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Physics-informed neural networks (PINNs) are a promising approach that combines the power of neural networks with the interpretability of physical modeling.
Towards physics-informed deep learning for turbulent flow prediction
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Optimal global rates of convergence for nonparametric regression
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A simple weight decay can improve generalization
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Diffusions, Markov processes and Martingales , volume 1, Foundations
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Combinatorics of partial derivatives
M. Hardy · 2006
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Bracketing metric entropy rates and empirical central limit theorems for function classes of Besov- and Sobolev-type
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How neural networks extrapolate: From feedforward to graph neural networks
K. Xu, M. Zhang, J. Li, S.S. Du, K.-I. Kawarabayashi, and S. Jegelka · 2009
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Functional Analysis, Sobolev Spaces and Partial Differential Equations
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Partial Differential Equations , volume 19 of Graduate Studies in Mathematics
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On Sobolev extension domains in ℝ n \mathbb{R}^{n}
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Elliptic Problems in Nonsmooth Domains , volume 69 of Classics in Applied Mathematics
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Blood flow velocity field estimation via spatial regression with PDE penalization
L. Azzimonti, L.M. Sangalli, P. Secchi, M. Domanin, and F. Nobile · 2014
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Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains
M.S. Agranovich · 2015
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Probability in High Dimension
R. van Handel · 2016
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On calibration of modern neural networks
C. Guo, G. Pleiss, Y. Sun, and K.Q. Weinberger · 2017
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
M. Raissi, P. Perdikaris, and G.E. Karniadakis · 2018
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Deep learning for physical processes: Incorporating prior scientific knowledge
E. de Bézenac, A. Pajot, and P. Gallinari · 2019
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Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
A.D. Jagtap, K. Kawaguchi, and G.E. Karniadakis · 2019
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Decoupled weight decay regularization
I. Loshchilov and F. Hutter · 2019
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Physics-informed neural networks for cardiac activation mapping
F.S. Costabal, Y. Yang, P. Perdikaris, D.E. Hurtado, and E. Kuhl · 2020
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Sobolev norm learning rates for regularized least-squares algorithm
S. Fischer and I. Steinwart · 2020
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Physics-informed neural networks for multiphysics data assimilation with application to subsurface transport
Q. He, D. Barajas-Solano, G. Tartakovsky, and A.M. Tartakovsky · 2020
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Physics-informed and hybrid machine learning in additive manufacturing: Application to fused filament fabrication
B. Kapusuzoglu and S. Mahadevan · 2020
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Physics-driven regularization of deep neural networks for enhanced engineering design and analysis
M.A. Nabian and H. Meidani · 2020
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Solving the frequency-domain acoustic vti wave equation using physics-informed neural networks
C. Song, T. Alkhalifah, and U.B. Waheed · 2021
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Informed machine learning – A taxonomy and survey of integrating prior knowledge into learning systems
L. von Rueden, S. Mayer, K. Beckh, B. Georgiev, S. Giesselbach, R. Heese, B. Kirsch, M. Walczak, J. Pfrommer, A. Pick, R. Ramamurthy, J. Garcke, C. Bauckhage, and J. Schuecker · 2021
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When and why PINNs fail to train: A neural tangent kernel perspective
S. Wang, X. Yu, and P. Perdikaris · 2021
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Some first results on the consistency of spatial regression with partial differential equation regularization
E. Arnone, A. Kneip, F. Nobile, and L.M. Sangalli · 2022
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Scientific machine learning through physics-informed neural networks: Where we are and what’s next
S. Cuomo, V.S. Di Cola, F. Giampaolo, G. Rozza, M. Raissi, and F. Piccialli · 2022
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Driven by data or derived through physics? A review of hybrid physics guided machine learning techniques with cyber-physical system (CPS) focus
R. Rai and C.K. Sahu · 2020
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On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs
Y. Shin · 2020
Cited alongside, same era.
Physics-informed neural network super resolution for advection-diffusion models
C. Wang, E. Bentivegna, W. Zhou, L. Klein, and B. Elmegreen · 2020
Cited alongside, same era.
Physics-guided convolutional neural network (PhyCNN) for data-driven seismic response modeling
R. Zhang, Y. Liu, and H. Sun · 2020
Cited alongside, same era.
Uncovering near-wall blood flow from sparse data with physics-informed neural networks
A. Arzani, J.-X. Wang, and R.M. D’Souza · 2021
Cited alongside, same era.
Physics-informed neural networks for heat transfer problems
S. Cai, Z. Wang, S. Wang, P. Perdikaris, and G.E. Karniadakis · 2021
Cited alongside, same era.
Using physics-informed regularization to improve extrapolation capabilities of neural networks
D. Davini, B. Samineni, B. Thomas, A.H. Tran, C. Zhu, K. Ha, G. Dasika, and L. White · 2021
Cited alongside, same era.
Physics-guided neural networks (PGNN): An application in lake temperature modeling
A. Daw, A. Karpatne, W.D. Watkins, J.S. Read, and V. Kumar · 2022
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Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs
T. De Ryck and S. Mishra · 2022
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Physics informed neural networks for control oriented thermal modeling of buildings
G. Gokhale, B. Claessens, and C. Develder · 2022
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Physics-informed machine learning: A survey on problems, methods and applications
Z. Hao, S. Liu, Y. Zhang, C. Ying, Y. Feng, H. Su, and J. Zhu · 2022
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Physics-informed regularisation procedure in neural networks: An application in blast protection engineering
J.J. Pannell, S.E. Rigby, and G. Panoutsos · 2022
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A data-driven multi-fidelity physics-informed learning framework for smart manufacturing: A composites processing case study
M. Ramezankhani, A. Nazemi, A. Narayan, H. Voggenreiter, M. Harandi, R. Seethaler, and A.S. Milani · 2022
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Convergence of physics-informed neural networks applied to linear second-order elliptic interface problems
S. Wu, A. Zhu, Y. Tang, and B. Lu · 2022
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Recipes for when physics fails: Recovering robust learning of physics informed neural networks
B. Chandrajit, L. McLennan, T. Andeen, and A. Roy · 2023
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A review of machine learning methods applied to structural dynamics and vibroacoustic
B. Cunha, C. Droz, A. Zine, S. Foulard, and M. Ichchou · 2023
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A data-driven physics-informed neural network for predicting the viscosity of nanofluids
I.C. Esfahani · 2023
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A physics-informed neural network framework to predict 3D temperature field without labeled data in process of laser metal deposition
S. Li, G. Wang, Y. Di, L. Wang, H. Wang, and Q. Zhou · 2023
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Estimates on the generalization error of physics-informed neural networks for approximating PDEs
S. Mishra and R. Molinaro · 2023
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Physics-informed neural networks for approximating dynamic (hyperbolic) PDEs of second order in time: Error analysis and algorithms
Y. Qian, Y. Zhang, Y. Huang, and S. Dong · 2023
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Error estimates of residual minimization using neural networks for linear PDEs
Y. Shin, Z. Zhang, and G.E. Karniadakis · 2023
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Integrating scientific knowledge with machine learning for engineering and environmental systems
J. Willard, X. Jia, S. Xu, M. Steinbach, and V. Kumar · 2023
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