Generalizing Dynamics Modeling More Easily from Representation Perspective

Authors: Yiming Wang, Zhengnan Zhang, Genghe Zhang, Jiawen Dan, Changchun Li, Chenlong Hu, Chris Nugent, Jun Liu, Ximing Li, Bo Yang Date: 2026-03-24 Paper ID: openalex:2603.22655

Summary

This work proposes the Pre-trained Dynamics EncoDER (PDEDER) to improve the generalization of neural dynamics modeling across different complex systems by learning a universal latent representation. PDEDER is pre-trained by minimizing the Lyapunov exponent objective, which encourages stability and structure in the latent dynamics space learned from a diverse corpus of 152 real-world and synthetic datasets. Auxiliary reconstruction and forecasting objectives are used to maintain fidelity against overly smoothed representations. The resulting encoder can then be quickly fine-tuned with specific dynamics models, showing strong generalizability in cross-domain forecasting benchmarks.

Key Contributions

• Introduced the Pre-trained Dynamics EncoDER (PDEDER), a generalized encoder that maps observations into a latent space suitable for capturing dynamics across diverse complex systems.
• Developed a novel pre-training methodology for PDEDER by minimizing the Lyapunov exponent objective to enforce locally stable and well-structured latent dynamics.
• Incorporated reconstruction and forecasting objectives during pre-training to prevent the latent space from becoming overly smoothed or losing essential dynamic information.
• Demonstrated significant effectiveness and generalizability of PDEDER across 12 dynamic systems in both in-domain and cross-domain short/long-term forecasting settings.

Limitations

The paper mentions the risk of obtaining an over-smoothed latent space, which is addressed by auxiliary objectives, but potential limitations in truly capturing highly chaotic or non-deterministic dynamics remain an implicit challenge.

Open Questions & Future Work

• lyapunov-exponent-invariance-under-latent-embedding
• optimal-balance-of-pde-der-pretraining-objectives

Key Concepts

• pretrained-dynamics-encoder-pdeder: A generalized encoder designed to map system observations into a latent space where dynamics are more easily captured, pre-trained using a Lyapunov exponent objective.
• lyapunov-exponent-pretraining-objective: A pre-training objective that minimizes the Lyapunov exponent of the learned latent dynamics to promote locally stable and structured representations.

Archivist Review

Archivist review kept only candidates judged central to the paper and reusable across future work. Approved 2 concept(s), 2 open question(s), and 0 dataset(s), with 2 rejected candidate note(s).

Approved Concepts

• Pre-trained Dynamics EncoDER: PDEDER is the core proposed architecture designed for generalized representation learning to ease subsequent dynamics modeling across different systems.
• Lyapunov Exponent Pre-training Objective: This objective directly constrains the learned latent space dynamics to be stable, which is a novel and specific method for improving generalization in dynamics modeling.

Approved Open Questions

• Lyapunov Exponent Invariance Preservation: Preserving the Lyapunov exponent’s invariance during embedding is crucial for latent space methods aiming to faithfully represent system chaos/stability, as non-invariance complicates interpretability and transferability of chaotic properties.
• Optimizing PDE-DER Pre-training Objectives: The interplay between learning stable latent dynamics (via MLE) and preserving fine-grained local information (via reconstruction/forecasting) is a key architectural tuning problem for representation-based dynamics modeling.

Rejected Candidates

• [concept] PLM Pre-training for Dynamics (pre-trained-language-model-adaptation) - subcomponent_of_broader_mechanism: The paper uses a PLM as an initialization/backbone for the encoder, but the novelty lies in the dynamics objectives (Lyapunov, reconstruction) applied to the resulting encoder, not the PLM adaptation itself.
• [open_question] System-Agnostic Data Projection (system-agnostic-data-projection-for-pde-der) - generic: The concept of improving generalization by removing system-specific projection layers during fine-tuning is a standard future direction for transfer learning, not a specific unresolved mechanism identified by the paper’s core novelty.

Links

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