# PhyxMamba: Chaotic System Reconstruction from Short Context Observations with Generative State-Space Models

arXiv: https://arxiv.org/abs/2505.23863 · HTML: https://mlsanity.com/paper/2505.23863/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 54 references that are in the map.
- First posted on arXiv 29 May 2025.

## Builds on (most cited first, 27 of 27)

- [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)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [PredRNN: A Recurrent Neural Network for Spatiotemporal Predictive Learning](https://mlsanity.com/paper/2103.09504/) (2021)
- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [TSMixer: Lightweight MLP-Mixer Model for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2306.09364/) (2023)
- [Is Mamba Effective for Time Series Forecasting?](https://mlsanity.com/paper/2403.11144/) (2024)
- [Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors](https://mlsanity.com/paper/2305.18803/) (2023)
- [Chaos as an interpretable benchmark for forecasting and data-driven modelling](https://mlsanity.com/paper/2110.05266/) (2021)
- [On the difficulty of learning chaotic dynamics with RNNs](https://mlsanity.com/paper/2110.07238/) (2021)
- [Generalized Teacher Forcing for Learning Chaotic Dynamics](https://mlsanity.com/paper/2306.04406/) (2023)
- [Training neural operators to preserve invariant measures of chaotic attractors](https://mlsanity.com/paper/2306.01187/) (2023)
- [DySLIM: Dynamics Stable Learning by Invariant Measure for Chaotic Systems](https://mlsanity.com/paper/2402.04467/) (2024)
- [Zero-shot forecasting of chaotic systems](https://mlsanity.com/paper/2409.15771/) (2024)
- [True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statistics](https://mlsanity.com/paper/2505.13192/) (2025)
- [Context parroting: A simple but tough-to-beat baseline for foundation models in scientific machine learning](https://mlsanity.com/paper/2505.11349/) (2025)
- [Parallel Machine Learning for Forecasting the Dynamics of Complex Networks](https://mlsanity.com/paper/2108.12129/) (2021)
- [Generative Pretrained Hierarchical Transformer for Time Series Forecasting](https://mlsanity.com/paper/2402.16516/) (2024)
- [Deep Time Series Forecasting with Shape and Temporal Criteria](https://mlsanity.com/paper/2104.04610/) (2021)
- [Toward Physics-guided Time Series Embedding](https://mlsanity.com/paper/2410.06651/) (2024)
- [Spatiotemporal Observer Design for Predictive Learning of High-Dimensional Data](https://mlsanity.com/paper/2402.15284/) (2024)

## Abstract (arXiv)

Understanding chaotic dynamics is a fundamental problem across scientific disciplines, including climate science, neuroscience, and fluid dynamics, yet direct experimentation and intervention in such systems are often infeasible. Chaotic system reconstruction aims to identify a surrogate dynamical model that preserves a system's invariant geometric and long-term temporal signatures from observed time series, thereby providing a controllable foundation for probing its mechanisms through systematic perturbation and analysis. However, faithful system reconstruction is hampered by high observational costs, which often restrict data to short, discontinuous sequences spanning only limited timescales. Conventional approaches such as reservoir computing struggle in this data-scarce regime since they typically require long-term synchronization windows to localize states on the attractor. Similarly, while deep learning-based time-series forecasting models effectively fit local trajectories, they often fail to capture global invariants, leading to a collapse of long-term dynamical integrity. Here, we propose PhyxMamba, a framework that synergizes Mamba-based state-space models with physics-informed principles. By leveraging time-delay embeddings to reconstruct the attractor manifold and employing a generative training scheme with geometry-aware regularization, PhyxMamba effectively captures both fine-grained local evolution and global physical constraints. Extensive experiments on simulated and real-world chaotic systems demonstrate that PhyxMamba achieves superior reconstruction performance, outperforming the strongest baseline by over 44% in prediction accuracy and 8% in topological fidelity on the Lorenz96 system, while exhibiting strong robustness against partial observations and noise. Codes are available at https://github.com/changliu01/PhyxMamba.