# PHAST: Port-Hamiltonian Architecture for Structured Temporal Dynamics Forecasting

arXiv: https://arxiv.org/abs/2602.17998 · HTML: https://mlsanity.com/paper/2602.17998/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 34 references that are in the map.
- First posted on arXiv 20 Feb 2026.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learning](https://mlsanity.com/paper/2002.08860/) (2020)
- [Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems](https://mlsanity.com/paper/2107.08024/) (2021)
- [Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately](https://mlsanity.com/paper/2201.10085/) (2022)
- [Recipes for when Physics Fails: Recovering Robust Learning of Physics Informed Neural Networks](https://mlsanity.com/paper/2110.13330/) (2021)
- [Pseudo-Hamiltonian neural networks for learning partial differential equations](https://mlsanity.com/paper/2304.14374/) (2023)
- [Learning to Dissipate Energy in Oscillatory State-Space Models](https://mlsanity.com/paper/2505.12171/) (2025)
- [Volume-Preserving Transformers for Learning Time Series Data with Structure](https://mlsanity.com/paper/2312.11166/) (2023)
- [Reinforcement Learning for Molecular Dynamics Optimization: A Stochastic Pontryagin Maximum Principle Approach](https://mlsanity.com/paper/2212.03320/) (2022)
- [Motion Code: Robust Time Series Classification and Forecasting via Sparse Variational Multi-Stochastic Processes Learning](https://mlsanity.com/paper/2402.14081/) (2024)
- [GRL-SNAM: Geometric Reinforcement Learning with Path Differential Hamiltonians for Simultaneous Navigation and Mapping in Unknown Environments](https://mlsanity.com/paper/2601.00116/) (2025)
- [Physics-informed neural networks via stochastic Hamiltonian dynamics learning](https://mlsanity.com/paper/2111.08108/) (2021)
- [A Differential and Pointwise Control Approach to Reinforcement Learning](https://mlsanity.com/paper/2404.15617/) (2024)
- [Learning Generalized Hamiltonian Dynamics with Stability from Noisy Trajectory Data](https://mlsanity.com/paper/2509.07280/) (2025)

## Built on by (most cited first, 2 of 2)

- [Identify then Realize: Contrastive Learning of Latent Port-Hamiltonian Dynamics from Partial Observations](https://mlsanity.com/paper/2605.16682/) (2026)
- [LaGSplat: Inferring Physics-Governed Interactive Simulation from Monocular Video Using Latent Lagrangian Gaussian Splatting](https://mlsanity.com/paper/2608.16324/) (2026)

## 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.