[2403.13724] Probabilistic Forecasting with Stochastic Interpolants and Föllmer Processes

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Summary:We suggest a framework for probabilistic forecasting of dynamical techniques primarily based on generative modeling. Given observations of the system state over time, we formulate the forecasting downside as sampling from the conditional distribution of the longer term system state given its present state. To this finish, we leverage the framework of stochastic interpolants, which facilitates the development of a generative mannequin between an arbitrary base distribution and the goal. We design a fictitious, non-physical stochastic dynamics that takes as preliminary situation the present system state and produces as output a pattern from the goal conditional distribution in finite time and with out bias. This course of due to this fact maps a degree mass centered on the present state onto a probabilistic ensemble of forecasts. We show that the drift coefficient coming into the stochastic differential equation (SDE) reaching this process is non-singular, and that it may be realized effectively by sq. loss regression over the time-series knowledge. We present that the drift and the diffusion coefficients of this SDE will be adjusted after coaching, and {that a} particular selection that minimizes the impression of the estimation error offers a Föllmer course of. We spotlight the utility of our method on a number of complicated, high-dimensional forecasting issues, together with stochastically compelled Navier-Stokes and video prediction on the KTH and CLEVRER datasets.