Probabilistic Deep Learning for Real-Time Large Deformation Simulations

TL;DR

This paper introduces a fast, deep-learning-based surrogate model using U-Net architecture for real-time simulation of large deformations, incorporating probabilistic uncertainty estimation via Variational Bayes.

Contribution

It presents a novel probabilistic deep learning framework for real-time large deformation simulations, combining U-Net with Variational Bayes for uncertainty quantification.

Findings

Accurately predicts large deformation responses in real-time

Effectively captures uncertainties in predictions

Demonstrates strong performance on benchmark examples

Abstract

For many novel applications, such as patient-specific computer-aided surgery, conventional solution techniques of the underlying nonlinear problems are usually computationally too expensive and are lacking information about how certain can we be about their predictions. In the present work, we propose a highly efficient deep-learning surrogate framework that is able to accurately predict the response of bodies undergoing large deformations in real-time. The surrogate model has a convolutional neural network architecture, called U-Net, which is trained with force-displacement data obtained with the finite element method. We propose deterministic and probabilistic versions of the framework. The probabilistic framework utilizes the Variational Bayes Inference approach and is able to capture all the uncertainties present in the data as well as in the deep-learning model. Based on several benchmark examples, we show the predictive capabilities of the framework and discuss its possible limitations