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Physics-informed machine learning

Journal Article · · Nature Reviews Physics

Not provided.

Research Organization:
Univ. of Pennsylvania, Philadelphia, PA (United States); Brown Univ., Providence, RI (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
DOE Contract Number:
SC0019116; SC0019453
OSTI ID:
1852843
Journal Information:
Nature Reviews Physics, Journal Name: Nature Reviews Physics Journal Issue: 6 Vol. 3; ISSN 2522-5820
Publisher:
Springer Nature
Country of Publication:
United States
Language:
English

References (124)

Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations journal June 2020
Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences journal November 2019
DeepXDE: A Deep Learning Library for Solving Differential Equations journal January 2021
Coupled Time‐Lapse Full‐Waveform Inversion for Subsurface Flow Problems Using Intrusive Automatic Differentiation journal August 2020
Physically informed artificial neural networks for atomistic modeling of materials journal May 2019
Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics journal June 2020
Machine learning of linear differential equations using Gaussian processes journal November 2017
Gaussian measure in Hilbert space and applications in numerical analysis journal September 1972
Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks journal March 2020
Stochastic spectral methods for efficient Bayesian solution of inverse problems journal June 2007
SciANN: A Keras/TensorFlow wrapper for scientific computations and physics-informed deep learning using artificial neural networks journal January 2021
Solving initial-boundary value problems for systems of partial differential equations using neural networks and optimization techniques journal November 2009
Prediction of vegetation dynamics using NDVI time series data and LSTM journal February 2018
Learning unknown physics of non-Newtonian fluids journal July 2021
Training a 3-node neural network is NP-complete journal January 1992
Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains journal June 2020
Multi-Scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains journal June 2020
Multigrid with Rough Coefficients and Multiresolution Operator Decomposition from Hierarchical Information Games journal January 2017
Invariant Scattering Convolution Networks journal August 2013
Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks journal June 2020
Jamming transition as a paradigm to understand the loss landscape of deep neural networks journal July 2019
Environmental Sensor Networks: A revolution in the earth system science? journal October 2006
Physics‐Informed Deep Neural Networks for Learning Parameters and Constitutive Relationships in Subsurface Flow Problems journal May 2020
Reconciling modern machine-learning practice and the classical bias–variance trade-off journal July 2019
Unpaired Image-to-Image Translation Using Cycle-Consistent Adversarial Networks conference October 2017
Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks journal March 2021
Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems journal November 2019
PFNN: A penalty-free neural network method for solving a class of second-order boundary-value problems on complex geometries journal March 2021
A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks journal June 2021
Deep learning of free boundary and Stefan problems journal March 2021
Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks journal January 2020
A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems journal January 2020
Coarse-graining auto-encoders for molecular dynamics journal December 2019
Benchmark Analysis of Representative Deep Neural Network Architectures journal January 2018
Error estimates for DeepONets: a deep learning framework in infinite dimensions journal March 2022
hp-VPINNs: Variational physics-informed neural networks with domain decomposition journal February 2021
Extraction of mechanical properties of materials through deep learning from instrumented indentation journal March 2020
A jamming transition from under- to over-parametrization affects generalization in deep learning journal October 2019
A Proposal on Machine Learning via Dynamical Systems journal March 2017
Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks journal February 2020
Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems journal May 2019
Learning dynamical systems from data: A simple cross-validation perspective, part I: Parametric kernel flows journal July 2021
A Correspondence Between Bayesian Estimation on Stochastic Processes and Smoothing by Splines journal April 1970
“Forget time”: Essay written for the FQXi contest on the Nature of Time journal May 2011
Deep learning for universal linear embeddings of nonlinear dynamics journal November 2018
Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations journal October 2020
Ab initio solution of the many-electron Schrödinger equation with deep neural networks journal September 2020
Artificial neural networks for solving ordinary and partial differential equations journal January 1998
An Emergent Space for Distributed Data With Hidden Internal Order Through Manifold Learning journal January 2018
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations journal January 2002
Transfer learning enhanced physics informed neural network for phase-field modeling of fracture journal April 2020
Artificial Neural Network Method for Solution of Boundary Value Problems With Exact Satisfaction of Arbitrary Boundary Conditions journal August 2009
On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton–Jacobi partial differential equations journal January 2021
Deep Residual Learning for Image Recognition conference June 2016
Deep learning and process understanding for data-driven Earth system science journal February 2019
B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data journal January 2021
Relu Deep Neural Networks and Linear Finite Elements journal February 2020
Reynolds averaged turbulence modelling using deep neural networks with embedded invariance journal October 2016
NeuroDiffEq: A Python package for solving differential equations with neural networks journal February 2020
Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review journal March 2017
Identification of distributed parameter systems: A neural net based approach journal March 1998
DGM: A deep learning algorithm for solving partial differential equations journal December 2018
fPINNs: Fractional Physics-Informed Neural Networks journal January 2019
Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization journal January 2019
Geometric Deep Learning: Going beyond Euclidean data journal July 2017
Fast Parallel Algorithms for Short-Range Molecular Dynamics journal March 1995
Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification journal December 2018
DISCRETE- vs. CONTINUOUS-TIME NONLINEAR SIGNAL PROCESSING OF Cu ELECTRODISSOLUTION DATA journal November 1992
A point-cloud deep learning framework for prediction of fluid flow fields on irregular geometries journal February 2021
Adversarial uncertainty quantification in physics-informed neural networks journal October 2019
DPM: A deep learning PDE augmentation method with application to large-eddy simulation journal December 2020
Uncovering turbulent plasma dynamics via deep learning from partial observations journal August 2021
DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators journal December 2021
Deep Potential Molecular Dynamics: A Scalable Model with the Accuracy of Quantum Mechanics journal April 2018
Large scale and linear scaling DFT with the CONQUEST code journal April 2020
Scaling description of generalization with number of parameters in deep learning journal February 2020
Universal Differential Equations for Scientific Machine Learning preprint August 2020
Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems journal June 2020
Discovering governing equations from data by sparse identification of nonlinear dynamical systems journal March 2016
AutoML: A survey of the state-of-the-art journal January 2021
A robotic Intelligent Towing Tank for learning complex fluid-structure dynamics journal November 2019
Inverse problems: A Bayesian perspective journal May 2010
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators journal March 2021
Uncovering electron scattering mechanisms in NiFeCoCrMn derived concentrated solid solution and high entropy alloys journal January 2019
Enforcing statistical constraints in generative adversarial networks for modeling chaotic dynamical systems journal April 2020
A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems journal January 2020
Predicting molecular properties with covariant compositional networks journal June 2018
Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations journal January 2020
Bayesian differential programming for robust systems identification under uncertainty
  • Yang, Yibo; Aziz Bhouri, Mohamed; Perdikaris, Paris
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 476, Issue 2243 https://doi.org/10.1098/rspa.2020.0290
journal November 2020
A Limited Memory Algorithm for Bound Constrained Optimization journal September 1995
Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations journal January 2020
Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data journal October 2019
Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks
  • Jagtap, Ameya D.; Kawaguchi, Kenji; Em Karniadakis, George
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 476, Issue 2239 https://doi.org/10.1098/rspa.2020.0334
journal July 2020
Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks journal January 2020
Pushing the Limit of Molecular Dynamics with Ab Initio Accuracy to 100 Million Atoms with Machine Learning conference November 2020
On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks journal October 2021
On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs journal June 2020
Inferring solutions of differential equations using noisy multi-fidelity data journal April 2017
ConvPDE-UQ: Convolutional neural networks with quantified uncertainty for heterogeneous elliptic partial differential equations on varied domains journal October 2019
DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia journal May 2017
Transformer Dissection: An Unified Understanding for Transformer’s Attention via the Lens of Kernel
  • Tsai, Yao-Hung Hubert; Bai, Shaojie; Yamada, Makoto
  • Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP) https://doi.org/10.18653/v1/D19-1443
conference January 2019
SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems journal December 2020
Kernel Flows: From learning kernels from data into the abyss journal July 2019
DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks journal July 2021
SeqGAN: Sequence Generative Adversarial Nets with Policy Gradient journal February 2017
Solving high-dimensional partial differential equations using deep learning journal August 2018
Systematic Construction of Neural Forms for Solving Partial Differential Equations Inside Rectangular Domains, Subject to Initial, Boundary and Interface Conditions journal August 2020
Discovering Physical Concepts with Neural Networks journal January 2020
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations journal February 2019
Understanding deep convolutional networks journal April 2016
A mean field view of the landscape of two-layer neural networks journal July 2018
Double-slit photoelectron interference in strong-field ionization of the neon dimer journal January 2019
The Harvard Clean Energy Project: Large-Scale Computational Screening and Design of Organic Photovoltaics on the World Community Grid journal August 2011
Metric-based upscaling journal January 2007
Learning constitutive relations using symmetric positive definite neural networks journal March 2021
Distilling Free-Form Natural Laws from Experimental Data journal April 2009
Bayesian Numerical Homogenization journal January 2015
Exascale Deep Learning for Climate Analytics conference November 2018
Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations journal January 2018
Physics-Informed Neural Network for Ultrasound Nondestructive Quantification of Surface Breaking Cracks journal August 2020
Deep neural network approach to forward-inverse problems journal January 2020
Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces journal April 2007
Neural-net-induced Gaussian process regression for function approximation and PDE solution journal May 2019
MgNet: A unified framework of multigrid and convolutional neural network journal May 2019

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