# Physics Consistency and Latent Dynamics in Spatiotemporal Physics Field Generation

arXiv: https://arxiv.org/abs/2505.11578 · HTML: https://mlsanity.com/paper/2505.11578/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Time series forecasting with SSMs, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 29 of its 44 references that are in the map.
- First posted on arXiv 16 May 2025.

## Placed in

- State-space sequence models (S4, Mamba) / [Time series forecasting with SSMs](https://mlsanity.com/ssm/time-series-forecasting-with-ssms/)

## Builds on (most cited first, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Robust Speech Recognition via Large-Scale Weak Supervision](https://mlsanity.com/paper/2212.04356/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Visual Prompt Tuning](https://mlsanity.com/paper/2203.12119/) (2022)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [MIONet: Learning multiple-input operators via tensor product](https://mlsanity.com/paper/2202.06137/) (2022)
- [PointMamba: A Simple State Space Model for Point Cloud Analysis](https://mlsanity.com/paper/2402.10739/) (2024)
- [Graph-Mamba: Towards Long-Range Graph Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2402.00789/) (2024)
- [DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problems](https://mlsanity.com/paper/2405.19143/) (2024)
- [Point Mamba: A Novel Point Cloud Backbone Based on State Space Model with Octree-Based Ordering Strategy](https://mlsanity.com/paper/2403.06467/) (2024)
- [PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks](https://mlsanity.com/paper/2307.11833/) (2023)
- [Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators](https://mlsanity.com/paper/2402.12365/) (2024)
- [Mamba YOLO: A Simple Baseline for Object Detection with State Space Model](https://mlsanity.com/paper/2406.05835/) (2024)
- [Machine learning for modelling unstructured grid data in computational physics: a review](https://mlsanity.com/paper/2502.09346/) (2025)

## Abstract (arXiv)

Data-driven models for spatiotemporal physical field generation, such as flow and acoustic fields, often deviate from governing equations and lack interpretability in latent temporal dynamics. To address these challenges, we propose HMT-PF, a hybrid Mamba-Transformer architecture for physical field generation. The framework incorporates a query-based gradient computation mechanism and a physics-informed fine-tuning strategy to enhance physical consistency. Analysis of the latent space reveals that the initial latent state vector evolves as an autonomous dynamical system under the Mamba backbone. Principal component analysis (PCA) indicates that a small number of dominant modes in initial latent state vector govern the key evolution patterns of the physical field, while a Jacobian-based temporal sensitivity analysis characterizes the intrinsic dynamical structure and stability of the latent evolution. Experiments across five benchmark datasets demonstrate strong performance, and physics-informed fine-tuning further reduces physical residuals, highlighting the effectiveness of the proposed latent-level fusion strategy. An empirical scaling law between prediction error and physical residual is identified, revealing a consistent exponential relationship in the low-error regime. Based on this observation, an dual-metric framework is proposed to jointly evaluate numerical accuracy and physical realism.