14:30-15:30 So Takao.
Title: Improving data-assimilation for weather forecasting: A graph-based Bayesian perspective
Data assimilation plays a crucial role in weather forecasting by fusing physical models with observations to enhance forecast accuracy. However, achieving exact inference in this context is computationally infeasible due to the exceedingly large state dimension and observation size, as well as the nonlinearities that are present in the physical models. To address these challenges, we present a novel approach that casts data assimilation as Bayesian inference on a graph derived from the physical model. This in turn allows us to employ local message passing techniques for approximate inference, enabling us to utilise parallel computation across GPU threads, accelerating the compute time and reducing memory requirements. In this talk, we will showcase the initial results of our proposed method and discuss how our approach opens up new possibilities for advancing data assimilation techniques in weather forecasting.
Dr. So Takao is formerly a Senior Research Fellow at the Centre for Artificial Intelligence in University College London specialising in statistical machine learning. His main interests are in developing cutting-edge machine learning models with useful inductive biases, such as coming from physics or geometry, and adopting this to address complex challenges posed by weather/climate science. Prior to this, he obtained his PhD in Mathematics from Imperial College London under the mentorship of Professor Darryl Holm, where he focused on the development and analysis of stochastic fluid models using differential geometric techniques.
16:00-17:00 Michael Samuel Albergo.
Title: “Stochastic Interpolants: A Unifying Framework for Flows and Diffusions”
I will discuss recent work on unifying flow-based and diffusion based methods through a generative modeling paradigm we call stochastic interpolants. These models enable the use of a broad class of continuous-time stochastic processes called `stochastic interpolants’ to bridge any two arbitrary probability density functions exactly in finite time. The interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent probability density function of the stochastic interpolant is shown to satisfy a first-order transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion. Upon consideration of the time evolution of an individual sample, this viewpoint immediately leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise. The drift coefficients entering these models are time-dependent velocity fields characterized as the unique minimizers of simple quadratic objective functions, one of which is a new objective for the score of the interpolant density. Remarkably, we show that minimization of these quadratic objectives leads to control of the likelihood for any of our generative models built upon stochastic dynamics. By contrast, we establish that generative models based upon a deterministic dynamics must, in addition, control the Fisher divergence between the target and the model. We also construct estimators for the likelihood and the cross-entropy of interpolant-based generative models, discuss connections with other stochastic bridges, and demonstrate that such models recover the Schr”odinger bridge between the two target densities when explicitly optimizing over the interpolant.
|Date||August 18, 2023 (Fri) 14:30 - 17:00|