Towards Learning from Multiple Low-Fidelity Models in Bayesian Inverse Analysis
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Physics-based computational models have immense predictive potential, especially when used as digital twins in data-scarce settings. To mimic the physical twin, the computational model needs to be calibrated, meaning its parameters need to be learned from data of the real-world system in question. Bayesian inverse analysis is a powerful framework for this calibration because it accounts for remaining parameter uncertainties. These uncertainties are then propagated to the model’s predictions, vitally informing real-world decisions based on the digital twin. Nevertheless, Bayesian inverse analysis remains challenging for many physics-based computational models. One challenge is the lack of informative data, which can be mitigated via multi-physics-enhanced Bayesian inverse analysis [1] or Bayesian optimal experimental design [2]. Another challenge is the high computational cost, especially when the number of inferred parameters is high or when model gradients are unavailable. Recent research has approached this via an efficient black-box variational inference scheme [3] or a multi-fidelity scheme that leverages low-fidelity models with gradients [4]. In particular, the latter approach holds great promise for integrating existing methods in active learning, surrogate modeling, and reduced-order modeling. Our research focuses on this integration and explores the benefits of combining these strategies. The central idea is to exploit several inexpensive, partially informative models and correct their predictions using an actively learned probabilistic correction model. Using multiple low-fidelity models has the potential to substantially reduce the computational cost of high-dimensional Bayesian inverse analysis based on non-differentiable computational models while maintaining reliable parameter estimates. Our findings suggest that this approach may serve as a viable pathway toward making digital twins more practical in complex, real-world settings. [1] Haeusel et al., Multi-physics-enhanced Bayesian inverse analysis: Information gain from additional fields, Comput. Methods Appl. Mech. Eng., 2026. [2] Ryan et al., A Review of Modern Computational Algorithms for Bayesian Optimal Design, Int. Stat. Rev., 2016. [3] Rei et al., A Black Box Variational Inference Scheme for...Demanding Physics-Based Models, arXiv, 2025. [4] Nitzler et al., Efficient Bayesian multi-fidelity inverse analysis for...high stochastic dimensions, Comput. Methods Appl. Mech. Eng., 2026.
