Data-driven identification of 2D Partial Differential Equations using extracted physical features

Learning dominant physical processes with data-driven balance models

(2021) Jared L. Callaham et al.   Nature Communications

Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems

(2020) Ameya D. Jagtap et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Data-driven discovery of PDEs in complex datasets

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

Identification of physical processes via combined data-driven and data-assimilation methods

(2019) Haibin Chang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Prediction of turbulent heat transfer using convolutional neural networks

(2019) Junhyuk Kim et al.   JOURNAL OF FLUID MECHANICS

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

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

Hidden physics models: Machine learning of nonlinear partial differential equations

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

Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks

(2018) Pantelis R. Vlachas et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

DGM: A deep learning algorithm for solving partial differential equations

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

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

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

Machine learning of linear differential equations using Gaussian processes

(2017) Maziar Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Learning partial differential equations via data discovery and sparse optimization

(2017) Hayden Schaeffer   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Data-driven discovery of partial differential equations

(2017) Samuel H. Rudy et al.   Science Advances

Discovering governing equations from data by sparse identification of nonlinear dynamical systems

(2016) Steven L. Brunton et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Propagation speed of the maximum of the fundamental solution to the fractional diffusion–wave equation

(2013) Yuri Luchko et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Distilling Free-Form Natural Laws from Experimental Data

(2009) Michael Schmidt et al.   SCIENCE