Scientific Machine Learning (SciML)

Scientific Machine Learning (SciML) is increasingly essential in the engineering sciences due to the complexity of engineering systems. Purely first-principles models often too expensive to perform uncertainty quantification tasks, while purely data-driven methods may yield unphysical results. SciML seeks to bridge this gap by integrating physical laws, structural constraints, and observational data into unified computational models. In our group, we view SciML as a broad design space encompassing Gaussian processes with embedded physics, structure-preserving and symmetry-aware models, physics-based surrogate and reduced-order methods, and more. A central pillar of our work is information field theory, which provides a principled Bayesian framework for learning over infinite-dimensional fields while rigorously quantifying uncertainty. Our goal is to develop scalable, trustworthy models that respect governing equations and conservation laws while remaining adaptive to data and model-form uncertainty.