PHAST: Port-Hamiltonian Architecture for Structured Temporal Dynamics Forecasting

TL;DR

This paper introduces PHAST, a port-Hamiltonian based neural architecture for forecasting structured physical system dynamics from position-only data, ensuring stability and meaningful parameter recovery.

Contribution

PHAST is a novel structured neural model that decomposes Hamiltonians into potential, mass, and damping components across different knowledge regimes, enabling stable long-term forecasting and parameter interpretability.

Findings

Achieves state-of-the-art long-horizon forecasting across diverse physical systems.

Enables physically meaningful parameter recovery with sufficient structural anchors.

Identifies the fundamental ill-posedness of parameter identification without anchors.

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.