On Foundation Models for Dynamical Systems from Purely Synthetic Data

• URL: http://arxiv.org/abs/2412.00395v2
• Date: Tue, 17 Dec 2024 12:04:32 GMT
• Title: On Foundation Models for Dynamical Systems from Purely Synthetic Data
• Authors: Martin Ziegler, Andres Felipe Posada-Moreno, Friedrich Solowjow, Sebastian Trimpe,
• Abstract summary: Foundation models have demonstrated remarkable generalization, data efficiency, and robustness properties across various domains. These models are available in fields like natural language processing and computer vision, but do not exist for dynamical systems. We address this challenge by pretraining a transformer-based foundation model exclusively on synthetic data. Our results demonstrate the feasibility of foundation models for dynamical systems that outperform specialist models in terms of generalization, data efficiency, and robustness.
• Score: 5.004576576202551
• License:
• Abstract: Foundation models have demonstrated remarkable generalization, data efficiency, and robustness properties across various domains. In this paper, we explore the feasibility of foundation models for applications in the control domain. The success of these models is enabled by large-scale pretaining on Internet-scale datasets. These are available in fields like natural language processing and computer vision, but do not exist for dynamical systems. We address this challenge by pretraining a transformer-based foundation model exclusively on synthetic data and propose to sample dynamics functions from a reproducing kernel Hilbert space. Our pretrained model generalizes for prediction tasks across different dynamical systems, which we validate in simulation and hardware experiments, including cart-pole and Furuta pendulum setups. Additionally, the model can be fine-tuned effectively to new systems to increase performance even further. Our results demonstrate the feasibility of foundation models for dynamical systems that outperform specialist models in terms of generalization, data efficiency, and robustness.

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