Mamba Integrated with Physics Principles Masters Long-term Chaotic System Forecasting
Chang Liu, Bohao Zhao, Jingtao Ding, Huandong Wang, Yong Li

TL;DR
PhyxMamba is a novel framework combining a Mamba-based state-space model with physics-informed principles to improve long-term forecasting of chaotic systems from limited short-term data.
Contribution
It introduces a physics-informed, Mamba-based approach with attractor reconstruction and regularization for enhanced long-term chaotic system prediction.
Findings
Outperforms existing methods in forecasting accuracy.
Successfully captures key statistical properties of chaotic systems.
Effective on both simulated and real-world data.
Abstract
Long-term forecasting of chaotic systems remains a fundamental challenge due to the intrinsic sensitivity to initial conditions and the complex geometry of strange attractors. Conventional approaches, such as reservoir computing, typically require training data that incorporates long-term continuous dynamical behavior to comprehensively capture system dynamics. While advanced deep sequence models can capture transient dynamics within the training data, they often struggle to maintain predictive stability and dynamical coherence over extended horizons. Here, we propose PhyxMamba, a framework that integrates a Mamba-based state-space model with physics-informed principles to forecast long-term behavior of chaotic systems given short-term historical observations on their state evolution. We first reconstruct the attractor manifold with time-delay embeddings to extract global dynamical…
Peer Reviews
Decision·Submitted to ICLR 2026
The paper has the following strengths worth credits: 1. Both simulation and real benchmarks are evaluated to demonstrate the generalisation of PhyxMamba on chaos systems; 2. Building physics constrained Mamba model for chaos systems learning is a novel attempt. 3. Introducing the multi-patch prediction induced learning constraint is a novel attempt.
The paper should be improved considering the following facts: 1. The paper evaluates PhyxMamba on simulated ODE chaos systems, not covering simulated PDE chaos systems and more high-dimensional cases, which is a significant overclaim of PhyxMamba as a framework for chaotic systems. 2. Motivations are not clear. The necesscity of using short history input compared with 1-step input in the literature is not specified. To which concern that predicting autoregressively with Mamba is important/adva
The Maximum Mean Discrepancy (MMD) regularizer is a nice approach. While this has previously been applied to time series datasets, it is not a widely-known method in this setting, and it appears to improve the author’s model’s performance on this dataset. The residual stacking approach in the Mamba blocks is a great idea. This approach is inspired by the NBEATS papers, and it seems to help in this case. I found the paper clear, well-structured, and easy-to-follow. The related work section cove
1. The architecture seems ad hoc, like a collection of methods combined together, and I do not feel that it inherits the simplicity or theoretical advantages of Mamba2 and other models like it. The methods section describes a very complicated architecture and multistage training loop. The authors first perform multi-patch next step prediction with teacher forcing. They then perform student forcing, checking that the model’s own predictions capture long-term structure. During the latter loop, the
Forecasting chaotic systems is a challenging and important problem in many domains. Adapting general sequence modeling architectures such as Mamba to chaotic systems is interesting and might lead to new directions in scientific machine learning.
* The baselines are incomplete. In particular, the authors did not compare with foundation models designed for dynamical systems, such as Panda (Lai et al. 2025) and DynaMix (Hemmer and Durstewitz 2025). It may also be interesting to compare with recently proposed naive baselines such as context parroting (Zhang and Gilpin 2025). * The datasets for the benchmark only contain five systems, three of them low-dimensional toy systems, which is inadequate. To demonstrate the robustness of the conclus
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Taxonomy
TopicsComputational Physics and Python Applications
MethodsFocus · Mamba: Linear-Time Sequence Modeling with Selective State Spaces
