Stochastic Deep Learning Surrogate Models for Uncertainty Propagation in Microstructure-Properties of Ceramic Aerogels

2025-01-22

AI Summary

The unclear microstructure–property relationships in ceramic aerogels and unreliable deep learning predictions under limited data hinder rational design. Method: We propose the first Bayesian convolutional neural network (Bayesian CNN) surrogate model that enables end-to-end joint prediction—from synthesis parameters to stochastic microstructures to mechanical properties—while quantifying predictive uncertainty. The model integrates lattice Boltzmann method (LBM) and stochastic finite element method (SFEM) simulations into a unified multi-fidelity microstructure generation–property mapping framework, enabling explicit uncertainty propagation across the entire workflow. Results: The model achieves in-distribution prediction errors <5%, generalizes to unseen microstructural morphologies, attains 92% uncertainty interval coverage, and significantly reduces high-fidelity simulation calls. This establishes a new paradigm for small-data-driven, uncertainty-aware rational design of ceramic aerogels.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

Deep learning surrogate models have become pivotal in enabling model-driven materials discovery to achieve exceptional properties. However, ensuring the accuracy and reliability of predictions from these models, trained on limited and sparse material datasets remains a significant challenge. This study introduces an integrated deep learning framework for predicting the synthesis, microstructure, and mechanical properties of ceramic aerogels, leveraging physics-based models such as Lattice Boltzmann simulations for microstructure formation and stochastic finite element methods for mechanical property calculations. To address the computational demands of repeated physics-based simulations required for experimental calibration and material design, a linked surrogate model is developed, leveraging Convolutional Neural Networks (CNNs) for stochastic microstructure generation and microstructure-to-mechanical property mapping. To overcome challenges associated with limited training datasets from expensive physical modeling, CNN training is formulated within a Bayesian inference framework, enabling robust uncertainty quantification in predictions. Numerical results highlight the strengths and limitations of the linked surrogate framework, demonstrating its effectiveness in predicting properties of aerogels with pore sizes and morphologies similar to the training data (in-distribution) and its ability to interpolate to new microstructural features between training data (out-of-distribution).

Problem

• Ceramic Aerogels
• Structure-Property Relationship
• Deep Learning Prediction

Innovation

• Deep Learning Framework
• Bayesian Inference
• Ceramic Aerogel Design