Physically implemented neural networks hold the potential to achieve the performance of deep learning models by exploiting the innate physical properties of devices as computational tools. This exploration of physical processes for computation requires to also consider their intrinsic dynamics, which can serve as valuable resources to process information. However, existing computational methods are unable to extend the success of deep learning techniques to parameters influencing device dynamics, which often lack a precise mathematical description. In this work, we formulate a universal framework to optimise interactions with dynamic physical systems in a fully data-driven fashion. The framework adopts neural stochastic differential equations as differentiable digital twins, effectively capturing both deterministic and stochastic behaviours of devices. Employing differentiation through the trained models provides the essential mathematical estimates for optimizing a physical neural network, harnessing the intrinsic temporal computation abilities of its physical nodes. To accurately model real devices' behaviours, we formulated neural-SDE variants that can operate under a variety of experimental settings. Our work demonstrates the framework's applicability through simulations and physical implementations of interacting dynamic devices, while highlighting the importance of accurately capturing system stochasticity for the successful deployment of a physically defined neural network.

翻译：物理实现的神经网络通过利用器件固有的物理特性作为计算工具，有望达到深度学习模型的性能。这种基于物理过程进行计算的探索需要同时考虑其内在动力学特性，这些特性可作为处理信息的有价值资源。然而，现有计算方法无法将深度学习技术的成功扩展至影响器件动力学的参数——这些参数往往缺乏精确的数学描述。在本工作中，我们构建了一个通用框架，以完全数据驱动的方式优化与动态物理系统的交互。该框架采用神经随机微分方程作为可微分的数字孪生模型，有效捕捉器件的确定性和随机性行为。通过训练模型进行微分运算，可为优化物理神经网络提供必要的数学估计，从而利用其物理节点固有的时间计算能力。为精确建模真实器件行为，我们提出了可在多种实验设置下运行的神经随机微分方程变体。通过交互式动态器件的仿真与物理实现，本工作验证了该框架的适用性，同时强调精确捕捉系统随机性对于成功部署物理定义神经网络的关键作用。