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.

翻译：真实物理系统具有耗散性——摆锤会减速，电路电荷会以热能形式耗散——而基于部分观测对其动力学进行预测是科学机器学习的核心挑战。我们针对仅位置问题：仅给定离散时间下的广义位置$q_t$（动量$p_t$为隐变量），学习一个结构化模型，使其能够（a）产生稳定的长时程预测，且（b）在提供充分结构信息时恢复具有物理意义的参数。端口-哈密顿框架通过$\dot{x}=(J-R)\nabla H(x)$显式表达保守-耗散分解，当$R\succeq 0$时保证$dH/dt\le 0$。我们提出PHAST，该架构将哈密顿量分解为势能$V(q)$、质量$M(q)$和阻尼$D(q)$三个知识域，涵盖已知、部分已知与未知三种情形，采用高效低秩PSD/SPD参数化方法，并利用Strang分裂推进动力学演化。在涵盖机械、电气、分子、热力学、引力及生态系统的十三项仅位置基准测试中，PHAST在竞争性基线中实现了最佳的长时程预测性能，并在知识域提供充分锚点时实现了具有物理意义的参数恢复。我们证明若无此类锚点（规范自由度），系统辨识本质上是病态的，由此提出将预测稳定性与可辨识性分离的双轴评估框架。