PHAST: Port-Hamiltonian Architecture for Structured Temporal Dynamics Forecasting

2026-02-20

AI Summary

This work proposes the PHAST architecture for discrete-time series observed only in generalized coordinates (q-only), explicitly separating conservative and dissipative dynamics within a port-Hamiltonian framework. By leveraging Strang splitting for time evolution and integrating low-rank positive semi-definite/definite parameterizations with three knowledge-based modeling paradigms, the method achieves both long-term predictive stability and physical parameter identifiability. Notably, it is the first to reveal the gauge freedom inherent in unanchored parameter identification under q-only observations. Evaluated across 13 benchmark systems spanning mechanical, electrical, and molecular domains, PHAST significantly outperforms existing approaches and accurately recovers physically meaningful system parameters when sufficient structural priors are available.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Relational Probabilistic Models

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• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

Abstract

Real physical systems are dissipative -- a pendulum slows, a circuit loses charge to heat -- and forecasting their dynamics from partial observations is a central challenge in scientific machine learning. We address the \emph{position-only} (q-only) problem: given only generalized positions~$q_t$ at discrete times (momenta~$p_t$ latent), learn a structured model that (a)~produces stable long-horizon forecasts and (b)~recovers physically meaningful parameters when sufficient structure is provided. The port-Hamiltonian framework makes the conservative-dissipative split explicit via $\dot{x}=(J-R)\nabla H(x)$, guaranteeing $dH/dt\le 0$ when $R\succeq 0$. We introduce \textbf{PHAST} (Port-Hamiltonian Architecture for Structured Temporal dynamics), which decomposes the Hamiltonian into potential~$V(q)$, mass~$M(q)$, and damping~$D(q)$ across three knowledge regimes (KNOWN, PARTIAL, UNKNOWN), uses efficient low-rank PSD/SPD parameterizations, and advances dynamics with Strang splitting. Across thirteen q-only benchmarks spanning mechanical, electrical, molecular, thermal, gravitational, and ecological systems, PHAST achieves the best long-horizon forecasting among competitive baselines and enables physically meaningful parameter recovery when the regime provides sufficient anchors. We show that identification is fundamentally ill-posed without such anchors (gauge freedom), motivating a two-axis evaluation that separates forecasting stability from identifiability.

Problem

• dissipative systems
• position-only forecasting
• physical parameter recovery
• long-horizon prediction
• partial observations

Innovation

• port-Hamiltonian
• structured forecasting
• dissipative dynamics
• parameter identifiability
• Strang splitting