PIDM-DP: Physics-Informed Diffusion with Dormand-Prince Integration for Chaotic System Identification and State Reconstruction across Multiple Dynamical Regimes
arXiv:2605.26619v1 Announce Type: new Abstract: Reconstructing continuous state trajectories of chaotic dynamical systems from sparse, noisy observations remains a fundamental open problem in nonlinear science. We introduce the Physics-Informed Diffusion Model with Dormand-Prince Integration (PIDM-DP), which embeds a fully differentiable 5th-order Dormand-Prince (DP-RK45) ODE integrator directly into the reverse sampling loop of a Denoising Diffusion Probabilistic Model (DDPM). At each denoising step, physics residuals are back-propagated via automatic differentiation, constraining every gener
This paper leverages recent advancements in diffusion models and physics-informed machine learning to address a long-standing challenge in nonlinear science. The combination of differentiable ODE integrators with generative models represents an active research frontier.
Accurately reconstructing and understanding chaotic systems is critical for progress in diverse fields, from climate modeling and neuroscience to finance and engineering, enabling better prediction and control.
The ability to reconstruct continuous state trajectories from sparse and noisy data, even in chaotic systems, could significantly improve our capacity to model and predict complex phenomena where traditional methods struggle.
- · AI researchers
- · Climate scientists
- · Neuroscientists
- · Engineers in control systems
- · Traditional statistical modeling approaches for chaotic systems
Improved accuracy in predicting and understanding complex, chaotic natural and engineered systems.
Accelerated discovery and development in fields reliant on precise system identification and state estimation.
Potential for new autonomous control systems that can adapt and optimize in highly unpredictable environments.
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Read at arXiv cs.LG