Neural Operators for Many-Body Complex Systems
Open Access DepositedKuramoto 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.
(1) coarse-graining operators inspired by geometric and laplacian renormalization groups
large systems of more than 1M nodes, long-range interactions, and noisy input-output data for two contrasting examples
(II) adapting the attention mechanism to learn multiscale interactions
(2) a multiscale attention mechanism that learns multiscale interactions
and (III) extending operator learning methods to solve coupled many-body systems. We apply this framework in challenging conditions
While deductive methods have been remarkably successful in physics, such methods face major difficulties in describing many-body complex systems such as brain networks and social systems. These systems exhibit emergent properties that cannot be fully explained by mechanistic understanding of their individual components, thereby requiring effective theories at the scale(s) of observation. Data-driven discovery of effective dynamics is an appealing approach to learning such theories, but without incorporation of strong physical priors, black-box neural solvers offer little interpretability and may fail to generalize due to lack of physical realism. Moreover, learning effective dynamics for many-body complex systems is challenging due to factors such as non-equilibrium behavior, long-range interactions, and large system size. To this end, we present a machine learning framework, ROMA (Renormalized Operators with Multiscale Attention), that introduces several novel and complementary innovations aimed specifically at learning effective dynamics of complex systems. This includes several composable neural modules
and (3) a conditioning mechanism that incorporates multiscale interactions for enhanced forecasting and discovery of effective dynamics. The main advances of this work are
(I) defining a neural renormalization procedure for complex systems
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