Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks

Scaled boundary cubature scheme for numerical integration over planar regions with affine and curved boundaries

(2021) Eric B. Chin et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

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

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

(2021) Amuthan A. Ramabathiran et al.   JOURNAL OF COMPUTATIONAL 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

Solution of Biharmonic Equation in Complicated Geometries With Physics Informed Extreme Learning Machine

(2020) Vikas Dwivedi et al.   JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING

High-order maximum-entropy collocation methods

(2020) F. Greco et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

PFNN: A penalty-free neural network method for solving a class of second-order boundary-value problems on complex geometries

(2020) Hailong Sheng et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Modeling curved interfaces without element‐partitioning in the extended finite element method

(2019) Eric B. Chin et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

Deep ReLU networks and high-order finite element methods

(2019) Joost A. A. Opschoor et al.   Analysis and Applications

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

(2019) Vikas Dwivedi et al.   NEUROCOMPUTING

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 convolutional neural networks for eigenvalue problems in mechanics

(2018) David Finol et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

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

On Variational and PDE-Based Distance Function Approximations

(2015) Alexander G. Belyaev et al.   COMPUTER GRAPHICS FORUM

Cell-based maximum-entropy approximants

(2015) Daniel Millán et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Generalized barycentric coordinates and applications

(2015) Michael S. Floater   ACTA NUMERICA

Algebraic distance estimations for enriched isogeometric analysis

(2014) K. Upreti et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

A gradient-based implicit blend

(2013) Olivier Gourmel et al.   ACM TRANSACTIONS ON GRAPHICS

Signed -distance fields

(2012) Alexander Belyaev et al.   COMPUTER-AIDED DESIGN

Finite element analysis in situ

(2011) Michael Freytag et al.   FINITE ELEMENTS IN ANALYSIS AND DESIGN

Hybrid Method of Engineering Analysis: Combining Meshfree Method with Distance Fields and Collocation Technique

(2011) Igor Tsukanov et al.   JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING

Artificial Neural Network Method for Solution of Boundary Value Problems With Exact Satisfaction of Arbitrary Boundary Conditions

(2009) K.S. McFall et al.   IEEE TRANSACTIONS ON NEURAL NETWORKS

On the optimum support size in meshfree methods: A variational adaptivity approach with maximum-entropy approximants

(2009) Adrian Rosolen et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

Transfinite mean value interpolation in general dimension

(2009) Solveig Bruvoll et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Transfinite mean value interpolation

(2008) Christopher Dyken et al.   COMPUTER AIDED GEOMETRIC DESIGN