Improving the accuracy of the deep energy method

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

Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement

Thomas J.R. Hughes, J. Austin Cottrell, Yuri Bazilevs · Computer Methods in Applied Mechanics and Engineering · 2005 · 6.2K citations · Full text

Computing, Computational Engineering, Computer Science +17

The finite element method. Linear static and dynamic finite element analysis

Thomas Zimmermann · Computer Methods in Applied Mechanics and Engineering · 1987 · 5.1K citations

Engineering, Computational Engineering, Mechanical Engineering +12

Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Nature Machine Intelligence · 2021 · 2.8K citations · Full text

Computing, Computer Science, Mathematics +10

Artificial neural networks for solving ordinary and partial differential equations

IEEE Transactions on Neural Networks · 1998 · 2.2K citations · Full text

Natural Sciences, Computational Engineering, Computer Science +17