Seminar Title: Constrained Gaussian Processes with Continuous Linear Boundary Restrictions for Physics-informed Modeling of States
Abstract: Gaussian processes (GPs) are flexible statistical models for describing smooth, temporally or spatially varying states. A challenge in working with GPs is the difficulty of directly enforcing physical constraints while retaining modeling and computational flexibility. Boundary constraints arise in many physical, environmental, and engineering applications as fixed-state or fixed-derivative (insulated) boundary conditions, and restrictions that involve the state and the derivatives, such as in models of heat transfer. We develop a framework for constructing linearly boundary-constrained Gaussian processes over multi-dimensional domains by constructing custom linear transformations of unconstrained GPs of sufficient regularity. The framework is showcased in a variety of applications where boundary constraints add physically motivated information to the inference procedure and lead to performance improvements over their unconstrained counterparts including probabilistic numerics, data-driven discovery of dynamical systems, and inference on states with change points. We then consider the applied problem of recovering a displacement field given data from a tensile testing experiment, an important step for ensuring that materials used in industrial application meet safety and performance standards.
