Multi-Fidelity Bayesian machine learning with uncertainty disentanglement for material modeling and design

Abstract

Machine learning delivers strong predictive performance in scientific and engineering tasks when high-fidelity data are abundant. Yet, real-world models seldom quantify aleatoric (data) and epistemic (model) uncertainties, leading to overfitting on noisy inputs. In addition, collecting adequate high-fidelity data is often expensive or infeasible, whereas low-fidelity data are more accessible but less reliable. To address these challenges, this thesis proposes a general multi-fidelity Bayesian learning framework that enables trustworthy uncertainty disentanglement, and extends its application to constitutive modeling and design of recycled composite materials.

The thesis begins with an introduction to regression from a Bayesian perspective, establishing the connection between deterministic and probabilistic treatments, and covering models from linear to kernel and deep neural network regressions. This chapter provides the theoretical foundation for the remainder of the thesis by formalizing inference techniques, uncertainty quantification strategies, and model evaluation metrics.

Two core machine learning methods are developed to tackle the challenges of uncertainty estimation and multi-fidelity data fusion. First, a cooperative training scheme is proposed that combines a variance estimation neural network with a Bayesian mean neural network, enabling explicit disentanglement of aleatoric and epistemic uncertainties while improving mean prediction. The approach demonstrates strong scalability and generality across tasks and network architectures. Second, a practical multi-fidelity Bayesian learning framework is introduced, which fuses low- and high-fidelity data via a deterministic model, a transfer-learning module, and a Bayesian residual learner. This architecture balances expressiveness and computational efficiency, yielding robust predictions in both data-scarce and data-rich regimes.

To support data-driven mechanics, the proposed framework is extended to generalized constitutive modeling of history-dependent materials. A hierarchical learning scheme is developed that spans from single-fidelity deterministic networks to multi-fidelity Bayesian recurrent neural networks. This addresses two major limitations in data-driven modeling: the reliance on large, clean datasets and the lack of interpretability in neural network predictions.

Finally, the methodology is applied to the sustainable design of recycled composite polymers, where uncertainty arises from microstructural variability and the use of compatibilizers. Leveraging the cooperative training framework, both aleatoric and epistemic uncertainties are quantified, and a novel polymer design is optimized to achieve better expected performance and lower data variation.

Together, this thesis presents a unified and scalable framework for Bayesian learning under uncertainty and multi-fidelity conditions, with broad applicability in scientific computing, materials modeling, and sustainable engineering. The thesis concludes by summarizing key findings, discussing current limitations, and outlining future research directions.