Physics‐Informed Deep Neural Networks for Learning Parameters and Constitutive Relationships in Subsurface Flow Problems

Learning to fail: Predicting fracture evolution in brittle material models using recurrent graph convolutional neural networks

(2019) Max Schwarzer et al.   COMPUTATIONAL MATERIALS SCIENCE

Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data

(2019) Yinhao Zhu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Adversarial uncertainty quantification in physics-informed neural networks

(2019) Yibo Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Water and sediment temperature dynamics in shallow tidal environments: The role of the heat flux at the sediment-water interface

(2018) M. Pivato et al.   ADVANCES IN WATER RESOURCES

Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics

(2018) Christoph Wehmeyer et al.   JOURNAL OF CHEMICAL PHYSICS

Bayesian deep convolutional encoder–decoder networks for surrogate modeling and uncertainty quantification

(2018) Yinhao Zhu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Variable Projection Methods for an Optimized Dynamic Mode Decomposition

(2018) Travis Askham et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

VAMPnets for deep learning of molecular kinetics

(2018) Andreas Mardt et al.   Nature Communications

A unified deep artificial neural network approach to partial differential equations in complex geometries

(2018) Jens Berg et al.   NEUROCOMPUTING

Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous media

(2018) Shaoxing Mo et al.   WATER RESOURCES RESEARCH

Deep learning for universal linear embeddings of nonlinear dynamics

(2018) Bethany Lusch et al.   Nature Communications

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

(2018) M. Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Chaos as an intermittently forced linear system

(2017) Steven L. Brunton et al.   Nature Communications

A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition

(2015) Matthew O. Williams et al.   JOURNAL OF NONLINEAR SCIENCE

Linear functional minimization for inverse modeling

(2015) D. A. Barajas-Solano et al.   WATER RESOURCES RESEARCH

Nonlinear Laplacian spectral analysis for time series with intermittency and low-frequency variability

(2012) D. Giannakis et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems

(2010) Chad Lieberman et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Inverse problems: A Bayesian perspective

(2010) A. M. Stuart   ACTA NUMERICA