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Condensed Matter > Disordered Systems and Neural Networks
Title: A deep learning approach to the measurement of long-lived memory kernels from Generalised Langevin Dynamics
(Submitted on 27 Feb 2023 (v1), last revised 28 Jun 2023 (this version, v2))
Abstract: Memory effects are ubiquitous in a wide variety of complex physical phenomena, ranging from glassy dynamics and metamaterials to climate models. The Generalised Langevin Equation (GLE) provides a rigorous way to describe memory effects via the so-called memory kernel in an integro-differential equation. However, the memory kernel is often unknown, and accurately predicting or measuring it via e.g. a numerical inverse Laplace transform remains a herculean task. Here we describe a novel method using deep neural networks (DNNs) to measure memory kernels from dynamical data. As proof-of-principle, we focus on the notoriously long-lived memory effects of glassy systems, which have proved a major challenge to existing methods. Specifically, we learn a training set generated with the Mode-Coupling Theory (MCT) of hard spheres. Our DNNs are remarkably robust against noise, in contrast to conventional techniques which require ensemble averaging over many independent trajectories. Finally, we demonstrate that a network trained on data generated from analytic theory (hard-sphere MCT) generalises well to data from simulations of a different system (Brownian Weeks-Chandler-Andersen particles). We provide a general pipeline, KernelLearner, for training networks to extract memory kernels from any non-Markovian system described by a GLE. The success of our DNN method applied to glassy systems suggests deep learning can play an important role in the study of dynamical systems that exhibit memory effects.
Submission history
From: Max Kerr Winter [view email][v1] Mon, 27 Feb 2023 11:38:25 GMT (844kb,D)
[v2] Wed, 28 Jun 2023 06:01:55 GMT (2918kb)
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