Stochastic Flow Matching for Resolving Small-Scale Physics

• URL: http://arxiv.org/abs/2410.19814v1
• Date: Thu, 17 Oct 2024 21:09:13 GMT
• Title: Stochastic Flow Matching for Resolving Small-Scale Physics
• Authors: Stathi Fotiadis, Noah Brenowitz, Tomas Geffner, Yair Cohen, Michael Pritchard, Arash Vahdat, Morteza Mardani,
• Abstract summary: In physical sciences such as weather, super-resolving small-scale details poses significant challenges. We propose encoding the inputs to a latent base distribution, followed by flow matching to generate small-scale physics. We conduct extensive experiments on both the real-world CWA weather dataset and the PDE-based Kolmogorov dataset.
• Score: 28.25905372253442
• License:
• Abstract: Conditioning diffusion and flow models have proven effective for super-resolving small-scale details in natural images.However, in physical sciences such as weather, super-resolving small-scale details poses significant challenges due to: (i) misalignment between input and output distributions (i.e., solutions to distinct partial differential equations (PDEs) follow different trajectories), (ii) multi-scale dynamics, deterministic dynamics at large scales vs. stochastic at small scales, and (iii) limited data, increasing the risk of overfitting. To address these challenges, we propose encoding the inputs to a latent base distribution that is closer to the target distribution, followed by flow matching to generate small-scale physics. The encoder captures the deterministic components, while flow matching adds stochastic small-scale details. To account for uncertainty in the deterministic part, we inject noise into the encoder output using an adaptive noise scaling mechanism, which is dynamically adjusted based on maximum-likelihood estimates of the encoder predictions. We conduct extensive experiments on both the real-world CWA weather dataset and the PDE-based Kolmogorov dataset, with the CWA task involving super-resolving the weather variables for the region of Taiwan from 25 km to 2 km scales. Our results show that the proposed stochastic flow matching (SFM) framework significantly outperforms existing methods such as conditional diffusion and flows.

Related papers

• Physics-guided Active Sample Reweighting for Urban Flow Prediction [75.24539704456791]
  Urban flow prediction is a nuanced-temporal modeling that estimates the throughput of transportation services like buses, taxis and ride-driven models. Some recent prediction solutions bring remedies with the notion of physics-guided machine learning (PGML) We develop a atized physics-guided network (PN), and propose a data-aware framework Physics-guided Active Sample Reweighting (P-GASR)
  arXiv  Detail & Related papers  (2024-07-18T15:44:23Z)
• On the Trajectory Regularity of ODE-based Diffusion Sampling [79.17334230868693]
  Diffusion-based generative models use differential equations to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models.
  arXiv  Detail & Related papers  (2024-05-18T15:59:41Z)
• DifFlow3D: Toward Robust Uncertainty-Aware Scene Flow Estimation with Diffusion Model [20.15214479105187]
  We propose a novel uncertainty-aware scene flow estimation network (DifFlow3D) with the diffusion probabilistic model. Our method achieves an unprecedented millimeter-level accuracy (0.0078m in EPE3D) on the KITTI dataset.
  arXiv  Detail & Related papers  (2023-11-29T08:56:24Z)
• PSRFlow: Probabilistic Super Resolution with Flow-Based Models for Scientific Data [11.15523311079383]
  PSRFlow is a novel normalizing flow-based generative model for scientific data super-resolution. Our results demonstrate superior performance and robust uncertainty quantification compared with existing methods.
  arXiv  Detail & Related papers  (2023-08-08T22:10:29Z)
• A Geometric Perspective on Diffusion Models [57.27857591493788]
  We inspect the ODE-based sampling of a popular variance-exploding SDE. We establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm.
  arXiv  Detail & Related papers  (2023-05-31T15:33:16Z)
• Hierarchical Integration Diffusion Model for Realistic Image Deblurring [71.76410266003917]
  Diffusion models (DMs) have been introduced in image deblurring and exhibited promising performance. We propose the Hierarchical Integration Diffusion Model (HI-Diff), for realistic image deblurring. Experiments on synthetic and real-world blur datasets demonstrate that our HI-Diff outperforms state-of-the-art methods.
  arXiv  Detail & Related papers  (2023-05-22T12:18:20Z)
• The Score-Difference Flow for Implicit Generative Modeling [1.309716118537215]
  Implicit generative modeling aims to produce samples of synthetic data matching a target data distribution. Recent work has approached the IGM problem from the perspective of pushing synthetic source data toward the target distribution. We present the score difference between arbitrary target and source distributions as a flow that optimally reduces the Kullback-Leibler divergence between them.
  arXiv  Detail & Related papers  (2023-04-25T15:21:12Z)
• High-dimensional scaling limits and fluctuations of online least-squares SGD with smooth covariance [16.652085114513273]
  We derive high-dimensional scaling limits and fluctuations for the online least-squares Gradient Descent (SGD) algorithm. Our results have several applications, including characterization of the limiting mean-square estimation or prediction errors and their fluctuations.
  arXiv  Detail & Related papers  (2023-04-03T03:50:00Z)
• Reduced-order modeling for parameterized large-eddy simulations of atmospheric pollutant dispersion [0.0]
  Large-eddy simulations (LES) have the potential to accurately represent pollutant concentration spatial variability. LES become prohibitively costly to deploy to understand how plume flow and tracer dispersion change with various atmospheric and source parameters. We propose a non-intrusive reduced-order model combining proper decomposition (POD) and Gaussian process regression (GPR) to predict LES field statistics of interest associated with tracer concentrations.
  arXiv  Detail & Related papers  (2022-08-02T15:06:22Z)
• Efficient CDF Approximations for Normalizing Flows [64.60846767084877]
  We build upon the diffeomorphic properties of normalizing flows to estimate the cumulative distribution function (CDF) over a closed region. Our experiments on popular flow architectures and UCI datasets show a marked improvement in sample efficiency as compared to traditional estimators.
  arXiv  Detail & Related papers  (2022-02-23T06:11:49Z)
• Uncertainty Estimation Using a Single Deep Deterministic Neural Network [66.26231423824089]
  We propose a method for training a deterministic deep model that can find and reject out of distribution data points at test time with a single forward pass. We scale training in these with a novel loss function and centroid updating scheme and match the accuracy of softmax models.
  arXiv  Detail & Related papers  (2020-03-04T12:27:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.