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

2025-11-06

AI Summary

This work addresses efficient probabilistic surrogate modeling for large-scale, partially observed dynamical systems—such as fluid flows governed by the Navier–Stokes equations—with the goal of generating high-fidelity 2D spatiotemporal slices from extremely sparse observations to enable real-time 3D inflow field synthesis. Methodologically, we conduct the first systematic comparison and extension of diverse generative paradigms—including direct distillation, progressive distillation, adversarial diffusion distillation, Wasserstein GANs, and rectified flow models—and introduce a novel coupling of flow matching with slice prediction to accommodate the intrinsic sparsity and high dimensionality of spatiotemporal PDE data. Evaluated on multiple challenging nonlinear dynamical systems, our framework reduces sampling cost by 10–50× while preserving physical consistency and predictive accuracy. The approach establishes a new paradigm for scalable PDE surrogate modeling and real-time boundary condition generation.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Natural Language Processing: Generation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

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.

Problem

• Forecasting partially-observed large-scale dynamical systems
• Reducing sampling steps in flow matching techniques
• Directly predicting 2D slices from 3D simulations

Innovation

• Extends flow matching to reduce sampling steps
• Compares distillation methods and generative networks
• Predicts 2D slices from 3D simulations efficiently