Gaussian process regression + deep neural network autoencoder for probabilistic surrogate modeling in nonlinear mechanics of solids

2024-07-15

arXiv.org

AI Summary

To address low prediction accuracy and poor uncertainty quantification in high-dimensional nonlinear solid mechanics simulations, this paper proposes a coupled surrogate model—Deep Autoencoder–Gaussian Process (DAE-GP). The method uniquely integrates the nonlinear dimensionality reduction capability of deep autoencoders with the Bayesian regression and probabilistic uncertainty modeling capacity of Gaussian processes, thereby overcoming the longstanding challenge of jointly achieving high accuracy and reliable uncertainty estimation for complex, high-dimensional nonlinear responses. Driven by nonlinear finite element simulation data, the DAE-GP model significantly improves both predictive accuracy and computational efficiency while delivering physically interpretable, pointwise uncertainty estimates. Experimental results demonstrate its strong generalization and robustness under challenging scenarios involving complex boundary conditions and material nonlinearity. This work establishes a new paradigm for high-fidelity real-time simulation and reliability analysis in computational solid mechanics.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Many real-world applications demand accurate and fast predictions, as well as reliable uncertainty estimates. However, quantifying uncertainty on high-dimensional predictions is still a severely under-investigated problem, especially when input-output relationships are non-linear. To handle this problem, the present work introduces an innovative approach that combines autoencoder deep neural networks with the probabilistic regression capabilities of Gaussian processes. The autoencoder provides a low-dimensional representation of the solution space, while the Gaussian process is a Bayesian method that provides a probabilistic mapping between the low-dimensional inputs and outputs. We validate the proposed framework for its application to surrogate modeling of non-linear finite element simulations. Our findings highlight that the proposed framework is computationally efficient as well as accurate in predicting non-linear deformations of solid bodies subjected to external forces, all the while providing insightful uncertainty assessments.

Problem

• Complex Data Relationships
• Accurate Prediction
• Solid Stress Behavior

Innovation

• Autoencoder Neural Networks
• Gaussian Processes
• Prediction Uncertainty