一种从广义朗之万动力学中测量长寿命记忆核的深度学习方法
A deep learning approach to the measurement of long-lived memory kernels from Generalised Langevin Dynamics
AI总结：
针对广义朗之万方程中记忆核难以测量的问题，提出基于深度神经网络的KernelLearner流程，利用硬球MCT数据训练，在含噪及跨系统模拟数据上表现出强鲁棒性与泛化能力。
摘要：
记忆效应在从玻璃态动力学、超材料到气候模型的各种复杂物理现象中无处不在。广义朗之万方程（GLE）通过积分微分方程中的所谓记忆核，为描述记忆效应提供了严格的方法。然而，记忆核通常是未知的，并且例如通过数值逆拉普拉斯变换来准确预测或测量它仍然是一项极其艰巨的任务。在此，我们描述了一种使用深度神经网络（DNNs）从动力学数据中测量记忆核的新方法。作为原理验证，我们重点关注出了名长寿命的玻璃态系统记忆效应，这对现有方法构成了重大挑战。具体来说，我们学习了一个由硬球模耦合理论（MCT）生成的训练集。与需要对许多独立轨迹进行系综平均的传统技术相比，我们的DNNs对噪声表现出极强的鲁棒性。最后，我们证明了在解析理论（硬球MCT）生成的数据上训练的网络，能够很好地泛化到来自不同系统（布朗Weeks-Chandler-Andersen粒子）模拟的数据。我们提供了一个通用流程KernelLearner，用于训练网络从由GLE描述的任何非马尔可夫系统中提取记忆核。我们的DNN方法在玻璃态系统上的成功表明，深度学习可以在研究表现出记忆效应的动力学系统中发挥重要作用。
英文摘要：
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.
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