Probabilistic deep learning for real-time large deformation simulations

DOI10.1016/j.cma.2022.115307OpenAlexW4285082580MaRDI QIDQ2160483

Jakub Lengiewicz, Saurabh Deshpande, Stéphane Pierre Alain Bordas

Publication date: 3 August 2022

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.01867

zbMATH Keywords

finite element methodlarge deformationsBayesian inferencereal-time simulationsconvolutional neural networkBayesian deep learning

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Probabilistic models, generic numerical methods in probability and statistics (65C20)

Related Items (2)

Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: application to planar soft tissues ⋮ Identification of material parameters and traction field for soft bodies in contact

Uses Software

• Gmsh
• TensorFlow
• Keras
• Adam
• GitHub
• MeshCNN
• U-Net
• MgNet
• DeepONet

Cites Work

• Unnamed Item
• A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics
• Bridging proper orthogonal decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems
• DeepONet
• Bayesian learning for neural networks
• A Bayesian multiscale CNN framework to predict local stress fields in structures with microscale features
• Quantifying the uncertainty in a hyperelastic soft tissue model with stochastic parameters
• An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• MgNet: a unified framework of multigrid and convolutional neural network
• A nonlinear manifold-based reduced order model for multiscale analysis of heterogeneous hyperelastic materials
• Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
• A method of finite element tearing and interconnecting and its parallel solution algorithm
• Model order reduction for hyperelastic materials
• The Mathematical Theory of Finite Element Methods

This page was built for publication: Probabilistic deep learning for real-time large deformation simulations