Connecting the geometry and dynamics of many-body complex systems with message passing neural operators

• URL: http://arxiv.org/abs/2502.15913v1
• Date: Fri, 21 Feb 2025 20:04:09 GMT
• Title: Connecting the geometry and dynamics of many-body complex systems with message passing neural operators
• Authors: Nicholas A. Gabriel, Neil F. Johnson, George Em Karniadakis,
• Abstract summary: We introduce a scalable AI framework, ROMA, for learning multiscale evolution operators of many-body complex systems.<n>An attention mechanism is used to model multiscale interactions by connecting geometric representations of local subgraphs and dynamical operators.<n>We demonstrate that the ROMA framework improves scalability and positive transfer between forecasting and effective dynamics tasks.
• Score: 1.8434042562191815
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: The relationship between scale transformations and dynamics established by renormalization group techniques is a cornerstone of modern physical theories, from fluid mechanics to elementary particle physics. Integrating renormalization group methods into neural operators for many-body complex systems could provide a foundational inductive bias for learning their effective dynamics, while also uncovering multiscale organization. We introduce a scalable AI framework, ROMA (Renormalized Operators with Multiscale Attention), for learning multiscale evolution operators of many-body complex systems. In particular, we develop a renormalization procedure based on neural analogs of the geometric and laplacian renormalization groups, which can be co-learned with neural operators. An attention mechanism is used to model multiscale interactions by connecting geometric representations of local subgraphs and dynamical operators. We apply this framework in challenging conditions: large systems of more than 1M nodes, long-range interactions, and noisy input-output data for two contrasting examples: Kuramoto oscillators and Burgers-like social dynamics. We demonstrate that the ROMA framework improves scalability and positive transfer between forecasting and effective dynamics tasks compared to state-of-the-art operator learning techniques, while also giving insight into multiscale interactions. Additionally, we investigate power law scaling in the number of model parameters, and demonstrate a departure from typical power law exponents in the presence of hierarchical and multiscale interactions.

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