| Time: | January 10, 2023, 5:30 p.m. (CET) |
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| The talk will take place online on January 10th, 2023, 17:30 on Webex (link below). | |
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We are pleased to announce our upcoming Distinguished Lecture Series talk by Simo Särkkä (Aalto University, Finnish Center for Artificial Intelligence)!
Probabilistic differential equation solving as Bayesian filtering and smoothing
The aim of the talk is to discuss probabilistic solvers for ordinary and partial differential equations (ODEs/PDEs) and their implementation using Bayesian filters and smoothers. Probabilistic numerical solving of ODEs can be formulated as Gaussian process (GP) regression, where the observations are derivatives of the vector field (i.e., the right-hand side) of the ODE. When the GP has a state-space representation, the problem can be reduced to a non-linear Bayesian filtering and smoothing problem. In particular, the iterated extended Kalman smoother (IEKS) can be used to compute maximum a posteriori (MAP) estimate of the solution along with its uncertainty. We also discuss the extension of the IEKS solution to PDEs of non-linear Cauchy type. In these models, the PDE can be approximated in the spatial direction using finite differences or basis function expansions, which then reduces the PDE to an ODE, where the IEKS solution can be applied.
Simo Särkkä is an Associate Professor at Aalto University, Finland. He is also a Fellow of European Laboratory for Learning and Intelligent Systems (ELLIS), member of the ELLIS Program for Theory, Algorithms and Computation, and member of ELLIS Unit Helsinki. He also leads the AI Across Fields (AIX) program of Finnish Center for Artificial Intelligence (FCAI). His and his group's research interests are in multi-sensor data processing systems which combine Bayesian statistics, stochastic processes, machine learning, and other interesting technology. His books "Bayesian Filtering and Smoothing" and "Applied Stochastic Differential Equations" have been published via the Cambridge University Press.