PDE: Partial Differentiable Equation
Neural Operators: Learning nonlinear mappings between function spaces.
Contributed by Chunyang Zhang.
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Physics-informed machine learning. Nature Reviews Physics, 2021. paper
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Neural operator: Learning maps between function spaces. JMLR, 2023. paper
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Integrating scientific knowledge with machine learning for engineering and environmental systems. ACM Computing Surveys, 2023. paper
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Scientific machine learning through physics–informed neural networks: Where we are and what’s next. Beyond Traditional AI: The Impact of Machine Learning on Scientific Computing, 2022. book
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When physics meets machine learning: A survey of physics-informed machine learning. arXiv, 2022. paper
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Physics-guided, physics-informed, and physics-encoded neural networks in scientific computing. arXiv, 2022. paper
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Physics-informed machine learning: A survey on problems, methods and applications. arXiv, 2022. paper
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Combining machine learning and domain decomposition methods for the solution of partial differential equations—A review. GAMM‐Mitteilungen, 2021. paper
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Physics-guided, physics-informed, and physics-encoded neural networks in scientific computing. arXiv, 2022. paper
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Partial differential equations meet deep neural networks: A survey. arXiv, 2022. paper
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Solving differential equations with deep learning: A beginner's guide. arXiv, 2023. paper
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Deep learning algorithms for solving differential equations: A survey. Journal of Experimental & Theoretical Artificial Intelligence, 2023. paper
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An expert's guide to training physics-informed neural networks. arXiv, 2023. paper
Sifan Wang, Shyam Sankaran, Hanwen Wang, and Paris Perdikaris.
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A survey on physics informed reinforcement learning: Review and open problems. arXiv, 2023. paper
Chayan Banerjee, Kien Nguyen, Clinton Fookes, and Maziar Raissi.
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Machine learning and domain decomposition methods -- A survey. arXiv, 2023. paper
Axel Klawonn, Martin Lanser, and Janine Weber.
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The transformative potential of machine learning for experiments in fluid mechanics. Nature Reviews Physics, 2023. paper
Ricardo Vinuesa, Steven L. Brunton, and Beverley J. McKeon.
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Physics-informed machine learning for reliability and systems safety applications: State of the art and challenges. Reliability Engineering & System Safety, 2023. paper
Yanwen Xu, Sara Kohtz, Jessica Boakye, Paolo Gardoni, and Pingfeng Wang.
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Operator learning: Algorithms and analysis. arXiv, 2024. paper
Nikola B. Kovachki, Samuel Lanthaler, and Andrew M. Stuart.
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Neural operators for accelerating scientific simulations and design. Nature Reviews Physics, 2024. paper
Kamyar Azizzadenesheli, Nikola Kovachki, Zongyi Li, Miguel Liu-Schiaffini, Jean Kossaifi, and Anima Anandkumar.
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Learning dynamical systems from data: An introduction to physics-guided deep learning. PNAS, 2024. paper
Rose Yu and Rui Wang.
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Promising directions of machine learning for partial differential equations. NCS, 2024. paper
Steven L. Brunton and Nathan Kutz .
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Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations. Science, 2020. paper
Raissi Maziar, Alireza Yazdani, and George Em Karniadakis.
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Deep hidden physics models: Deep learning of nonlinear partial differential equations. JMLR, 2018. paper
Maziar Raissi.
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A universal PINNs method for solving partial differential equations with a point source. IJCAI, 2022. paper
Xiang Huang, Hongsheng Liu, Beiji Shi, Zidong Wang, Kang Yang, Yang Li, Min Wang, Haotian Chu, Jing Zhou, Fan Yu, Bei Hua, Bin Dong, and Lei Chen.
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Parallel physics-informed neural networks via domain decomposition. JCP, 2021. paper
Khemraj Shukla, Ameya D.Jagtap, and George Em Karniadakis.
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Kolmogorov n–width and Lagrangian physics-informed neural networks: A causality-conforming manifold for convection-dominated PDEs. CMAME, 2023. paper
Rambod Mojgani, Maciej Balajewicz, and Pedram Hassanzadeh.
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Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks. CMAME, 2022. paper
N.Sukumar and Ankit Srivastava.
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Physics-informed multi-LSTM networks for meta-modeling of nonlinear structures. CMAME, 2020. paper
Ruiyang Zhang, Yang Liu, and Hao Sun.
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Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems. CMAME, 2022. paper
Jeremy Yu, Lu Lu, Xuhui Meng, and George Em Karniadakis.
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Multi-output physics-informed neural networks for forward and inverse PDE problems with uncertainties. CMAME, 2022. paper
MingyuanYang and John T.Foster
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PPINN: Parareal physics-informed neural network for time-dependent PDEs. CMAME, 2020. paper
Xuhui Meng, Zhen Li, Dongkun Zhang, and George Em Karniadakis.
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CAN-PINN: A fast physics-informed neural network based on coupled-automatic–numerical differentiation method. CMAME, 2022. paper
Pao-Hsiung Chiu, Jian Cheng Wong, Chinchun Ooi, My Ha Dao, and Yew-Soon Ong.
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Derivative-informed projected neural networks for high-dimensional parametric maps governed by PDEs. CMAME, 2022. paper
Thomas O’Leary-Roseberry, Umberto Villa, Peng Chen, and Omar Ghattas.
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Physics-augmented learning: A new paradigm beyond physics-informed learning. NIPS, 2021. paper
Ziming Liu, Yuanqi Du, Yunyue Chen, and Max Tegmark.
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Data-driven vector soliton solutions of coupled nonlinear Schrödinger equation using a deep learning algorithm. Physics Letters A, 2021. paper
Yifan Mo, Liming Ling, and Delu Zeng.
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Solving Benjamin–Ono equation via gradient balanced PINNs approach. The European Physical Journal Plus, 2022. paper
Xiangyu Yang and Zhen Wang.
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Robust learning of physics informed neural networks. arXiv, 2021. paper
Chandrajit Bajaj, Luke McLennan, Timothy Andeen, and Avik Roy.
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Learning physics-informed neural networks without stacked back-propagation. AISTATS, 2023. paper
Di He, Wenlei Shi, Shanda Li, Xiaotian Gao, Jia Zhang, Jiang Bian, Liwei Wang, and Tieyan Liu.
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NeuralPDE: Automating physics-informed neural networks (PINNs) with error approximations. arXiv, 2021. paper
Kirill Zubov, Zoe McCarthy, Yingbo Ma, Francesco Calisto, Valerio Pagliarino, Simone Azeglio, Luca Bottero, Emmanuel Luján, Valentin Sulzer, Ashutosh Bharambe, Nand Vinchhi, Kaushik Balakrishnan, Devesh Upadhyay, and Chris Rackauckas.
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Physics informed RNN-DCT networks for time-dependent partial differential equations. ICCS, 2022. paper
Benjamin Wu, Oliver Hennigh, Jan Kautz, Sanjay Choudhry, and Wonmin Byeon.
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Theory-guided physics-informed neural networks for boundary layer problems with singular perturbation. JCP, 2022. paper
Amirhossein Arzani, Kevin W.Cassel, and Roshan M.D'Souza.
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A-PINN: Auxiliary physics informed neural networks for forward and inverse problems of nonlinear integro-differential equations. JCP, 2022. paper
Lei Yuan, Yiqing Ni, Xiangyun Deng, and Shuo Hao.
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A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: Comparison with finite element method. CMAME, 2022. paper
Shahed Rezaei, Ali Harandi, Ahmad Moeineddin, Baixiang Xua, and Stefanie Reese.
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Physics-informed neural networks combined with polynomial interpolation to solve nonlinear partial differential equations. Computers & Mathematics with Applications, 2023. paper
Siping Tang, Xinlong Feng, Wei Wu, and Hui Xu.
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A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations. CMAME, 2022. paper
Revanth Mattey and Susanta Ghosh.
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RPINNs: Rectified-physics informed neural networks for solving stationary partial differential equations. Computers and Fluids, 2022. paper
Pai Peng, Jiangong Pan, Hui Xu, and Xinlong Feng.
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A-WPINN algorithm for the data-driven vector-soliton solutions and parameter discovery of general coupled nonlinear equations. Physica D: Nonlinear Phenomena, 2022. paper
Shumei Qin, Min Li, Tao Xu, and Shaoqun Dong.
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Physics-informed neural networks with adaptive localized artificial viscosity. arXiv, 2022. paper
E.J.R. Coutinho, M. Dall'Aqua, L. McClenny, M. Zhong, U. Braga-Neto, and E. Gildin.
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Physics-informed neural operator for learning partial differential equations. arXiv, 2021. paper
Zongyi Li, Hongkai Zheng, Nikola Kovachki, David Jin, Haoxuan Chen, Burigede Liu, Kamyar Azizzadenesheli, and Anima Anandkumar.
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Anisotropic, sparse and interpretable physics-informed neural networks for PDEs. arXiv, 2022. paper
Amuthan A. Ramabathiran and Prabhu Ramachandran.
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Fast neural network based solving of partial differential equations. arXiv, 2022. paper
Jaroslaw Rzepecki, Daniel Bates, and Chris Doran.
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Discontinuity computing using physics-informed neural network. arXiv, 2022. paper
Li Liu, Shengping Liu, Hui Xie, Fansheng Xiong, Tengchao Yu, Mengjuan Xiao, Lufeng Liu, and Heng Yong.
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Learning differentiable solvers for systems with hard constraints. arXiv, 2022. paper
Geoffrey Négiar, Michael W. Mahoney, and Aditi S. Krishnapriyan.
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Momentum diminishes the effect of spectral bias in physics-informed neural networks. arXiv, 2022. paper
Ghazal Farhani, Alexander Kazachek, and Boyu Wang.
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Δ-PINNs: Physics-informed neural networks on complex geometries. arXiv, 2022. paper
Francisco Sahli Costabal, Simone Pezzuto, and Paris Perdikaris.
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Replacing automatic differentiation by Sobolev Cubatures fastens physics informed neural nets and strengthens their approximation power. arXiv, 2022. paper
Juan Esteban Suarez Cardona and Michael Hecht.
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FO-PINNs: A first-order formulation for physics informed neural networks. arXiv, 2022. paper
Rini J. Gladstone, Mohammad A. Nabian, and Hadi Meidani.
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Augmented physics-informed neural networks (APINNs): A gating network-based soft domain decomposition methodology. arXiv, 2022. paper
Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis, and Kenji Kawaguchi.
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Physics-informed neural networks for operator equations with stochastic data. arXiv, 2022. paper
Paul Escapil-Inchauspé and Gonzalo A. Ruz.
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Physics-informed neural networks with unknown measurement noise. arXiv, 2022. paper
Philipp Pilar and Niklas Wahlstrom.
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On the compatibility between a neural network and a partial differential equation for physics-informed learning. arXiv, 2022. paper
Kuangdai Leng and Jeyan Thiyagalingam.
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Pre-training strategy for solving evolution equations based on physics-informed neural networks. arXiv, 2022. paper
Jiawei Guo, Yanzhong Yao, Han Wang, and Tongxiang Gu.
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L-HYDRA: Multi-head physics-informed neural networks. arXiv, 2023. paper
Zongren Zou and George Em Karniadakis.
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PINN for dynamical partial differential equations is not training deeper networks rather learning advection and time variance. arXiv, 2023. paper
Siddharth Rout.
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Wavelets based physics informed neural networks to solve non-linear differential equations. Scientific Reports, 2023. paper
Ziya Uddin, Sai Ganga, Rishi Asthana, and Wubshet Ibrahim.
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Improved training of physics-informed neural networks using energy-based priors: A study on electrical impedance tomography. ICLR, 2023. paper
Akarsh Pokkunuru, Pedram Rooshenas, Thilo Strauss, Anuj Abhishek, and Taufiquar Khan.
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Adaptive weighting of Bayesian physics informed neural networks for multitask and multiscale forward and inverse problems. arXiv, 2023. paper
Sarah Perez, Suryanarayana Maddu, Ivo F. Sbalzarini, and Philippe Poncet.
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Efficient physics-informed neural networks using hash encoding. arXiv, 2023. paper
Xinquan Huang and Tariq Alkhalifah.
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Ensemble learning for physics informed neural networks: A gradient boosting approach. arXiv, 2023. paper
Zhiwei Fang, Sifan Wang, and Paris Perdikaris.
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On the limitations of physics-informed deep learning: Illustrations using first order hyperbolic conservation law-based traffic flow models. arXiv, 2023. paper
Archie J. Huang and Shaurya Agarwal.
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Achieving high accuracy with PINNs via energy natural gradients. arXiv, 2023. paper
Johannes Müller and Marius Zeinhofer.
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Implicit stochastic gradient descent for training physics-informed neural networks. arXiv, 2023. paper
Ye Li, Songcan Chen, and Shengjun Huang.
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NSGA-PINN: A multi-objective optimization method for physics-informed neural network training. arXiv, 2023. paper
Binghang Lu, Christian B. Moya, and Guang Lin.
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Improving physics-informed neural networks with meta-learned optimization. JMLR, 2024. paper
Alex Bihlo.
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Separable physics-informed neural networks. NIPS, 2023. paper
Junwoo Cho, Seungtae Nam, Hyunmo Yang, Seok-Bae Yun, Youngjoon Hong, and Eunbyung Park
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MetaPhysiCa: OOD robustness in physics-informed machine learning. arXiv, 2023. paper
S Chandra Mouli, Muhammad Ashraful Alam, and Bruno Ribeiro.
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HomPINNs: Homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions. arXiv, 2023. paper
Haoyang Zheng, Yao Huang, Ziyang Huang, Wenrui Hao, and Guang Lin.
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iPINNs: Incremental learning for physics-informed neural networks. arXiv, 2023. paper
Aleksandr Dekhovich, Marcel H.F. Sluiter, David M.J. Tax, and Miguel A. Bessa.
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Global convergence of deep Galerkin and PINNs methods for solving partial differential equations. arXiv, 2023. paper
Francisco Eiras, Adel Bibi, Rudy Bunel, Krishnamurthy Dj Dvijotham, Philip Torr, and M. Pawan Kumar.
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Provably correct physics-informed neural networks. arXiv, 2023. paper
Deqing Jiang, Justin Sirignano, and Samuel N. Cohen.
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Predictive limitations of physics-informed neural networks in vortex shedding. arXiv, 2023. paper
Pi-Yueh Chuang and Lorena A. Barba.
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Residual-based error bound for physics-informed neural networks. arXiv, 2023. paper
Shuheng Liu, Xiyue Huang, and Pavlos Protopapas.
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Automatic boundary fitting framework of boundary dependent physics-informed neural network solving partial differential equation with complex boundary conditions. CMAME, 2023. paper
Yuchen Xie, Yu Ma, and Yahui Wang.
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Solving a class of multi-scale elliptic PDEs by means of Fourier-based mixed physics informed neural networks. arXiv, 2023. paper
Xi'an Li, Jinran Wu, Zhi-Qin John Xu, and You-Gan Wang.
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Separable physics informed neural networks. arXiv, 2023. paper
Junwoo Cho, Seungtae Nam, Hyunmo Yang, Seok-Bae Yun, Youngjoon Hong, and Eunbyung Park.
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Achieving high accuracy with PINNs via energy natural gradient descent. ICML, 2023. paper
Johannes Müller and Marius Zeinhofer.
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Gradient descent finds the global optima of two-layer physics-informed neural networks. ICML, 2023. paper
Yihang Gao, Yiqi Gu, and Michael Ng.
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Residual-based attention in physics-informed neural networks. CMAME, 2024. paper
Sokratis J. Anagnostopoulos, Juan Diego Toscano, Nikolaos Stergiopulos, and George Em Karniadakis.
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Auxiliary-tasks learning for physics-informed neural network-based partial differential equations solving. arXiv, 2023. paper
Junjun Yan, Xinhai Chen, Zhichao Wang, Enqiang Zhou, and Jie Liu.
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Tackling the curse of dimensionality with physics-informed neural networks. arXiv, 2023. paper
Zheyuan Hu, Khemraj Shukla, George Em Karniadakis, and Kenji Kawaguchi.
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Solving PDEs on spheres with physics-informed convolutional neural networks. arXiv, 2023. paper
Guanhang Lei, Zhen Lei, Lei Shi, Chenyu Zeng, and Dingxuan Zhou.
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Solving PDEs on spheres with physics-informed convolutional neural networks. arXiv, 2023. paper
Guanhang Lei, Zhen Lei, Lei Shi, Chenyu Zeng, and Dingxuan Zhou.
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Tensor-compressed back-propagation-free training for (physics-informed) neural networks. arXiv, 2023. paper
Yequan Zhao, Xinling Yu, Zhixiong Chen, Ziyue Liu, Sijia Liu, and Zheng Zhang.
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How to select physics-informed neural networks in the absence of ground truth: A pareto front-based strategy. ICML, 2023. paper
Zhao Wei, Jian Cheng Wong, Nicholas Wei Yong Sung, Abhishek Gupta, Chin Chun Ooi, Pao-Hsiung Chiu, My Ha Dao, and Yew-Soon Ong.
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A gradient-enhanced physics-informed neural network (gPINN) scheme for the coupled non-fickian/non-fourierian diffusion-thermoelasticity analysis: A novel gPINN structure. EAAI, 2023. paper
Katayoun Eshkofti and Seyed Mahmoud Hosseini.
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Learning only on boundaries: A physics-informed neural operator for solving parametric partial differential equations in complex geometries. arXiv, 2023. paper
Zhiwei Fang, Sifan Wang, and Paris Perdikaris.
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Exact and soft boundary conditions in physics-informed neural networks for the variable coefficient poisson equation. arXiv, 2023. paper
Sebastian Barschkis.
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Investigating the ability of PINNs to solve burgers’ PDE near finite-time blowup. arXiv, 2023. paper
Dibyakanti Kumar and Anirbit Mukherjee.
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Correcting model misspecification in physics-informed neural networks (PINNs). CMAME, 2024. paper
Zongren Zou, Xuhui Meng, and George Em Karniadakis.
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On residual minimization for PDEs: Failure of PINN, modified equation, and implicit bias. arXiv, 2023. paper
Tao Luo and Qixuan Zhou.
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Operator learning enhanced physics-informed neural networks for solving partial differential equations characterized by sharp solutions. arXiv, 2023. paper
Bin Lin, Zhiping Mao, Zhicheng Wang, and George Em Karniadakis.
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PINNs-TF2: Fast and user-friendly physics-informed neural networks in TensorFlow V2. NIPS, 2023. paper
Reza Akbarian Bafghi and Maziar Raissi.
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Filtered partial differential equations: A robust surrogate constraint in physics-informed deep learning framework. arXiv, 2023. paper
Dashan Zhang, Yuntian Chen, and Shiyi Chen.
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Enhanced physics-informed neural networks with domain scaling and residual correction methods for multi-frequency elliptic problems. arXiv, 2023. paper
Deok-Kyu Jang, Hyea Hyun Kim, and Kyungsoo Kim.
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Physics-informed neural networks for transformed geometries and manifolds. arXiv, 2023. paper
Samuel Burbulla.
Zheyuan Hu, Zhouhao Yang, Yezhen Wang, George Em Karniadakis, and Kenji Kawaguchi.
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Neuro-PINN: A hybrid framework for efficient nonlinear projection equation solutions. The International Journal for Numerical Methods in Engineering, 2023. paper
Dawen Wu and Abdel Lisser.
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Exactly conservative physics-informed neural networks and deep operator networks for dynamical systems. arXiv, 2023. paper
Elsa Cardoso-Bihlo and Alex Bihlo.
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Semi-analytic PINN methods for boundary layer problems in a rectangular domain. arXiv, 2023. paper
Gungmin Gie, Youngjoon Hong, Chang-Yeol Jung, and Tselmuun Munkhjin.
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PICL: Physics informed contrastive learning for partial differential equations. arXiv, 2024. paper
Cooper Lorsung and Amir Barati Farimani.
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Fourier warm start for physics-informed neural networks. EAAI, 2024. paper
Ge Jin, Jian Cheng Wong, Abhishek Gupta, Shipeng Li, and Yew-Soon Ong.
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Preconditioning for physics-informed neural networks. ICML, 2024. paper
Songming Liu, Chang Su, Jiachen Yao, Zhongkai Hao, Hang Su, Youjia Wu, and Jun Zhu.
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RBF-PINN: Non-Fourier positional embedding in physics-informed neural networks. arXiv, 2024. paper
Chengxi Zeng, Tilo Burghardt, and Alberto M Gambaruto.
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Training dynamics in physics-informed neural networks with feature mapping. arXiv, 2024. paper
Chengxi Zeng, Tilo Burghardt, and Alberto M Gambaruto.
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Score-based physics-informed neural networks for high-dimensional Fokker-Planck equations. arXiv, 2024. paper
Zheyuan Hu, Zhongqiang Zhang, George Em Karniadakis, and Kenji Kawaguchi.
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Investigation of compressor cascade flow using physics-informed neural networks with adaptive learning strategy. AIAA Journal, 2024. paper
Zhihui Li, Francesco Montomoli, and Sanjiv Sharma.
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Exact enforcement of temporal continuity in sequential physics-informed neural networks. arXiv, 2024. paper
Pratanu Roy and Stephen Castonguay.
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Multiple scattering simulation via physics-informed neural networks. arXiv, 2024. paper
Siddharth Nair, Timothy F. Walsh, Greg Pickrell, and Fabio Semperlotti.
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Toward a better understanding of Fourier neural operators: Analysis and improvement from a spectral perspective. arXiv, 2024. paper
Shaoxiang Qin, Fuyuan Lyu, Wenhui Peng, Dingyang Geng, Ju Wang, Naiping Gao, Xue Liu, and Liangzhu Leon Wang.
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Anti-derivatives approximator for enhancing physics-informed neural networks. CMAME, 2024. paper
Jeongsu Lee.
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GMC-PINNs: A new general Monte Carlo PINNs methodfor solving fractional partial differential equations on irregular domains. arXiv, 2024. paper
Shupeng Wang and George Em Karniadakis.
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CEENs: Causality-enforced evolutional networks for solving time-dependent partial differential equations. CMAME, 2024. paper
Jeahan Jung, Heechang Kim, Hyomin Shin, and Minseok Choi.
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PTPI-DL-ROMs: Pre-trained physics-informed deep learning-based reduced order models for nonlinear parametrized PDEs. arXiv, 2024. paper
Simone Brivio, Stefania Fresca, and Andrea Manzoni.
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Closed-form symbolic solutions: A new perspective on solving partial differential equations. arXiv, 2024. paper
Shu Wei, Yanjie Li, Lina Yu, Min Wu, Weijun Li, Meilan Hao, Wenqiang Li, Jingyi Liu, and Yusong Deng.
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RoPINN: Region optimized physics-informed neural networks. arXiv, 2024. paper
Haixu Wu, Huakun Luo, Yuezhou Ma, Jianmin Wang, and Mingsheng Long.
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Interface PINNs (I-PINNs): A physics-informed neural networks framework for interface problems. CMAME, 2024. paper
Antareep Kumar Sarma, Sumanta Roy, Chandrasekhar Annavarapu, Pratanu Roy, and Shriram Jagannathan.
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Parameterized physics-informed neural networks for parameterized PDEs. ICML, 2024. paper
Woojin Cho, Minju Jo, Haksoo Lim, Kookjin Lee, Dongeun Lee, Sanghyun Hong, and Noseong Park.
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Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. NMI, 2021. paper
Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, and George Em Karniadakis.
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Learning the solution operator of parametric partial differential equations with physics-informed DeepONets. SA, 2021. paper
Wang Sifan, Hanwen Wang, and Paris Perdikaris.
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Deep transfer operator learning for partial differential equations under conditional shift. NMI, 2022. paper
Somdatta Goswami, Katiana Kontolati, Michael D. Shields, and George Em Karniadakis.
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Variable-input deep operator networks. arXiv, 2022. paper
Michael Prasthofer, Tim De Ryck, and Siddhartha Mishra.
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MIONet: Learning multiple-input operators via tensor product. arXiv, 2022. paper
Jeremy Yu, Lu Lu, Xuhui Meng, and George Em Karniadakis.
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Long-time integration of parametric evolution equations with physics-informed DeepONets. arXiv, 2021. paper
Sifan Wang and Paris Perdikaris.
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Improved architectures and training algorithms for deep operator networks. Journal of Scientific Computing, 2022. paper
Sifan Wang, Hanwen Wang, and Paris Perdikaris.
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SVD perspectives for augmenting DeepONet flexibility and interpretability. arXiv, 2022. paper
Simone Venturi and Tiernan Casey.
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Accelerated replica exchange stochastic gradient Langevin diffusion enhanced Bayesian DeepONet for solving noisy parametric PDEs. arXiv, 2021. paper
Guang Lin, Christian Moya, and Zecheng Zhang.
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Bi-fidelity modeling of uncertain and partially unknown systems using DeepONet. arXiv, 2022. paper
Subhayan De, Matthew Reynolds, Malik Hassanaly, Ryan N. King, and Alireza Doostan.
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MultiAuto-DeepONet: A multi-resolution autoencoder DeepONet for nonlinear dimension reduction, uncertainty quantification and operator learning of forward and inverse stochastic problems. arXiv, 2022. paper
Jiahao Zhang, Shiqi Zhang, and Guang Lin.
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Transfer learning enhanced DeepONet for long-time prediction of evolution equations. AAAI, 2023. paper
Wuzhe Xu, Yulong Lu, and Li Wang.
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B-DeepONet: An enhanced Bayesian DeepONet for solving noisy parametric PDEs using accelerated replica exchange SGLD. JCP, 2023. paper
Guang Lin, Christian Moy, and Zecheng Zhang.
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VB-DeepONet: A Bayesian operator learning framework for uncertainty quantification. EAAI, 2023. paper
Shailesh Garg and Souvik Chakraborty.
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Sequential deep learning operator network (S-DeepONet) for time-dependent loads. arXiv, 2023. paper
Jaewan Park, Shashank Kushwaha, Junyan He, Seid Koric, Diab Abueidda, and Iwona Jasiuk.
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Asymptotic-preserving convolutional DeepONets capture the diffusive behavior of the multiscale linear transport equations. arXiv, 2023. paper
Keke Wu, Xiong-bin Yan, Shi Jin, and Zheng Ma.
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A hybrid decoder-DeepONet operator regression framework for unaligned observation data. arXiv, 2023. paper
Bo Chen, Chenyu Wang, Weipeng Li, and Haiyang Fu.
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Improving physics-informed DeepONets with hard constraints. arXiv, 2023. paper
Rüdiger Brecht, Dmytro R. Popovych, Alex Bihlo, and Roman O. Popovych.
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Capturing the diffusive behavior of the multiscale linear transport equations by asymptotic-preserving convolutional DeepONets. CMAME, 2023. paper
Keke Wu, Xiong-Bin Yan, Shi Jin, and Zheng Ma.
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DON-LSTM: Multi-resolution learning with DeepONets and long short-term memory neural networks. arXiv, 2023. paper
Katarzyna Michałowska, Somdatta Goswami, George Em Karniadakis, and Signe Riemer-Sørensen.
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DeepOnet based preconditioning strategies for solving parametric linear systems of equations. arXiv, 2024. paper
Alena Kopaničáková and George Em Karniadakis.
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Derivative-enhanced deep operator network. arXiv, 2024. paper
Yuan Qiu, Nolan Bridges, and Peng Chen.
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Real-time prediction of gas flow dynamics in diesel engines using a deep neural operator framework. Applied Intelligence, 2023. paper
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The improved backward compatible physics-informed neural networks for reducing error accumulation and applications in data-driven higher-order rogue waves. arXiv, 2023. paper
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Learning characteristic parameters and dynamics of centrifugal pumps under multi-phase flow using physics-informed neural networks. arXiv, 2023. paper
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On the locality of local neural operator in learning fluid dynamics. arXiv, 2023. paper
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Solving the one dimensional vertical suspended sediment mixing equation with arbitrary eddy diffusivity profiles using temporal normalized physics-informed neural networks. Physics of Fluids, 2024. paper
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Physics-informed neural networks for transonic flow around a cylinder with high Reynolds number. Physics of Fluids, 2024. paper
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SPI-MIONet for surrogate modeling in phase-field hydraulic fracturing. CMAME, 2024. paper
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Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations. arXiv, 2024. paper
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Physics-informed machine learning of the correlation functions in bulk fluids. Physics of Fluids, 2024. paper
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Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold networks. arXiv, 2024. paper
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Machine learning accelerated PDE backstepping observers. arXiv, 2022. paper
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Physics-informed kernel embeddings: Integrating prior system knowledge with data-driven control. arXiv, 2023. paper
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Distributed control of partial differential equations using convolutional reinforcement learning. arXiv, 2023. paper
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Neural control of parametric solutions for high-dimensional evolution PDEs. arXiv, 2023. paper
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AONN: An adjoint-oriented neural network method for all-at-once solutions of parametric optimal control problems. arXiv, 2023. paper
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Neural operators for bypassing gain and control computations in PDE backstepping. arXiv, 2023. paper
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Neural operators of backstepping controller and observer gain functions for reaction-diffusion PDEs. arXiv, 2023. paper
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Leveraging multi-time Hamilton-Jacobi PDEs for certain scientific machine learning problems. arXiv, 2023. paper
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Learning to control PDEs with differentiable physics. ICLR, 2020. paper
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A generalizable physics-informed learning framework for risk probability estimation. L4DC, 2020. paper
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Optimal temperature trajectory for tubular reactor using physics informed neural networks. JCP, 2023. paper
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Physics-informed recurrent neural network modeling for predictive control of nonlinear processes. Journal of Process Control, 2023. paper
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Optimal Dirichlet boundary control by Fourier neural operators applied to nonlinear optics. arXiv, 2023. paper
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Neural operators for delay-compensating control of hyperbolic PIDEs. arXiv, 2023. paper
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Physics-informed online learning of gray-box models by moving horizon estimation. European Journal of Control, 2023. paper
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Online identification and control of PDEs via reinforcement learning methods. arXiv, 2023. paper
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The hard-constraint PINNs for interface optimal control problems. arXiv, 2023. paper
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Physics-informed state-space neural networks for transport phenomena. arXiv, 2023. paper
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A comparison of mesh-free differentiable programming and data-driven strategies for optimal control under PDE constraints. arXiv, 2023. paper
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A data-driven tracking control framework using physics-informed neural networks and deep reinforcement learning for dynamical systems. JCP, 2023. paper
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Physics-informed neural network Lyapunov functions: PDE characterization, learning, and verification. arXiv, 2023. paper
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Taming waves: A physically-interpretable machine learning framework for realizable control of wave dynamics. arXiv, 2023. paper
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Neural operators for boundary stabilization of stop-and-go traffic. arXiv, 2023. paper
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Neural operator approximations of backstepping kernels for 2×2 hyperbolic PDEs. arXiv, 2023. paper
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Lyapunov-based physics-informed long short-term memory (LSTM) neural network-based adaptive control. IEEE Control Systems Letters, 2023. paper
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Gain scheduling with a neural operator for a transport PDE with nonlinear recirculation. arXiv, 2024. paper
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Physics-informed deep learning approach to solve optimal control problem. AIAA, 2024. paper
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Adaptive neural-operator backstepping control of a benchmark hyperbolic PDE. arXiv, 2024. paper
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Physical-informed neural network for MPC-based trajectory tracking of vehicles with noise considered. TIV, 2024. paper
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Nonlinear discrete-time observers with physics-informed neural networks. arXiv, 2024. paper
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Modelling atmospheric dynamics with spherical Fourier neural operators. ICLR, 2023. paper
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Spatiotemporal modeling of European paleoclimate using doubly sparse Gaussian processes. NIPS, 2022. paper
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Seismic traveltime simulation for variable velocity models using physics-informed Fourier neural operator. arXiv, 2023. paper
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DeepPhysiNet: Bridging deep learning and atmospheric physics for accurate and continuous weather modeling. arXiv, 2024. paper
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Exact Dirichlet boundary physics-informed neural network EPINN for solid mechanics. CMAME, 2023. paper
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Solving multi-material problems in solid mechanics using physics-informed neural networks based on domain decomposition technology. CMAME, 2023. paper
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A novel key performance analysis method for permanent magnet coupler using physics-informed neural networks. Engineering with Computers, 2023. paper
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Mechanical characterization and inverse design of stochastic architected metamaterials using neural operators. arXiv, 2023. paper
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Physics-informed neural networks for magnetostatic problems on axisymmetric transformer geometries. IEEE Journal of Emerging and Selected Topics in Industrial Electronics, 2023. paper
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Neural born series operator for biomedical ultrasound computed tomography. arXiv, 2023. paper
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Learning thermoacoustic interactions in combustors using a physics-informed neural network. arXiv, 2024. paper
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Flight dynamic uncertainty quantification modeling using physics-informed neural networks. AIAA, 2024. paper
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Peridynamic neural operators: A data-driven nonlocal constitutive model for complex material responses. arXiv, 2024. paper
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Stochastic dynamics of aircraft ground taxiing via improved physics-informed neural networks. Nonlinear Dynamics, 2024. paper
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Damage identification for plate structures using physics-informed neural networks. MSSP, 2024. paper
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Quantification of gradient energy coefficients using physics-informed neural networks. International Journal of Mechanical Sciences, 2024. paper
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MPIPN: A multi physics-informed PointNet for solving parametric acoustic-structure systems. arXiv, 2024. paper
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A hierarchically normalized physics-informed neural network for solving differential equations: Application for solid mechanics problems. EAAI, 2024. paper
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A hard constraint and domain decomposition based physics-informed neural network framework for nonhomogeneous transient thermal analysis. TCPMT, 2024. paper
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Online parameter estimation using physics-informed deep learning for vehicle stability algorithms. arXiv, 2023. paper
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A locality-based neural solver for optical motion capture. SIGGRAPH, 2023. paper
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Approximating high-dimensional minimal surfaces with physics-informed neural networks. arXiv, 2023. paper
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A spatial-temporally adaptive PINN framework for 3D bi-ventricular electrophysiological simulations and parameter inference. MICCAI, 2023. paper
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Using the Transformer model for physical simulation: An application on transient thermal analysis for 3D printing process simulation. NIPS, 2023. paper
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Physics-informed neural network for solution of forward and inverse kinematic wave problems. Journal of Hydrology, 2024. paper
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PhyGrasp: Generalizing robotic grasping with physics-informed large multimodal models. arXiv, 2024. paper
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Dynamic weights enabled physics-informed neural network for simulating the mobility of engineered nano-particles in a contaminated aquifer. NIPS, 2022. paper
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Learning two-phase microstructure evolution using neural operators and autoencoder architectures. NPJ Computational Materials, 2022. paper
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Predicting glass structure by physics-informed machine learning. NPJ Computational Materials, 2022. paper
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Physics-informed deep learning for solving phonon Boltzmann transport equation with large temperature non-equilibrium. NPJ Computational Materials, 2022. paper
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Design of Turing systems with physics-informed neural networks. arXiv, 2022. paper
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