Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Keywords

Partial differential equation, Nonlinear system, Artificial neural network, Context (archaeology), Inverse problem

References

• Spectral/hp Element Methods for Computational Fluid DynamicsGeorge Em Karniadakis, Spencer J. Sherwin — 2005
• Predicting the sequence specificities of DNA- and RNA-binding proteins by deep learningBabak Alipanahi, Andrew Delong, Matthew T. Weirauch — 2015
• Evaluation of machine learning algorithms for prediction of regions of high Reynolds averaged Navier Stokes uncertaintyJulia Ling, Jeremy Alan Templeton — 2015
• Bayesian Numerical HomogenizationHouman Owhadi — 2014
• Fermi, Pasta, Ulam, and a mysterious ladyThierry Dauxois — 2008
• A hybrid neural network‐first principles approach to process modelingDimitris C. Psichogios, Lyle Ungar — 1992
• When Are Quasi-Monte Carlo Algorithms Efficient for High Dimensional Integrals?Ian H. Sloan, Henryk Woźniakowski — 1998
• A first course in the numerical analysis of differential equationsArieh Iserles, John Guckenheimer — 1996
• Large sample properties of simulations using latin hypercube samplingMichael L. Stein — 1987
• Spectral and finite difference solutions of the Burgers equationC. Basdevant, Michel Deville, Pierre Haldenwang — 1986
• Brittleness of Bayesian Inference Under Finite Information in a Continuous WorldHouman Owhadi, Clint Scovel, Tim Sullivan — 2013
• On the limited memory BFGS method for large scale optimizationDong C. Liu, Jorge Nocedal — 1989
• Neural network modeling for near wall turbulent flowMichele Milano, Petros Koumoutsakos — 2002
• A paradigm for data-driven predictive modeling using field inversion and machine learningEric Parish, Karthik Duraisamy — 2016
• Practical Bayesian Optimization of Machine Learning AlgorithmsJasper Snoek, Hugo Larochelle, Ryan P. Adams — 2012
• Multilayer feedforward networks are universal approximatorsKurt Hornik, Maxwell B. Stinchcombe, Halbert White — 1989
• Continuous-time nonlinear signal processing: a neural network based approach for gray box identificationRamiro Rico-Martı́nez, Jason S. Anderson, I.G. Kevrekidis — 1994
• Artificial neural networks for solving ordinary and partial differential equationsI.E. Lagaris, A. Likas, D.I. Fotiadis — 1997
• ImageNet classification with deep convolutional neural networksAlex Krizhevsky, Ilya Sutskever, Geoffrey E. Hinton — 2012
• Human-level concept learning through probabilistic program inductionBrenden M. Lake, Ruslan Salakhutdinov, Joshua B. Tenenbaum — 2015

Cited by

• Review of multi-fidelity modelsM. Giselle Fernández-Godino — 2016
• Partial inversion of elliptic operator to speed up computation of likelihood in Bayesian inferenceAlexander Litvinenko — 2017
• Neural networks catching up with finite differences in solving partial differential equations in higher dimensionsVsevolod I. Avrutskiy — 2017
• A Deep Neural Network Surrogate for High-Dimensional Random Partial Differential EquationsMohammad Amin Nabian, Hadi Meidani — 2018
• Discovering physical concepts with neural networksRaban Iten, Tony Metger, Henrik Wilming — 2018
• Identification of physical processes via combined data-driven and data-assimilation methodsHaibin Chang, Dongxiao Zhang — 2018
• Convolutional neural networks in phase space and inverse problemsGünther Uhlmann, Yiran Wang — 2018
• Adversarial Uncertainty Quantification in Physics-Informed Neural NetworksYibo Yang, Paris Perdikaris — 2018
• fPINNs: Fractional Physics-Informed Neural NetworksGuofei Pang, Lu Lu, George Em Karniadakis — 2018
• Deep learning for fast simulation of seismic waves in complex mediaBenjamin Moseley, Andrew Markham, Tarje Nissen‐Meyer — 2018
• InversionNet: An Efficient and Accurate Data-Driven Full Waveform InversionYue Wu, Youzuo Lin — 2018
• Deep Learning of Turbulent Scalar MixingMaziar Raissi, Hessam Babaee, Peyman Givi — 2018
• A mesh-free method for interface problems using the deep learning approachZhongjian Wang, Zhiwen Zhang — 2019
• Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled DataYinhao Zhu, Nicholas Zabaras, Phaedon‐Stelios Koutsourelakis — 2019
• Massive computational acceleration by using neural networks to emulate mechanism-based biological modelsShangying Wang, Kai Fan, Nan Luo — 2019
• A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problemsXuhui Meng, George Em Karniadakis — 2019
• Modal Analysis of Fluid Flows: Applications and OutlookKunihiko Taira, Maziar S. Hemati, Steven L. Brunton — 2019
• Sparse Identification of Truncation ErrorsStephan Thaler, Ludger Paehler, Nikolaus A. Adams — 2019
• A comparative study of physics-informed neural network models for learning unknown dynamics and constitutive relationsRamakrishna Tipireddy, Paris Perdikaris, Panos Stinis — 2019
• Artificial Neural Network Methods for the Solution of Second Order Boundary Value ProblemsCosmin Anitescu, Elena Atroshchenko, Naif Alajlan — 2019

Related papers

• Automatic Differentiation of Functions of DerivativesRobert E. Kalaba, Leigh Tesfatsion — 1986
• Reinitialized partial moments for the identification of the heat equation parametersMohamed Farah, Reegis Ouvrard, Guillaume Mercère — 2015
• Solutions of Linear Partial Differential Equations with Mixed Partial Derivatives by Elzaki Substitution MethodMd. Babul Hossain, Mousumi Datta — 2018
• Complex differentiation tools for geophysical inversionAbdulwahab A. Abokhodair — 2009
• Aberration calculation and lens tolerancing using automatic differentiationRobert Herloski — 1986