Uncertainty Quantification and Physical Consistency in Machine Learning

An event held by the SciML Community at Leeds Institute for Data Analytics

Speaker: Dr Honglin Wen, from Shanghai Jiao Tong University and Imperial College London

Scientific machine learning (SciML) has achieved remarkable progress in diverse domains—from weather forecasting to protein structure prediction. Yet, despite these successes in accuracy, major challenges remain in achieving trustworthiness. In particular, many current approaches lack rigorous uncertainty quantification and fail to ensure physical consistency, leading to unreliable extrapolations, violation of conservation laws, and limited transparency.

In this talk, I will discuss how ideas from probabilistic machine learning, Bayesian inference, and computational physics can provide a foundation for trustworthy SciML. I will review representative strategies for capturing uncertainty—ranging from Bayesian deep learning and ensemble methods—and methods for embedding physical structure, including constraint-preserving architectures and projection-based consistency layers. Building on these insights, I will discuss operator-based probabilistic modeling and open challenges, such as non-Gaussian field modeling and the interplay between data fidelity and physical laws.