mesbah, arXiv:2109.01621 [cs], 2021. [paper]
10. Spectral PINNs: Fast Uncertainty Propagation with Physics-Informed Neural Networks, Björn Lütjens, Catherine H. Crawford, Mark Veillette, Dava Newman, NIPS, 2021. [paper]
11. Robust Learning of Physics Informed Neural Networks, Ch Bajaj, rajit, Luke McLennan, Timothy Andeen, Avik Roy, Arxiv, 2021. [paper]
12. Bayesian Physics Informed Neural Networks for real-world nonlinear dynamical systems, Kevin Linka, Amelie Schäfer, Xuhui Meng, Zongren Zou, George EmKarniadakis, Ellen Kuhl, Computer Methods in Applied Mechanics and Engineering, 2022. [paper]
13. Multi-output physics-informed neural networks for forward and inverse PDE problems with uncertainties, Mingyuan Yang, John T.Foster, Computer Methods in Applied Mechanics and Engineering, 2022. [paper]
14. RoPINN: Region Optimized Physics-Informed Neural Networks,Haixu Wu, Huakun Luo, Yuezhou Ma, Jianmin Wang, Mingsheng Long,NeurIPS,2024. [paper] [code]

Papers on Applications

1. Physics-informed neural networks for high-speed flows, Zhiping Mao, Ameya D. Jagtap, George Em Karniadakis, Computer Methods in Applied Mechanics and Engineering, 2020. [paper]
2. Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data, Luning Sun, Han Gao, Shaowu Pan, Jian-Xun Wang, Computer Methods in Applied Mechanics and Engineering, 2020. [paper]
3. Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations, Maziar Raissi, Alireza Yazdani, George Em Karniadakis, Science, 2020. [paper]
4. NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations, Xiaowei Jin, Shengze Cai, Hui Li, George Em Karniadakis, Journal of Computational Physics, 2021. [paper]
5. A High-Efficient Hybrid Physics-Informed Neural Networks Based on Convolutional Neural Network, Zhiwei Fang, IEEE Transactions on Neural Networks and Learning Systems, 2021. [paper]
6. A Study on a Feedforward Neural Network to Solve Partial Differential Equations in Hyperbolic-Transport Problems, Eduardo Abreu, Joao B. Florindo, ICCS, 2021. [paper]
7. A Physics Informed Neural Network Approach to Solution and Identification of Biharmonic Equations of Elasticity, Mohammad Vahab, Ehsan Haghighat, Maryam Khaleghi, Nasser Khalili, arXiv:2108.07243 [cs], 2021. [paper]
8. Prediction of porous media fluid flow using physics informed neural networks, Muhammad M. Almajid, Moataz O. Abu-Alsaud, Journal of Petroleum Science and Engineering, 2021. [paper]
9. Investigating a New Approach to Quasinormal Modes: Physics-Informed Neural Networks, Anele M. Ncube, Gerhard E. Harmsen, Alan S. Cornell, arXiv:2108.05867 [gr-qc], 2021. [paper]
10. Towards neural Earth system modelling by integrating artificial intelligence in Earth system science, Christopher Irrgang, Niklas Boers, Maike Sonnewald, Elizabeth A. Barnes, Christopher Kadow, Joanna Staneva, Jan Saynisch-Wagner, Nature Machine Intelligence, 2021. [paper]
11. Physics-informed Neural Network for Nonlinear Dynamics in Fiber Optics, Xiaotian Jiang, Danshi Wang, Qirui Fan, Min Zhang, Chao Lu, Alan Pak Tao Lau, arXiv:2109.00526 [physics], 2021. [paper]
12. On Theory-training Neural Networks to Infer the Solution of Highly Coupled Differential Equations, M. Torabi Rad, A. Viardin, M. Apel, arXiv:2102.04890 [physics], 2021. [paper]
13. Theory-training deep neural networks for an alloy solidification benchmark problem, M. Torabi Rad, A. Viardin, G. J. Schmitz, M. Apel, arXiv:1912.09800 [physics], 2019. [paper]
14. Explicit physics-informed neural networks for nonlinear closure: The case of transport in tissues, Ehsan Taghizadeh, Helen M. Byrne, Brian D. Wood, Journal of Computational Physics, 2022. [paper]
15. A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element method, Shahed Rezaei, Ali Harandi, Ahmad Moeineddin, Bai-Xiang Xu, Stefanie Reese, arXiv:2206.13103 [cs.CE], 2022. [paper]
16. A generalized framework for unsupervised learning and data recovery in computational fluid dynamics using discretized loss functions, Jot Singh Aulakh, Steven B. Beale, and Jon G. Pharoah, Physics of Fluids, 2022. [paper]
17. Physics-Informed Neural Networks for AC Optimal Power Flow, Rahul Nellikkath, Spyros Chatzivasileiadis, Electric Power Systems Research, 2022. [paper]
18. Physics-informed neural networks for the shallow-water equations on the sphere, Alex Bihlo, Roman O.Popovych, Journal of Computational Physics, 2022. [paper]
19. A Physics-Informed Machine Learning Approach for Estimating Lithium-Ion Battery Temperature, Gyouho Cho, Mengqi Wang, Youngki Kim, Jaerock Kwon, Wencong Su, IEEE Access, 2022. [paper]
20. Physically guided deep learning solver for time-dependent Fokker–Planck equation, Yang Zhang, Ka-Veng Yuen, International Journal of Non-Linear Mechanics, 2022. [paper]
21. A Physically Consistent Framework for Fatigue Life Prediction using Probabilistic Physics-Informed Neural Network, Taotao Zhou, Shan Jiang, Te Han, Shun-Peng Zhu, Yinan Cai, International Journal of Fatigue, 2022. [paper]
22. Inverse modeling of nonisothermal multiphase poromechanics using physics-informed neural networks, Danial Amini, Ehsan Haghighat, Ruben Juanes, Arxiv, 2022. [paper][code)]
23. AirPhyNet: Harnessing Physics-Guided Neural Networks for Air Quality Prediction,Kethmi Hirushini Hettige, Jiahao Ji,Shili Xiang,Cheng Long,Gao Cong,Jingyuan Wang,ICLR,2024. [paper] [code]
24. PIORF: Physics-Informed Ollivier-Ricci Flow for Long–Range Interactions in Mesh Graph Neural Networks,Youn-Yeol Yu,Jeongwhan Choi,Jaehyeon Park,Kookjin Lee,Noseong Park,ICLR,2025. [paper]
25. Physics-Informed Diffusion Models,Jan-Hendrik Bastek,WaiChing Sun,Dennis Kochmann,ICLR,2025. [paper] [code]
26. Air Quality Prediction with Physics-Guided Dual Neural ODEs in Open Systems,jindong tian,Yuxuan Liang, Ronghui Xu,Peng Chen,Chenjuan Guo,Aoying Zhou,Lujia Pan,Zhongwen Rao,Bin Yang,ICLR,2025. [paper] [code]
27. Generating Physical Dynamics under Priors,Zihan Zhou,Xiaoxue Wang,Tianshu Yu,ICLR,2025. [paper] [code]
28. PAPM: A Physics-aware Proxy Model for Process Systems,Pengwei Liu, Zhongkai Hao, Xingyu Ren, Hangjie Yuan, Jiayang Ren, Dong Ni,ICML,2024. [paper] [code]
29. Med-Real2Sim: Non-Invasive Medical Digital Twins using Physics-Informed Self-Supervised Learning, Keying Kuang, Frances Dean, Jack B. Jedlicki, David Ouyang, Anthony Philippakis, David Sontag, Ahmed Alaa,NeurIPS,2024. [paper] [code]
30. NTFields: Neural Time Fields for Physics-Informed Robot Motion Planning, Ruiqi Ni,Ahmed H.Qureshi, ICLR,2024. [paper] [code]
31. Improved Training of Physics-Informed Neural Networks Using Energy-Based Priors: a Study on Electrical Impedance Tomography, Akarsh Pokkunuru, Amirmohammad Rooshenas,Thilo Strauss, Anuj Abhishek, Taufiquar Khan, ICLR,2023. [paper] [code]
32. Long-Short-Range Message-Passing: A Physics-Informed Framework to Capture Non-Local Interaction for Scalable Molecular Dynamics Simulation,Yunyang Li,Yusong Wang, LinHuang, Han Yang, Xinran Wei, Tong Wang,Zun Wang,BinShao,Tie-YanLiu,ICLR,2024. [paper] [code]

Papers on PINN Analysis

1. Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs, Siddhartha Mishra, Roberto Molinaro, IMA Journal of Numerical Analysis, 2021. [paper]
2. Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs, Tim De Ryck, Siddhartha Mishra, arXiv:2106.14473 [cs, math], 2021. [paper]
3. Error Analysis of Deep Ritz Methods for Elliptic Equations, Yuling Jiao, Yanming Lai, Yisu Luo, Yang Wang, Yunfei Yang, arXiv:2107.14478 [cs, math], 2021. [paper]
4. Learning Partial Differential Equations in Reproducing Kernel Hilbert Spaces, George Stepaniants, arXiv:2108.11580 [cs, math, stat], 2021. [paper]
5. Simultaneous Neural Network Approximations in Sobolev Spaces, Sean Hon, Haizhao Yang, arXiv:2109.00161 [cs, math], 2021. [paper]
6. Characterizing possible failure modes in physics-informed neural networks, Aditi S. Krishnapriyan, Amir Gholami, Sh Zhe, ian, Robert M. Kirby, Michael W. Mahoney, arXiv:2109.01050 [physics], 2021. [paper]
7. Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks, Sifan Wang, Yujun Teng, Paris Perdikaris, SIAM Journal on Scientific Computing, 2021. [paper]
8. Variational Physics Informed Neural Networks: the role of quadratures and test functions, Stefano Berrone, Claudio Canuto, Moreno Pintore, arXiv:2109.02035 [cs, math], 2021. [paper]
9. Convergence Analysis for the PINNs, Yuling Jiao, Yanming Lai, Dingwei Li, Xiliang Lu, Yang Wang, Jerry Zhijian Yang, arXiv:2109.01780 [cs, math], 2021. [paper]
10. Characterizing possible failure modes in physics-informed neural networks, Aditi Krishnapriyan, Amir Gholami, Sh Zhe, ian, Robert Kirby, Michael W. Mahoney, NIPS, 2021. [paper]
11. Convergence rate of DeepONets for learning operators arising from advection-diffusion equations, Beichuan Deng, Yeonjong Shin, Lu Lu, Zhongqiang Zhang, George Em Karniadakis, arXiv:2102.10621 [math], 2021. [paper]
12. Estimates on the generalization error of physics-informed neural networks for approximating PDEs, Siddhartha Mishra, Roberto Molinaro, IMA Journal of Numerical Analysis, 2022. [paper]
13. Investigating and Mitigating Failure Modes in Physics-informed Neural Networks (PINNs), Shamsulhaq Basir, arXiv:2209.09988v1[cs], 2022. [paper][code]
14. On the Benefits of Memory for Modeling Time-Dependent PDEs,Ricardo Buitrago Ruiz,Tanya Marwah,Albert Gu,Andrej Risteski,ICLR,2025. [paper]
15. PhysPDE: Rethinking PDE Discovery and a Physical HYpothesis Selection Benchmark,Mingquan Feng,Yixin Huang,Yizhou Liu,Bofang Jiang,Junchi Yan,ICLR.2025. [paper]
16. Challenges in Training PINNs: A Loss Landscape Perspective，Pratik Rathore, Weimu Lei, Zachary Frangella, Lu Lu, Madeleine Udell,ICML,2024. [paper] [code]
17. Physics-Informed Neural Network Policy Iteration: Algorithms, Convergence, and Verification,Yiming Meng, Ruikun Zhou, Amartya Mukherjee, Maxwell Fitzsimmons, Christopher Song, Jun Liu,ICML,2024. [paper] [code]
18. Efficient Error Certification for Physics-Informed Neural Networks,Francisco Eiras, Adel Bibi, Rudy R Bunel, Krishnamurthy Dj Dvijotham, Philip Torr, M. Pawan Kumar ,ICML,2024. [paper]
19. Parameterized Physics-informed Neural Networks for Parameterized PDEs,Woojin Cho, Minju Jo, Haksoo Lim, Kookjin Lee, Dongeun Lee, Sanghyun Hong, Noseong Park*,ICML,2024. [paper] [code]
20. Learning from Integral Losses in Physics Informed Neural Networks,Ehsan Saleh, Saba Ghaffari, Tim Bretl, Luke Olson, Matthew West,ICML,2024. [paper] [code]
21. UGrid: An Efficient-And-Rigorous Neural Multigrid Solver for Linear PDEs,Xi Han, Fei Hou, Hong Qin,ICML,2024.[paper] [code]
22. How does PDE order affect the convergence of PINNs? Changhoon Song, Yesom Park, Myungjoo Kang, NeurIPS, 2024. [paper]
23. PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs,Zhongkai Hao, Jiachen Yao, Chang Su, Hang Su, Ziao Wang, Fanzhi Lu, Zeyu Xia, Yichi Zhang, Songming Liu, Lu Lu, Jun Zhu, NeurIPS,2024. [paper] [code]
24. The Challenges of the Nonlinear Regime for Physics-Informed Neural Networks,Andrea Bonfanti, Giuseppe Bruno, Cristina Cipriani,NeurIPS,2024. [paper]
25. Continuous PDE Dynamics Forecasting with Implicit Neural Representations,Yuan Yin,Matthieu Kirchmeyer, Alain Rakotomamonjy,Jean-Yves Franceschi,Patrick Gallinari,ICLR,2023.[paper] [code]

Neural Operator

1. An operator preconditioning perspective on training in physics-informed machine learning,Tim De Ryck, Florent Bonnet,Siddhartha Mishra,Emmanuel de Bézenac,ICLR,2024. [paper]
2. ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs,Yogesh Verma,Markus Heinonen,Vikas Garg,ICLR,2024. [paper] [code]
3. Solving High Frequency and Multi-Scale PDEs with Gaussian Processes,Shikai Fang,Madison Cooley,Da Long, Shibo Li,Mike Kirby,Shandian Zhe,ICLR,2024. [paper] [code]
4. BENO: Boundary-embedded Neural Operators for Elliptic PDEs,Haixin Wang,Jiaxin Li,Anubhav Dwivedi, Kentaro Hara, Tailin Wu.ICLR,2024. [paper] [code]
5. Better Neural PDE Solvers Through Data-Free Mesh Movers,Peiyan Hu,Yue Wang,Zhi-Ming Ma,ICLR,2024. [paper] [code]
6. Guaranteed Approximation Bounds for Mixed-Precision Neural Operators,Renbo Tu,Colin White,Jean Kossaifi,Boris Bonev,Gennady Pekhimenko,Kamyar Azizzadenesheli,anima anandkumar,ICLR,2024. [paper] [code]
7. Learning semilinear neural operators: A unified recursive framework for prediction and data assimilation, Ashutosh Singh,Ricardo Borsoi,Deniz Erdogmus,Tales Imbiriba,ICLR,2024. [paper] [code]
8. MgNO: Efficient Parameterization of Linear Operators via Multigrid,Juncai He,Xinliang Liu,Jinchao Xu, ICLR, 2024. [paper] [code]
9. Accelerating Data Generation for Neural Operators via Krylov Subspace Recycling,Hong Wang,Zhongkai Hao,Jie Wang,Zijie Geng,Zhen Wang,Bin Li,Feng Wu,ICLR,2024. [paper] [code]
10. PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems,Bocheng Zeng,Qi Wang,Mengtao Yan,Yang Liu,Ruizhi Chengze,Yi Zhang,Hongsheng Liu,Zidong Wang,Hao Sun,ICLR,2025. [paper] [code]
11. Text2PDE: Latent Diffusion Models for Accessible Physics Simulation,Anthony Zhou,Zijie Li,Michael Schneier, John Buchanan,Amir Barati Farimani,ICLR,2025. [paper] [code]
12. Boundary constrained Gaussian processes for robust physics-informed machine learning of linear partial differential equations,David Dalton,Alan Lazarus,Hao Gao,Dirk Husmeier,ICLR,2025. [paper] [code]
13. PRDP: Progressively Refined Differentiable Physics,Kanishk Bhatia,Felix Koehler,Nils Thuerey,ICLR,2025. [paper] [code]
14. Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems,Sung Woong Cho, Hwijae Son,ICLR,2025. [paper]
15. Fengbo: a Clifford Neural Operator pipeline for 3D PDEs in Computational Fluid Dynamics,Alberto Pepe, Mattia Montanari,Joan Lasenby,ICLR,2025. [paper]
16. Active Learning for Neural PDE Solvers,Daniel Musekamp,Marimuthu Kalimuthu,David Holzmüller,Makoto Takamoto,Mathias Niepert,ICLR,2025. [paper] [code]
17. GridMix: Exploring Spatial Modulation for Neural Fields in PDE Modeling,Honghui Wang,Shiji Song,Gao Huang.ICLR,2025. [paper]
18. SINGER: Stochastic Network Graph Evolving Operator for High Dimensional PDEs,Mingquan Feng,Yixin Huang,Weixin Liao,Yuhong Liu,Yizhou Liu,Junchi Yan,ICLR,2025. [paper] [code]
19. Wavelet Diffusion Neural Operator,Peiyan Hu,Rui Wang,Xiang Zheng,Tao Zhang,Haodong Feng,Ruiqi Feng,Long Wei,Yue Wang,Zhi-Ming Ma,Tailin Wu,ICLR,2025. [paper] [code]
20. Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations,Abdolmehdi Behroozi,Chaopeng Shen,Daniel Kifer,ICLR,2025. [paper]
21. Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups,Zakhar Shumaylov, Peter Zaika,James Rowbottom,Ferdia Sherry,Melanie Weber,Carola-Bibiane Schönlieb,ICLR,2025. [paper]
22. Spectral-Refiner: Accurate Fine-Tuning of Spatiotemporal Fourier Neural Operator for Turbulent Flows,Shuhao Cao,Francesco Brarda,Ruipeng Li,Yuanzhe Xi,LCLR,2025. [paper] [code]
23. Learning vector fields of differential equations on manifolds with geometrically constrained operator-valued kernels,Daning Huang,Hanyang He,John Harlim,Yan Li,ICLR,2025. [paper]
24. Discretization-invariance? On the Discretization Mismatch Errors in Neural Operators,Wenhan Gao, Ruichen Xu,Yuefan Deng,Yi Liu,ICLR,2025. [paper]
25. Generalizable Motion Planning via Operator Learning,Sharath Matada,Luke Bhan,Yuanyuan Shi,Nikolay Atanasov,ICLR,2025. [paper] [code]
26. Quantitative Approximation for Neural Operators in Nonlinear Parabolic Equations,Takashi Furuya,Koichi Taniguchi,Satoshi Okuda,ICLR,2025. [paper]
27. Neural operators meet conjugate gradients: The FCG-NO method for efficient PDE solving,Alexander Rudikov, Vladimir Fanaskov, Ekaterina Muravleva, Yuri M. Laevsky, Ivan Oseledets,ICML,2024. [paper] [code]
28. Reference Neural Operators: Learning the Smooth Dependence of Solutions of PDEs on Geometric Deformations,Ze Cheng, Zhongkai Hao, Xiaoqiang Wang, Jianing Huang, Youjia Wu, Xudan Liu, Yiru Zhao, Songming Liu, Hang Su,ICML,2024. [paper]
29. DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training,Zhongkai Hao, Chang Su, Songming Liu, Julius Berner, Chengyang Ying, Hang Su, Anima Anandkumar, Jian Song, Jun Zhu,ICML,2024. [paper] [code]
30. Using Uncertainty Quantification to Characterize and Improve Out-of-Domain Learning for PDEs,S Chandra Mouli, Danielle C. Maddix, Shima Alizadeh, Gaurav Gupta, Andrew Stuart, Michael W. Mahoney, Bernie Wang,ICML,2024. [paper] [code]
31. Accelerating PDE Data Generation via Differential Operator Action in Solution Space,Huanshuo Dong, Hong Wang, Haoyang Liu, Jian Luo, Jie Wang,ICML,2024. [paper] [code]
32. Graph Neural PDE Solvers with Conservation and Similarity-Equivariance,Masanobu Horie, Naoto Mitsume,ICML,2024. [paper] [code]
33. Harnessing the Power of Neural Operators with Automatically Encoded Conservation Laws,Ning Liu, Yiming Fan, Xianyi Zeng, Milan Klöwer, Lu Zhang, Yue Yu ,ICML,2024. [paper] [code]
34. Operator SVD with Neural Networks via Nested Low-Rank Approximation,Jongha Jon Ryu, Xiangxiang Xu, Hasan Sabri Melihcan Erol, Yuheng Bu, Lizhong Zheng, Gregory W. Wornell,ICML,2024.[paper] [code]
35. Hierarchical Neural Operator Transformer with Learnable Frequency-aware Loss Prior for Arbitrary-scale Super-resolution，Xihaier Luo, Xiaoning Qian, Byung-Jun Yoon,ICML,2024. [paper]
36. Equivariant Graph Neural Operator for Modeling 3D Dynamics,Minkai Xu, Jiaqi Han, Aaron Lou, Jean Kossaifi, Arvind Ramanathan, Kamyar Azizzadenesheli, Jure Leskovec, Stefano Ermon, Anima Anandkumar,ICML,2024.[paper] [code]
37. Neural Operators with Localized Integral and Differential Kernels,Neural Operators with Localized Integral and Differential Kernels,ICML,2024. [paper] [code]
38. Positional Knowledge is All You Need: Position-induced Transformer (PiT) for Operator Learning,Junfeng Chen, Kailiang Wu,ICML,2024. [paper] [code]
39. Improved Operator Learning by Orthogonal Attention,Zipeng Xiao, Zhongkai Hao, Bokai Lin, Zhijie Deng, Hang Su,ICML,2024. [paper]
40. Implicit Representations via Operator Learning,Sourav Pal, Harshavardhan Adepu, Clinton Wang, Polina Golland, Vikas Singh,ICML,2024. [paper] [code]
41. Beyond Regular Grids: Fourier-Based Neural Operators on Arbitrary Domains,Beyond Regular Grids: Fourier-Based Neural Operators on Arbitrary Domains,ICML,2024. [paper] [code]
42. HAMLET: Graph Transformer Neural Operator for Partial Differential Equations,Andrey Bryutkin, Jiahao Huang, Zhongying Deng, Guang Yang, Carola-Bibiane Schönlieb, Angelica I Aviles-Rivero,ICML,2024. [paper]
43. Gaussian Plane-Wave Neural Operator for Electron Density Estimation,Seongsu Kim, Sungsoo Ahn, ICML, 2024. [paper] [code]
44. Stochastic Taylor Derivative Estimator: Efficient amortization for arbitrary differential operators，Zekun Shi,Zheyuan Hu,Min Lin,Kenji Kawaguchi,NeurIPS,2024. [paper] [code]
45. Optimal deep learning of holomorphic operators between Banach spaces,Ben Adcock, Nick Dexter, Sebastian Moraga, NeurIPS,2024. [paper]
46. Nonlocal Attention Operator: Materializing Hidden Knowledge Towards Interpretable Physics Discovery, Yue Yu, Ning Liu, Fei Lu, Tian Gao, Siavash Jafarzadeh, Stewart Silling, NeurIPS, 2024. [paper] [code]
47. Learning to Predict Structural Vibrations,Jan van Delden, Julius Schultz, Christopher Blech, Sabine C. Langer, Timo Lüddecke, NeurIPS,2024. [paper] [code]
48. PACE: Pacing Operator Learning to Accurate Optical Field Simulation for Complicated Photonic Devices, Hanqing Zhu, Wenyan Cong, Guojin Chen, Shupeng Ning, Ray T. Chen, Jiaqi Gu, David Z. Pan,NeurIPS,2024. [paper] [code]
49. Latent Neural Operator for Solving Forward and Inverse PDE Problems,Tian Wang, Chuang Wang, NeurIPS, 2024. [paper] [code]
50. Can neural operators always be continuously discretized? ,Takashi Furuya, Michael Puthawala, Maarten V. de Hoop, Matti Lassas,NeurIPS,2024.[paper]
51. Amortized Fourier Neural Operators,Zipeng Xiao, Siqi Kou, Zhongkai Hao, Bokai Lin, Zhijie Deng, NeurIPS,2024.[paper]
52. Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs,Md Ashiqur Rahman, Robert Joseph George, Mogab Elleithy, Daniel Leibovici, Zongyi Li, Boris Bonev, Colin White, Julius Berner, Raymond A. Yeh, Jean Kossaifi, Kamyar Azizzadenesheli, Anima Anandkumar,NeurIPS,2024. [paper] [code]
53. Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators, Benedikt Alkin, Andreas Fürst, Simon Schmid, Lukas Gruber, Markus Holzleitner, Johannes Brandstetter, NeurIPS,2024. [paper] [code]
54. Clifford Neural Layers for PDE Modeling,Johannes Brandstetter,Johannes Brandstetter,MaxWelling,Jayesh K. Gupta,ICLR,2023. [paper] [code]
55. Nonlinear Reconstruction for Operator Learning of PDEs with Discontinuities, Samuel Lanthaler,Roberto Molinaro, Patrik Hadorn & Siddhartha Mishra,ICLR,2023.[paper]
56. Minimax Optimal Kernel Operator Learning via Multilevel Training ,Jikai Jin, Yiping Lu, Jose Blanchet,Lexing Ying,ICLR,2023. [paper]
57. HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetwork,Jae Yong Lee, Sung Woong Cho,Hyung Ju Hwang,ICLR,2023. [paper]
58. Neural ePDOs: Spatially Adaptive Equivariant Partial Differential Operator Based Networks,Lingshen He, Yuxuan Chen,Zhengyang Shen, Yibo Yang, Zhouchen Lin,ICLR,2023. [paper]
59. Koopman Neural Operator Forecaster for Time-series with Temporal Distributional Shifts, Rui Wang,Yihe Dong, Sercan Ö. Arik, Rose Yu,ICLR,2023.[paper] [code]
60. Factorized Fourier Neural Operators, Alasdair Tran, Alexander Mathews,Lexing Xie,Cheng Soon Ong,ICLR,2023.[paper] [code]
61. Guiding continuous operator learning through Physics-based boundary constraints,Nadim Saad,Gaurav Gupta, Shima Alizadeh, Danielle C. Maddix,ICLR,2023. [paper] [code]
62. Coupled Multiwavelet Operator Learning for Coupled Differential Equations,Xiongye Xiao,Gengshuo Liu, Defu Cao,Chenzhong Yin,Ruochen Yang,Radu Balan,Gaurav Gupta,Paul Bogdan,ICLR,2023. [paper] [code]
63. PAC-FNO: Parallel-Structured All-Component Fourier Neural Operators for Recognizing Low-Quality Images, Jinsung Jeo, Hyundong Jin, Jonghyun Choi, Sanghyun Hong, Dongeun Lee, Kookjin Lee, Noseong Park. ICLR,2024. [paper]