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

2025-11-24

AI Summary

Probabilistic forecasting of partially observable, long-memory dynamical systems—such as solar active region evolution—remains challenging, as conventional autoregressive methods struggle to integrate historical context and capture long-range temporal dependencies. Method: This paper proposes a physics-informed, multi-scale conditional diffusion model that jointly models fine-grained short-term dynamics and coarse-grained long-term trajectories along the time axis, explicitly encoding cross-scale temporal dependencies. Contribution/Results: Compared to standard autoregressive rollout, our approach significantly improves both predictive distribution accuracy and rollout stability. Evaluated on real solar physics data, it demonstrates superior capability in latent state inference and long-term evolution modeling. The framework provides an interpretable, robust paradigm for probabilistic forecasting of complex dynamical systems, bridging physical priors with scalable stochastic modeling.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• Predicting partially observable dynamical systems with limited measurement data
• Overcoming failure of standard methods to capture long-range temporal dependencies
• Developing multiscale inference scheme for diffusion models in physical processes

Innovation

• Multiscale inference scheme for diffusion models
• Generates fine-grained near present and coarser future
• Captures long-range dependencies without computational cost