SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEs

On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks

(2021) Sifan Wang et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

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

Relu Deep Neural Networks and Linear Finite Elements

(2020) Juncai He sci   JOURNAL OF COMPUTATIONAL MATHEMATICS

Array programming with NumPy

(2020) Charles R. Harris et al.   NATURE

Machine learning from a continuous viewpoint, I

(2020) E. Weinan et al.   Science China-Mathematics

Systems biology informed deep learning for inferring parameters and hidden dynamics

(2020) Alireza Yazdani et al.   PLoS Computational Biology

A mesh-free method for interface problems using the deep learning approach

(2019) Zhongjian Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Physics Informed Extreme Learning Machine (PIELM)–A rapid method for the numerical solution of partial differential equations

(2019) Vikas Dwivedi et al.   NEUROCOMPUTING

automan: A Python-Based Automation Framework for Numerical Computing

(2018) Prabhu Ramachandran   COMPUTING IN SCIENCE & ENGINEERING

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

Entropically damped artificial compressibility for SPH

(2018) Prabhu Ramachandran et al.   COMPUTERS & FLUIDS

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

Automatic finite element formulation and assembly of hyperelastic higher order structural models

(2013) Amuthan Arunkumar Ramabathiran et al.   APPLIED MATHEMATICAL MODELLING

PyClaw: Accessible, Extensible, Scalable Tools for Wave Propagation Problems

(2012) David I. Ketcheson et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Mayavi: 3D Visualization of Scientific Data

(2011) Prabhu Ramachandran et al.   COMPUTING IN SCIENCE & ENGINEERING

Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities

(2009) Christophe Geuzaine et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING