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[2508.01101] Fast and Flexible Probabilistic Forecasting of Dynamical Systems using Flow Matching and Physical Perturbation
Summary
This article presents a novel framework for probabilistic forecasting of dynamical systems, utilizing flow matching and physical perturbation to enhance accuracy and efficiency.
Why It Matters
The research addresses the challenges of forecasting in dynamical systems, particularly when data is incomplete or noisy. By improving the generation of perturbations and reducing computational costs, this framework has significant implications for fields relying on predictive modeling, such as climate science and robotics.
Key Takeaways
- Introduces a flow matching-based approach for generating physically consistent perturbations.
- Decouples perturbation generation from propagation for enhanced efficiency.
- Achieves state-of-the-art performance in probabilistic scoring and physical consistency.
- Validates the method on established benchmarks, outperforming diffusion-based models.
- Offers faster inference times, making it practical for real-world applications.
Computer Science > Machine Learning arXiv:2508.01101 (cs) [Submitted on 1 Aug 2025 (v1), last revised 26 Feb 2026 (this version, v2)] Title:Fast and Flexible Probabilistic Forecasting of Dynamical Systems using Flow Matching and Physical Perturbation Authors:Siddharth Rout, Eldad Haber, Stephane Gaudreault View a PDF of the paper titled Fast and Flexible Probabilistic Forecasting of Dynamical Systems using Flow Matching and Physical Perturbation, by Siddharth Rout and 2 other authors View PDF HTML (experimental) Abstract:Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture uncertainty, standard Gaussian or uniform perturbations often yield unphysical initial states in high-dimensional systems. Existing machine learning approaches address this via diffusion models, which rely on inference via computationally expensive stochastic differential equations (SDEs). We introduce a novel framework that decouples perturbation generation from propagation. First, we propose a flow matching-based generative approach to learn physically consistent perturbations of the initial conditions, avoiding artifacts caused by Gaussian noise. Second, we employ deterministic flow matching models with Ordinary Differential Equation (ODE) integrators for efficient ensemble propagation with fewer integration steps. We...
