Extreme theory of functional connections: A fast physics-informed neural network method for solving ordinary and partial differential equations

Physics-informed neural networks for rarefied-gas dynamics: Thermal creep flow in the Bhatnagar–Gross–Krook approximation

(2021) Mario De Florio et al.   PHYSICS OF FLUIDS

Physics informed neural networks for simulating radiative transfer

(2021) Siddhartha Mishra et al.   JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER

Physics-Informed Neural Networks and Functional Interpolation for Data-Driven Parameters Discovery of Epidemiological Compartmental Models

(2021) Enrico Schiassi et al.   Mathematics

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

(2020) Maziar Raissi et al.   SCIENCE

Solving the ruin probabilities of some risk models with Legendre neural network algorithm

(2020) Yanfei Lu et al.   DIGITAL SIGNAL PROCESSING

Solution of Ruin Probability for Continuous Time Model Based on Block Trigonometric Exponential Neural Network

(2020) Yinghao Chen et al.   Symmetry-Basel

The Multivariate Theory of Functional Connections: Theory, Proofs, and Application in Partial Differential Equations

(2020) Carl Leake et al.   Mathematics

Bijective Mapping Analysis to Extend the Theory of Functional Connections to Non-Rectangular 2-Dimensional Domains

(2020) Daniele Mortari et al.   Mathematics

On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton–Jacobi partial differential equations

(2020) Jérôme Darbon et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Neural network algorithm based on Legendre improved extreme learning machine for solving elliptic partial differential equations

(2019) Yunlei Yang et al.   SOFT COMPUTING

GLAM Bio-Lith RT: A Tool for Remote Sensing Reflectance Simulation and Water Components Concentration Retrieval in Glacial Lakes

(2019) Enrico Schiassi et al.   Frontiers in Earth Science

Physics-informed neural networks for high-speed flows

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

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

Solving Partial Differential Equation Based on Bernstein Neural Network and Extreme Learning Machine Algorithm

(2018) Hongli Sun et al.   NEURAL PROCESSING LETTERS

Numerical solution for ruin probability of continuous time model based on neural network algorithm

(2018) Zhou Tao et al.   NEUROCOMPUTING

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

(2018) Jens Berg et al.   NEUROCOMPUTING

A novel improved extreme learning machine algorithm in solving ordinary differential equations by Legendre neural network methods

(2018) Yunlei Yang et al.   Advances in Difference Equations

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

High accuracy least-squares solutions of nonlinear differential equations

(2018) Daniele Mortari et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Single Layer Chebyshev Neural Network Model for Solving Elliptic Partial Differential Equations

(2016) Susmita Mall et al.   NEURAL PROCESSING LETTERS

Bayesian inversion of coupled radiative and heat transfer models for asteroid regoliths and lakes

(2016) Enrico Schiassi et al.   Radiation Effects and Defects in Solids

The response matrix discrete ordinates solution to the 1D radiative transfer equation

(2015) Barry D. Ganapol   JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER

Picard Iteration, Chebyshev Polynomials and Chebyshev-Picard Methods: Application in Astrodynamics

(2015) John L. Junkins et al.   JOURNAL OF THE ASTRONAUTICAL SCIENCES