A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Maziar Raissi, Paris Perdikaris, George Em Karniadakis · Journal of Computational Physics · 2018 · 16.9K citations · Full text

Natural Sciences, Computer Science, Physics +16

On the distribution of points in a cube and the approximate evaluation of integrals

I. M. Sobol · USSR Computational Mathematics and Mathematical Physics · 1967 · 2.9K citations

Computing, Computer Science, Computational Geometry +11

A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code

Michael D. McKay, Richard J. Beckman, W. J. Conover · Technometrics · 2000 · 2.7K citations

Natural Sciences, Computer Science, Mathematics +17

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

Maziar Raissi, Alireza Yazdani, George Em Karniadakis · Science · 2020 · 2K citations · Full text

Computing, Computer Science, Physics +16

On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals

John H. Halton · Numerische Mathematik · 1960 · 2K citations

Natural Sciences, Computer Science, Probability Theory +10