Physics-based machine learning and uncertainty quantification

Complex scientific and engineering problems require models that are both physically consistent and statistically reliable. Neither purely data-driven machine learning nor purely physics-based modeling alone is sufficient. Our research integrates physics-based machine learning with principled uncertainty quantification (UQ) to build models that are interpretable, data-efficient, and decision-ready. By embedding physical laws and structured reasoning into learning architectures while rigorously accounting for uncertainty, we aim to develop intelligent systems that are not only predictive but also trustworthy for engineering design and discovery.

At the methodological level, we incorporate governing physics, domain constraints, and human-inspired reasoning mechanisms directly into ML architecture design to improve generalization and extrapolation. In parallel, we quantify both aleatoric uncertainty arising from intrinsic variability and epistemic uncertainty due to limited data or model inadequacy using Bayesian statistics and uncertainty-aware learning frameworks. This integrated approach has been applied to fatigue life modeling of metals and composites, probabilistic fatigue prediction in additive manufacturing considering process parameters and missing data, natural frequency prediction of bridges, nondestructive testing, automated materials characterization, and catalyst discovery.