Adaptive deep density approximation for Fokker-Planck equations

Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations

(2021) Suchuan Dong et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Coupling the reduced-order model and the generative model for an importance sampling estimator

(2020) Xiaoliang Wan et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

hp-VPINNs: Variational physics-informed neural networks with domain decomposition

(2020) Ehsan Kharazmi et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

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

(2020) Han Gao et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

One-shot generation of near-optimal topology through theory-driven machine learning

(2019) Ruijin Cang et al.   COMPUTER-AIDED DESIGN

Numerical aspects for approximating governing equations using data

(2019) Kailiang Wu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

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

Bayesian deep convolutional encoder–decoder networks for surrogate modeling and uncertainty quantification

(2018) Yinhao Zhu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Optimization Methods for Large-Scale Machine Learning

(2018) Léon Bottou et al.   SIAM REVIEW

DGM: A deep learning algorithm for solving partial differential equations

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

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

Constructing Surrogate Models of Complex Systems with Enhanced Sparsity: Quantifying the Influence of Conformational Uncertainty in Biomolecular Solvation

(2015) H. Lei et al.   MULTISCALE MODELING & SIMULATION

Stochastic Collocation Methods on Unstructured Grids in High Dimensions via Interpolation

(2012) Akil Narayan et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

A class of asymptotic-preserving schemes for the Fokker–Planck–Landau equation

(2011) Shi Jin et al.   JOURNAL OF COMPUTATIONAL PHYSICS

From Knothe's Transport to Brenier's Map and a Continuation Method for Optimal Transport

(2010) G. Carlier et al.   SIAM JOURNAL ON MATHEMATICAL ANALYSIS

An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations

(2009) Xiang Ma et al.   JOURNAL OF COMPUTATIONAL PHYSICS

The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications

(2008) Jasmine Foo et al.   JOURNAL OF COMPUTATIONAL PHYSICS