Predicting Dynamical Systems across Environments via Diffusive Model Weight Generation

2025-05-20

AI Summary

This work addresses zero-shot cross-environment prediction for dynamical systems—i.e., accurate dynamic modeling of unseen environments without access to target-environment trajectory data or prior environmental knowledge. We propose a diffusion-based, environment-conditioned weight generation mechanism that directly synthesizes prediction functions adapted to novel environments in parameter space. To mitigate the absence of environmental priors, we introduce physics-informed surrogate environment labels. Our approach integrates diffusion modeling, weight-space generation, an expert model library, and physics-constrained learning. With only 1 million parameters, it significantly outperforms a 500-million-parameter pretrained foundation model on multi-system cross-environment generalization tasks. To our knowledge, this is the first method enabling large-scale environmental adaptivity via a compact model, establishing a new paradigm for efficient, physics-aware zero-shot dynamical system forecasting.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Multiagent Systems: Adversarial Agents

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

Abstract

Data-driven methods offer an effective equation-free solution for predicting physical dynamics. However, the same physical system can exhibit significantly different dynamic behaviors in various environments. This causes prediction functions trained for specific environments to fail when transferred to unseen environments. Therefore, cross-environment prediction requires modeling the dynamic functions of different environments. In this work, we propose a model weight generation method, exttt{EnvAd-Diff}. exttt{EnvAd-Diff} operates in the weight space of the dynamic function, generating suitable weights from scratch based on environmental condition for zero-shot prediction. Specifically, we first train expert prediction functions on dynamic trajectories from a limited set of visible environments to create a model zoo, thereby constructing sample pairs of prediction function weights and their corresponding environments. Subsequently, we train a latent space diffusion model conditioned on the environment to model the joint distribution of weights and environments. Considering the lack of environmental prior knowledge in real-world scenarios, we propose a physics-informed surrogate label to distinguish different environments. Generalization experiments across multiple systems demonstrate that a 1M parameter prediction function generated by exttt{EnvAd-Diff} outperforms a pre-trained 500M parameter foundation model.

Problem

• Predicting dynamical systems across varying environments
• Generating model weights for zero-shot cross-environment prediction
• Overcoming performance drop in unseen environments without prior knowledge

Innovation

• Generates model weights dynamically for environments
• Uses diffusion model for joint weight-environment distribution
• Employs physics-informed labels without environmental priors