We will have a meeting on Friday (February 13) at 3pm in SAS 5270 with speaker Carter Hall.
Title: Probabilistic B-Spline Modeling for Uncertainty Quantification in Ordinary Differential Equations
Abstract: Uncertainty quantification for ordinary differential equation (ODE) models arises from both the latent system trajectories and the parameters governing the underlying dynamics. While Bayesian approaches to ODE model discovery emphasize identification of governing equations, they often obscure the interpretability and uncertainty associated with model parameters. In contrast, nonparametric approaches based on B-spline approximations typically rely on fixed knot configurations, thereby neglecting uncertainty in the solution representation itself. We propose a non-standard probabilistic prior that explicitly encodes the fidelity of a B-spline approximation to known governing equations, enabling coherent uncertainty quantification for both states and parameters. Computational tractability is achieved through an approximation that yields conditionally Gaussian block updates for spline coefficients and model parameters, implemented within an orthogonalized B-spline basis. The proposed framework is demonstrated on both scalar- and vector-valued ODE systems exhibiting varying degrees of linearity in states and parameters.