PHAST: Port-Hamiltonian Architecture for Structured Temporal Dynamics Forecasting
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Abstract (arXiv)
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 position-only (q-only) problem: given only generalized positions~qt at discrete times (momenta~pt 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 dotx=(J-R)nabla H(x), guaranteeing dH/dt≤ 0 when Rsucceq 0. We introduce 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.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 20 of its 34 references that are in the map. First posted on arXiv 20 Feb 2026.
Builds on
20 of 34 references.
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8 more
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Citing papers per year: 2026: 2.
2 papers.