用物理守恒与耗散结构建模，让仅知位置的系统长期预测更稳定、参数可解释。
PHAST: Port-Hamiltonian Architecture for Structured Temporal Dynamics Forecasting
- 将哈密顿量分解为势能、质量与阻尼，分三种知识状态处理
- 在13个跨领域基准上实现最优长程预测性能
- 提供物理参数恢复能力，适合需可解释动力学的科研场景
真实物理系统具有耗散性——摆锤会减速，电路会因发热丢失电荷——从部分观测中预测其动态是科学机器学习的核心挑战。本文解决‘仅位置’（q-only）问题：仅已知离散时间点的广义位置 $q_t$（动量 $p_t$ 隐含），学习一个结构化模型，既能生成稳定的长期预测，又能在结构充分时恢复物理上合理的参数。基于端口-哈密顿框架 $oldsymbol{ ext{d}x/dt}=(J-R) abla H(x)$，显式分离保守与耗散部分，保证 $dH/dt\≤0$（当 $R\succeq 0$）。提出 extbf{PHAST}（Port-Hamiltonian Architecture for Structured Temporal dynamics），将哈密顿量分解为势能 $V(q)$、质量 $M(q)$、阻尼 $D(q)$，适配已知、部分已知、未知三类知识状态，采用高效低秩正定/半正定参数化，并通过Strang分裂推进动力学。在涵盖机械、电路、分子、热、引力及生态系统的13个 q-only 基准上，PHAST 在长程预测中超越主流基线，且在提供足够先验锚点时可恢复物理意义明确的参数。我们证明无锚点时识别问题本质病态（规范自由度），因此提出双轴评估，区分预测稳定性与可辨识性。
原文摘要 · Abstract (English)
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.
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