Oksana Chkrebtii - Simon Frasier University

Title: Probabilistic solution of differential equations for Bayesian uncertainty quantification and inference. Abstract: In many scientific disciplines the time and space evolution of variables can be naturally described by differential equation models, which define states implicitly as functions of their own rates of change. Prediction and inference require an explicit representation of the states (the solution), which is typically not available in closed form, but may be approximated by a variety of discretization-based numerical techniques. In this talk, I will introduce a new probabilistic framework for characterizing discretization uncertainty in models defined by high-dimensional systems of differential equations with unknown solutions. Viewing solution estimation as an inference problem allows us to quantify and propagate discretization error into uncertainty in the model parameters and subsequent predictions. Our formalism will be demonstrated on a wide range of challenging forward and inverse problems.