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In this paper, we introduce a Meshfree Variational-Physics-Informed Neural Network.
VPINNs: Variational physics-informed neural networks for solving partial differential equations
Kharazmi, E.; Zhang, Z.; Karniadakis, G · 1912
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Artificial neural network methods in quantum mechanics
Lagaris, I.; Likas, A.; Fotiadis, D · 1997
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Domain decomposition methods for partial differential equations. In Parallel Numerical Algorithms
Smith, B.F · 1997
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Artificial neural networks for solving ordinary and partial differential equations
Lagaris, I.; Likas, A.; Fotiadis, D · 1998
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Early stopping-but when? In Neural Networks: Tricks of the Trade
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Lagaris, I.; Likas, A.; Papageorgiou, D · 2000
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Domain Decomposition Methods-Algorithms and Theory
Toselli, A.; Widlund, O · 2006
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Adam: A method for stochastic optimization
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Towards effective flow simulations in realistic discrete fracture networks
Berrone, S.; Pieraccini, S.; Scialò, S · 2016
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Raissi, M.; Perdikaris, P.; Karniadakis, G · 2017
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Raissi, M.; Perdikaris, P.; Karniadakis, G · 2017
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Raissi, M.; Perdikaris, P.; Karniadakis, G · 2018
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Learning parameters and constitutive relationships with physics informed deep neural networks
Tartakovsky, A.; Marrero, C.; Perdikaris, P.; Tartakovsky, G.; Barajas-Solano, D · 2018
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The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems
Weinan, E.; Yu, B · 2018
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DGM: A deep learning algorithm for solving partial differential equations
Sirignano, J.; Spiliopoulos, K · 2018
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Automatic differentiation in machine learning: A survey
Baydin, A.; Pearlmutter, B.; Radul, A.; Siskind, J · 2018
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PyTorch: An Imperative Style, High-Performance Deep Learning Library. In Advances in Neural Information Processing Systems 32
Paszke, A.; Gross, S.; Massa, F.; Lerer, A.; Bradbury, J.; Chanan, G.; Killeen, T.; Lin, Z.; Gimelshein, N.; Antiga, L.; et al · 2019
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Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
Zhu, Y.; Zabaras, N.; Koutsourelakis, P.; Perdikaris, P · 2019
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fPINNs: Fractional physics-informed neural networks
Pang, G.; Lu, L.; Karniadakis, G.E · 2019
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Physics-informed neural networks for inverse problems in nano-optics and metamaterials
Yuyao, C.; Lu, L.; Karniadakis, G.; Dal Negro, L · 2020
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Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems
Jagtap, A.; Kharazmi, E.; Karniadakis, G · 2020
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Estimating model inadequacy in ordinary differential equations with physics-informed neural networks
Viana, F.; Nascimento, R.; Dourado, A.; Yucesan, Y · 2020
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Extensions of the deep Galerkin method
Al-Aradi, A.; Correia, A.; Jardim, G.; de Freitas Naiff, D.; Saporito, Y · 2022
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An overview on deep learning-based approximation methods for partial differential equations
Beck, C.; Hutzenthaler, M.; Jentzen, A.; Kuckuck, B · 2022
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Scientific Machine Learning Through Physics-Informed Neural Networks: Where we are and What’s Next
Cuomo, S.; Di Cola, V.S.; Giampaolo, F.; Rozza, G.; Raissi, M.; Piccialli, F · 2022
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Physics-Informed Neural Network (PINN) Evolution and Beyond: A Systematic Literature Review and Bibliometric Analysis
Lawal, Z.; Yassin, H.; Lai, D.; Che Idris, A · 2022
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Solving PDEs by variational physics-informed neural networks: An a posteriori error analysis
Berrone, S.; Canuto, C.; Pintore, M · 2022
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B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
Yang, L.; Meng, X.; Karniadakis, G · 2020
Cited alongside, same era.
Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations
Yang, L.; Zhang, D.; Karniadakis, G · 2020
Cited alongside, same era.
Hybrid physics-informed neural networks for main bearing fatigue prognosis with visual grease inspection
Yucesan, Y.; Viana, F · 2020
Cited alongside, same era.
Solving localized wave solutions of the derivative nonlinear Schrödinger equation using an improved PINN method
Pu, J.; Li, J.; Chen, Y · 2021
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PhyGeoNet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain
Gao, H.; Sun, L.; Wang, J · 2021
Cited alongside, same era.
Physics-informed learning of governing equations from scarce data
Chen, Z.; Liu, Y.; Sun, H · 2021
Cited alongside, same era.
A priori generalization analysis of the deep Ritz method for solving high dimensional elliptic partial differential equations
Lu, Y.; Lu, J.; Wang, M · 2021
Cited alongside, same era.
Variational-Physics-Informed Neural Networks: The role of quadratures and test functions
Berrone, S.; Canuto, C.; Pintore, M · 2022
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Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks
Sukumar, N.; Srivastava, A · 2022
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High-dimensional inverse modeling of hydraulic tomography by physics informed neural network (HT-PINN)
Guo, Q.; Zhao, Y.; Lu, C.; Luo, J · 2023
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An extended physics informed neural network for preliminary analysis of parametric optimal control problems
Demo, N.; Strazzullo, M.; Rozza, G · 2023
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Finite Basis Physics-Informed Neural Networks (FBPINNs): A scalable domain decomposition approach for solving differential equations
Moseley, B.; Markham, A.; Nissen-Meyer, T · 2023
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Mycrunchgpt: A llm assisted framework for scientific machine learning
Kumar, V.; Gleyzer, L.; Kahana, A.; Shukla, K.; Karniadakis, G.E · 2023
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Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks
Berrone, S.; Canuto, C.; Pintore, M.; Sukumar, N · 2023
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TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems. 2015
Abadi, M.; Agarwal, A.; Barham, P.; Brevdo, E; Chen, Z.; Citro, C.; Corrado, G.S.; Davis, A.; Dean, J.; Devin, M.; et al · 2024
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Bradbury, J.; Frostig, R.; Hawkins, P.; Johnson, M.J.; Leary, C.; Maclaurin, D.; Necula, G.; Paszke, A.; VanderPlas, J.; Wanderman-Milne, S.; et al
2024
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Kan: Kolmogorov-arnold networks
Liu, Z.; Wang, Y.; Vaidya, S.; Ruehle, F.; Halverson, J.; Soljačić, M.; Hou, T.Y.; Tegmark, M · 2024
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Investigating KAN-Based Physics-Informed Neural Networks for EMI/EMC Simulations
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Extended physics-informed neural networks (XPINNs): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations
Jagtap, A.; Karniadakis, G · 2041
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