Predicting partially observable dynamical systems via diffusion models with a multiscale inference scheme

• URL: http://arxiv.org/abs/2511.19390v1
• Date: Mon, 24 Nov 2025 18:30:04 GMT
• Title: Predicting partially observable dynamical systems via diffusion models with a multiscale inference scheme
• Authors: Rudy Morel, Francesco Pio Ramunno, Jeff Shen, Alberto Bietti, Kyunghyun Cho, Miles Cranmer, Siavash Golkar, Olexandr Gugnin, Geraud Krawezik, Tanya Marwah, Michael McCabe, Lucas Meyer, Payel Mukhopadhyay, Ruben Ohana, Liam Parker, Helen Qu, François Rozet, K. D. Leka, François Lanusse, David Fouhey, Shirley Ho,
• Abstract summary: In this paper, we tackle the probabilistic prediction of partially observable, long-memory dynamical systems.<n>We show that standard inference schemes, such as autoregressive rollouts, fail to capture long-range dependencies in the data.<n>Our method generates trajectories that are temporally fine-grained near the present and coarser as we move farther away.
• Score: 43.7203026580194
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at a given time represents only a small fraction of what is needed to predict future states, either due to measurement uncertainty or because only a small fraction of the state can be observed. This is true for example in solar physics, where we can observe the Sun's surface and atmosphere, but its evolution is driven by internal processes for which we lack direct measurements. In this paper, we tackle the probabilistic prediction of partially observable, long-memory dynamical systems, with applications to solar dynamics and the evolution of active regions. We show that standard inference schemes, such as autoregressive rollouts, fail to capture long-range dependencies in the data, largely because they do not integrate past information effectively. To overcome this, we propose a multiscale inference scheme for diffusion models, tailored to physical processes. Our method generates trajectories that are temporally fine-grained near the present and coarser as we move farther away, which enables capturing long-range temporal dependencies without increasing computational cost. When integrated into a diffusion model, we show that our inference scheme significantly reduces the bias of the predicted distributions and improves rollout stability.

Related papers

• Calibrating Geophysical Predictions under Constrained Probabilistic Distributions [4.760743517243988]
  We introduce a calibration algorithm based on normalization and the Kernelized Stein Discrepancy (KSD) to enhance machine learning predictions.<n>This not only sharpens pointwise predictions but also enforces consistency with non-local statistical structures rooted in physical principles.
  arXiv  Detail & Related papers  (2025-11-28T07:15:40Z)
• RainDiff: End-to-end Precipitation Nowcasting Via Token-wise Attention Diffusion [64.49056527678606]
  We propose a Token-wise Attention integrated into not only the U-Net diffusion model but also the radar-temporal encoder.<n>Unlike prior approaches, our method integrates attention into the architecture without incurring the high resource cost typical of pixel-space diffusion.<n>Our experiments and evaluations demonstrate that the proposed method significantly outperforms state-of-the-art approaches, robustness local fidelity, generalization, and superior in complex precipitation forecasting scenarios.
  arXiv  Detail & Related papers  (2025-10-16T17:59:13Z)
• Dynamical Diffusion: Learning Temporal Dynamics with Diffusion Models [71.63194926457119]
  We introduce Dynamical Diffusion (DyDiff), a theoretically sound framework that incorporates temporally aware forward and reverse processes.<n>Experiments across scientifictemporal forecasting, video prediction, and time series forecasting demonstrate that Dynamical Diffusion consistently improves performance in temporal predictive tasks.
  arXiv  Detail & Related papers  (2025-03-02T16:10:32Z)
• Probabilistic Forecasting with Stochastic Interpolants and Föllmer Processes [18.344934424278048]
  We propose a framework for probabilistic forecasting of dynamical systems based on generative modeling. We show that the drift and the diffusion coefficients of this SDE can be adjusted after training, and that a specific choice that minimizes the impact of the estimation error gives a F"ollmer process.
  arXiv  Detail & Related papers  (2024-03-20T16:33:06Z)
• Weather Prediction with Diffusion Guided by Realistic Forecast Processes [49.07556359513563]
  We introduce a novel method that applies diffusion models (DM) for weather forecasting. Our method can achieve both direct and iterative forecasting with the same modeling framework. The flexibility and controllability of our model empowers a more trustworthy DL system for the general weather community.
  arXiv  Detail & Related papers  (2024-02-06T21:28:42Z)
• DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting [18.86526240105348]
  We propose an approach for efficiently training diffusion models for probabilistic forecasting. We train a time-conditioned interpolator and a forecaster network that mimic the forward and reverse processes of standard diffusion models. Our approach performs competitively on probabilistic forecasting of complex dynamics in sea surface temperatures, Navier-Stokes flows, and flows spring systems.
  arXiv  Detail & Related papers  (2023-06-03T02:46:31Z)
• RNN with Particle Flow for Probabilistic Spatio-temporal Forecasting [30.277213545837924]
  Many classical statistical models often fall short in handling the complexity and high non-linearity present in time-series data. In this work, we consider the time-series data as a random realization from a nonlinear state-space model. We use particle flow as the tool for approximating the posterior distribution of the states, as it is shown to be highly effective in complex, high-dimensional settings.
  arXiv  Detail & Related papers  (2021-06-10T21:49:23Z)
• Learning Interpretable Deep State Space Model for Probabilistic Time Series Forecasting [98.57851612518758]
  Probabilistic time series forecasting involves estimating the distribution of future based on its history. We propose a deep state space model for probabilistic time series forecasting whereby the non-linear emission model and transition model are parameterized by networks. We show in experiments that our model produces accurate and sharp probabilistic forecasts.
  arXiv  Detail & Related papers  (2021-01-31T06:49:33Z)
• Physics-aware, probabilistic model order reduction with guaranteed stability [0.0]
  We propose a generative framework for learning an effective, lower-dimensional, coarse-grained dynamical model. We demonstrate its efficacy and accuracy in multiscale physical systems of particle dynamics.
  arXiv  Detail & Related papers  (2021-01-14T19:16:51Z)
• Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems [65.44033635330604]
  We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system. We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony. Results are presented for a test case using load data from an electrical grid.
  arXiv  Detail & Related papers  (2020-10-08T20:25:52Z)

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.