Scientific ML

Scientific machine learning studies how to use machine learning for scientific prediction, simulation, and discovery while accounting for governing equations, physical constraints, and measurement processes. Common approaches include physics-informed neural networks, neural operators, hybrid models that augment classical solvers, and symbolic methods for learning equations; differentiable solvers and uncertainty estimates support inference and decision-making. Applications span problems such as fluid dynamics, climate, chemistry, materials, and astronomy, often where data are sparse or simulations are expensive. A central challenge is that physical structure can improve reliability when correctly specified but mislead when it does not fit the system, so predictive accuracy must be weighed against physical fidelity, generalization, uncertainty, and careful validation.