Scale-Adaptive Generative Flows for Multiscale Scientific Data

2025-09-02

AI Summary

Standard normalizing flows struggle to model fine-scale features in multiscale scientific data—such as broadband random fields or PDE solutions—often introducing numerical ill-conditioning and high reconstruction error. To address this, we propose Scale-Adaptive Flow (SA-Flow): a novel generative flow framework that, for the first time, aligns the noise spectral decay rate with the target data’s Fourier spectrum within a stochastic interpolation setting to regularize the initial drift field; and introduces a spectrum-aware adaptive time scheduling strategy to enable progressive, cross-scale feature modeling. SA-Flow integrates Fourier spectral analysis, non-Gaussian noise modeling, and normalizing flow architecture. Evaluated on Gaussian random fields and solutions to the Allen–Cahn and Navier–Stokes equations, it achieves significantly improved sample fidelity while reducing computational cost by 30–50% compared to conventional flow-based methods.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Flow-based generative models can face significant challenges when modeling scientific data with multiscale Fourier spectra, often producing large errors in fine-scale features. We address this problem within the framework of stochastic interpolants, via principled design of noise distributions and interpolation schedules. The key insight is that the noise should not be smoother than the target data distribution -- measured by Fourier spectrum decay rates -- to ensure bounded drift fields near the initial time. For Gaussian and near-Gaussian distributions whose fine-scale structure is known, we show that spectrum-matched noise improves numerical efficiency compared to standard white-noise approaches. For complex non-Gaussian distributions, we develop scale-adaptive interpolation schedules that address the numerical ill-conditioning arising from rougher-than-data noise. Numerical experiments on synthetic Gaussian random fields and solutions to the stochastic Allen-Cahn and Navier-Stokes equations validate our approach and demonstrate its ability to generate high-fidelity samples at lower computational cost than traditional approaches.

Problem

• Modeling scientific data with multiscale Fourier spectra using generative flows
• Addressing large errors in fine-scale features via noise distribution design
• Improving numerical efficiency for Gaussian and non-Gaussian multiscale distributions

Innovation

• Spectrum-matched noise distribution for Gaussian data
• Scale-adaptive interpolation schedules for non-Gaussian data
• Stochastic interpolants framework with improved numerical efficiency