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Karniadakis GE, Kevrekidis IG, Lu L, Perdikaris P, Wang S, Yang L. Physics-informed machine learning. Nature Reviews Physics 2021.
Raissi M, Perdikaris P, Karniadakis GE. Physics informed deep learning (part i): Data-driven solutions of nonlinear partial differential equations. arXiv preprint arXiv:171110561 2017.
Raissi M, Perdikaris P, Karniadakis GE. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 2019, 378: 686-707. PINN初始文章
Wang S, Sankaran S, Perdikaris P. Respecting causality is all you need for training physics-informed neural networks. arXiv preprint arXiv:220307404 2022. 好文,时序因果结构引入了数值方法的分步思想
Wang S, Yu X, Perdikaris P. When and why PINNs fail to train: A neural tangent kernel perspective. Journal of Computational Physics 2022, 449: 110768. 神经正切核
Wu C, Zhu M, Tan Q, Kartha Y, Lu L. A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering 2023, 403: 115671.
Lu L, Pestourie R, Yao W, Wang Z, Verdugo F, Johnson SG. Physics-informed neural networks with hard constraints for inverse design. arXiv preprint arXiv:210204626 2021. 硬边界条件
神经算子结构网络
Lu L, Jin P, Pang G, Zhang Z, Karniadakis GE. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nature Machine Intelligence 2021, 3(3): 218-229. DeepONet结构
Li Z, Kovachki N, Azizzadenesheli K, Liu B, Bhattacharya K, Stuart A, Anandkumar A. Fourier neural operator for parametric partial differential equations. arXiv preprint arXiv:201008895 2020. 傅里叶神经算子FNO结构
Wang S, Wang H, Perdikaris P. Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv preprint arXiv:210310974 2021. 物理信息DeepONet
Wang S, Perdikaris P. Long-time integration of parametric evolution equations with physics-informed DeepONets. Journal of Computational Physics 2023, 475: 111855. 长序列级联
Li Z, Zheng H, Kovachki N, Jin D, Chen H, Liu B, Azizzadenesheli K, Anandkumar A. Physics-Informed Neural Operator for Learning Partial Differential Equations. arXiv preprint arXiv:211103794 2021. 物理信息FNO
Jiang Z, Zhu M, Li D, Li Q, Yuan YO, Lu L. Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration. arXiv preprint arXiv:230304778 2023.
Zhu M, Zhang H, Jiao A, Karniadakis GE, Lu L. Reliable extrapolation of deep neural operators informed by physics or sparse observations. Computer Methods in Applied Mechanics and Engineering 2023, 412: 116064. 好文,新颖角度分析了泛化能力
Lu L, Meng X, Mao Z, Karniadakis GE. DeepXDE: A Deep Learning Library for Solving Differential Equations. SIAM Review 2021, 63(1): 208-228. 实用工具库
Lu L, Meng X, Cai S, Mao Z, Goswami S, Zhang Z, Karniadakis GE. A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data. Computer Methods in Applied Mechanics and Engineering 2022, 393: 114778. 性能比较
光网络物理信息嵌入
Zang Y, Yu Z, Xu K, Lan X, Chen M, Yang S, Chen H. **Principle-driven Fiber Transmission Model based on PINN Neural Network**. Journal of Lightwave Technology 2021. 光纤信道
物理信息与深度学习结合可以借鉴的角度
Chen Z, Liu Y, Sun H. Physics-informed learning of governing equations from scarce data. Nat Commun 2021, 12(1): 6136. 好文,参数识别
Chen RT, Rubanova Y, Bettencourt J, Duvenaud D. Neural ordinary differential equations. arXiv preprint arXiv:180607366 2018. NeuralODE
Lusch B, Kutz JN, Brunton SL. Deep learning for universal linear embeddings of nonlinear dynamics. Nat Commun 2018, 9(1): 4950. Koopman结构降维处理