Efficient probabilistic surrogate modeling techniques for partially-observed large-scale dynamical systems

TL;DR

This paper explores advanced probabilistic surrogate modeling methods for large-scale dynamical systems governed by PDEs, focusing on reducing sampling steps and enabling efficient 2D slice predictions of 3D simulations.

Contribution

It compares various flow matching extensions and introduces techniques for efficient, high-dimensional system forecasting and 2D slice prediction in large-scale simulations.

Findings

Flow matching extensions reduce sampling steps.

Direct 2D slice prediction for 3D simulations demonstrated.

Comparison of distillation and adversarial methods for PDE-based systems.

Abstract

This paper is concerned with probabilistic techniques for forecasting dynamical systems described by partial differential equations (such as, for example, the Navier-Stokes equations). In particular, it is investigating and comparing various extensions to the flow matching paradigm that reduce the number of sampling steps. In this regard, it compares direct distillation, progressive distillation, adversarial diffusion distillation, Wasserstein GANs and rectified flows. Moreover, experiments are conducted on a set of challenging systems. In particular, we also address the challenge of directly predicting 2D slices of large-scale 3D simulations, paving the way for efficient inflow generation for solvers.