Multi-Physics-Enhanced Bayesian Inverse Analysis: Information Gain from Additional Fields

2025-10-13

AI Summary

Limited single-physics measurement data lead to high parameter uncertainty in Bayesian inverse problems. Method: This paper proposes a multi-physics collaborative inversion framework that integrates weakly or unidirectionally coupled physical-field data (e.g., temperature, displacement, electric potential) without additional experimental cost. By extending finite-element-based multi-physics forward models and embedding them into a Bayesian inversion framework, the method enables joint probabilistic modeling of heterogeneous multi-source measurements and rigorous posterior uncertainty quantification. Contribution/Results: Experiments demonstrate that even sparse or noisy auxiliary field data significantly reduce posterior uncertainty of key parameters. The approach exhibits robustness and generality across both strongly and weakly coupled systems, as well as models of varying complexity, thereby enhancing inference reliability under data scarcity.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Machine Learning: Calibration & Uncertainty Quantification
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Mining multimedia, multimodal, multilingual, cross-lingual Web data
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Many real-world inverse problems suffer from limited data, often because they rely on measurements of a single physical field. Such data frequently fail to sufficiently reduce parameter uncertainty in Bayesian inverse analysis. Incorporating easily available data from additional physical fields can substantially decrease this uncertainty. We focus on Bayesian inverse analyses based on computational models, e.g., those using the finite element method. To incorporate data from additional physical fields, the computational model must be extended to include these fields. While this model extension may have little to no effect on forward model predictions, it can greatly enhance inverse analysis by leveraging the multi-physics data. Our work proposes this multi-physics-enhanced inverse approach and demonstrates its potential using two models: a simple model with one-way coupled fields and a complex computational model with fully coupled fields. We quantify the uncertainty reduction by comparing the effect of single-physics and multi-physics data on the information gain from the prior to the posterior. Our results show that even a few or noisy data points from an additional physical field can considerably increase the information gain, even if this field is weakly or one-way coupled. Although multi-physics data are often readily available, it is remarkable that their potential has been largely neglected in model calibration so far. Instead, costly and time-consuming additional experimental setups are often pursued. In contrast, incorporating multi-physics data requires minimal effort when multi-physics models are readily available or easy to implement, as is the case with uncoupled and one-way coupled models. This work proposes and promotes the future use of multi-physics-enhanced Bayesian inverse analysis as a cost- and time-saving game-changer across various fields of science and industry.

Problem

• Addresses limited data in Bayesian inverse analysis
• Incorporates multi-physics data to reduce uncertainty
• Enhances model calibration using additional physical fields

Innovation

• Incorporating multi-physics data to reduce parameter uncertainty
• Extending computational models to include additional physical fields
• Quantifying uncertainty reduction through multi-physics-enhanced Bayesian analysis