Simulation of hyperelastic materials in real-time using deep learning

• Published in: Medical image analysis Vol. 59; p. 101569
• Main Authors: Mendizabal, Andrea, Márquez-Neila, Pablo, Cotin, Stéphane
• Format: Journal Article
• Language: English
• Published: Netherlands Elsevier B.V 01.01.2020; Elsevier BV; Elsevier
• Subjects: Algorithms; Artificial Intelligence; Artificial neural networks; Cantilever beams; Cantilevers; Computer applications; Computer Science; Computer simulation; Computing costs; Contact force; Decomposition; Deep learning; Deep neural networks; Domain decomposition methods; Finite element method; Hyperelasticity; Learning algorithms; Machine learning; Mathematical models; Mechanics; Mechanics of materials; Meshing; Model reduction; Neural networks; Nonlinear programming; Numerical methods; Physics; Physics-based simulation; Proper Orthogonal Decomposition; Real-time simulation; Reduced order model; Topology; Finite element method; Deep neural networks; Physics-based simulation; Reduced order model; Real-time simulation; Hyperelasticity; Deep neural network; Deep neural net- works; Re- duced order model; Model reduction
• ISSN: 1361-8415; 1361-8423
• DOI: 10.1016/j.media.2019.101569

•Average error is bellow 1 mm for deformation amplitudes 1000 times larger.•Computation time bellow 4 ms for the deformed configuration of the static problem.•The method can be applied to any linear or non-linear elastic model.•The method outperforms Proper Orthogonal Decomposition techniques. [Display omitted] The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition, parallel computing, adaptive meshing, and model order reduction. In this paper we present U-Mesh: A data-driven method based on a U-Net architecture that approximates the non-linear relation between a contact force and the displacement field computed by a FEM algorithm. We show that deep learning, one of the latest machine learning methods based on artificial neural networks, can enhance computational mechanics through its ability to encode highly non-linear models in a compact form. Our method is applied to three benchmark examples: a cantilever beam, an L-shape and a liver model subject to moving punctual loads. A comparison between our method and proper orthogonal decomposition (POD) is done through the paper. The results show that U-Mesh can perform very fast simulations on various geometries and topologies, mesh resolutions and number of input forces with very small errors.