Application of a physics-informed neural network to solve the steady-state Bratu equation arising from solid biofuel combustion theory

Multilayer feedforward networks are universal approximators

Kurt Hornik, Maxwell B. Stinchcombe, Halbert White · Neural Networks · 1989 · 20.7K citations

Evolving Neural Network, Engineering, Machine Learning +5

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 · 14.4K citations · Full text

Engineering, Pde-constrained Optimization, Deep Learning Framework +6

On the approximate realization of continuous mappings by neural networks

Ken-ichi Funahashi · Neural Networks · 1989 · 4.2K citations

Artificial Intelligence, Evolving Neural Network, Engineering +9

Symmetry and related properties via the maximum principle

Basilis Gidas, Wei‐Ming Ni, Louis Nirenberg · Communications in Mathematical Physics · 1979 · 2.9K citations

Symmetry Principles, Symmetry (Physics), Extremal Set Theory +2

Automatic Differentiationin Machine Learning: a Survey

Atılım Güneş Baydin, Barak A. Pearlmutter, Alexey Radul et al. · MURAL - Maynooth University Research Archive Library (National University of Ireland, Maynooth) · 2018 · 2.1K citations