PhyGeoNet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain

Solving differential equations using deep neural networks

(2020) Craig Michoski et al.   NEUROCOMPUTING

Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

(2020) Maziar Raissi et al.   SCIENCE

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

(2020) Liu Yang et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Integration of Adversarial Autoencoders With Residual Dense Convolutional Networks for Estimation of Non‐Gaussian Hydraulic Conductivities

(2020) Shaoxing Mo et al.   WATER RESOURCES RESEARCH

Physics-Informed Neural Networks for Cardiac Activation Mapping

(2020) Francisco Sahli Costabal et al.   Frontiers in Physics

An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications

(2020) E. Samaniego et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Deep learning of subsurface flow via theory-guided neural network

(2020) Nanzhe Wang et al.   JOURNAL OF HYDROLOGY

A bi-fidelity surrogate modeling approach for uncertainty propagation in three-dimensional hemodynamic simulations

(2020) Han Gao et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Weak adversarial networks for high-dimensional partial differential equations

(2020) Yaohua Zang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Machine Learning Approach for Sequence Clustering with Applications to Ground-Motion Selection

(2020) Ruiyang Zhang et al.   JOURNAL OF ENGINEERING MECHANICS

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

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

Data-driven discovery of PDEs in complex datasets

(2019) Jens Berg et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Adversarial uncertainty quantification in physics-informed neural networks

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

MgNet: A unified framework of multigrid and convolutional neural network

(2019) Juncai He et al.   Science China-Mathematics

Prediction of aerodynamic flow fields using convolutional neural networks

(2019) Saakaar Bhatnagar et al.   COMPUTATIONAL MECHANICS

Flow Field Reduction Via Reconstructing Vector Data From 3-D Streamlines Using Deep Learning

(2019) Jun Han et al.   IEEE COMPUTER GRAPHICS AND APPLICATIONS

Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems

(2019) Dongkun Zhang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Multi-Fidelity Physics-Constrained Neural Network and Its Application in Materials Modeling

(2019) Dehao Liu et al.   JOURNAL OF MECHANICAL DESIGN

A deep learning solution approach for high-dimensional random differential equations

(2019) Mohammad Amin Nabian et al.   PROBABILISTIC ENGINEERING MECHANICS

Machine Learning for Fluid Mechanics

(2019) Steven L. Brunton et al.   Annual Review of Fluid Mechanics

Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data

(2019) Luning Sun et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks

(2019) Nicholas Geneva et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Knowledge-enhanced deep learning for simulation of tropical cyclone boundary-layer winds

(2019) Reda Snaiki et al.   JOURNAL OF WIND ENGINEERING AND INDUSTRIAL AERODYNAMICS

Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks

(2019) Georgios Kissas et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Physics-informed neural networks for high-speed flows

(2019) Zhiping Mao et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems

(2019) Xuhui Meng et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks

(2019) Sharmila Karumuri et al.   JOURNAL OF COMPUTATIONAL PHYSICS

PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network

(2019) Zichao Long et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Deep learning of turbulent scalar mixing

(2019) Maziar Raissi et al.   Physical Review Fluids

Enforcing statistical constraints in generative adversarial networks for modeling chaotic dynamical systems

(2019) Jin-Long Wu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

DGM: A deep learning algorithm for solving partial differential equations

(2018) Justin Sirignano et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

(2018) Jens Berg et al.   NEUROCOMPUTING

Solving high-dimensional partial differential equations using deep learning

(2018) Jiequn Han et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Deep learning of vortex-induced vibrations

(2018) Maziar Raissi et al.   JOURNAL OF FLUID MECHANICS

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

Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data

(2017) Jian-Xun Wang et al.   Physical Review Fluids

On-chip cooling by superlattice-based thin-film thermoelectrics

(2009) Ihtesham Chowdhury et al.   Nature Nanotechnology