DeepPhysics: A physics aware deep learning framework for real‐time simulation. (15th March 2022)

• Record Type: Journal Article
• Authors: Odot, Alban; Haferssas, Ryadh; Cotin, Stephane
• Is Part Of: International journal for numerical methods in engineering. Volume 123:Number 10(2022)
• Page Start: 2381
• Page End: 2398
• Publication Date: 2022-03-15
• Subjects: deep learning -- finite element method -- neural network -- Newton–Raphson -- physics informed neural network -- real‐time; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6943
• Languages: English
• ISSNs: 0029-5981

Abstract

Abstract: Real‐time simulation of elastic structures is essential in many applications, from computer‐guided surgical interventions to interactive design in mechanical engineering. The finite element method is often used as the numerical method of reference for solving the partial differential equations associated with these problems. Deep learning methods have recently shown that they could represent an alternative strategy to solve physics‐based problems. In this article, we propose a solution to simulate hyper‐elastic materials using a data‐driven approach, where a neural network is trained to learn the nonlinear relationship between boundary conditions and the resulting displacement field. We also introduce a method to guarantee the validity of the solution. In total, we present three contributions: an optimized data set generation algorithm based on modal analysis, a physics‐informed loss function, and a hybrid Newton–Raphson algorithm. The method is applied to two benchmarks: a cantilever beam and a propeller. The results show that our network architecture trained with a limited amount of data can predict the displacement field in less than a millisecond. The predictions on various geometries, topologies, mesh resolutions, and boundary conditions are accurate to a few micrometers for nonlinear deformations of several centimeters of amplitude.