Digital twins, the cornerstone of Industry 4.0, replicate real-world entities through computer models, revolutionising fields such as manufacturing management and industrial automation. Recent advances in machine learning provide data-driven methods for developing digital twins using discrete-time data and finite-depth models on digital computers. However, this approach fails to capture the underlying continuous dynamics and struggles with modelling complex system behaviour. Additionally, the architecture of digital computers, with separate storage and processing units, necessitates frequent data transfers and Analogue-Digital (A/D) conversion, thereby significantly increasing both time and energy costs. Here, we introduce a memristive neural ordinary differential equation (ODE) solver for digital twins, which is capable of capturing continuous-time dynamics and facilitates the modelling of complex systems using an infinite-depth model. By integrating storage and computation within analogue memristor arrays, we circumvent the von Neumann bottleneck, thus enhancing both speed and energy efficiency. We experimentally validate our approach by developing a digital twin of the HP memristor, which accurately extrapolates its nonlinear dynamics, achieving a 4.2-fold projected speedup and a 41.4-fold projected decrease in energy consumption compared to state-of-the-art digital hardware, while maintaining an acceptable error margin. Additionally, we demonstrate scalability through experimentally grounded simulations of Lorenz96 dynamics, exhibiting projected performance improvements of 12.6-fold in speed and 189.7-fold in energy efficiency relative to traditional digital approaches. By harnessing the capabilities of fully analogue computing, our breakthrough accelerates the development of digital twins, offering an efficient and rapid solution to meet the demands of Industry 4.0.

翻译：数字孪生作为工业4.0的基石，通过计算机模型复现现实世界实体，正在彻底变革制造管理与工业自动化等领域。机器学习的最新进展为利用离散时间数据和数字计算机上的有限深度模型开发数字孪生提供了数据驱动方法。然而，该方法无法捕捉潜在的连续动力学特性，且在建模复杂系统行为时面临困难。此外，数字计算机的架构采用独立的存储与处理单元，需要频繁的数据传输和模数（A/D）转换，从而显著增加了时间与能耗成本。本文提出一种用于数字孪生的忆阻神经常微分方程（ODE）求解器，该求解器能够捕捉连续时间动力学，并借助无限深度模型促进复杂系统建模。通过在模拟忆阻器阵列中实现存储与计算一体化，我们规避了冯·诺依曼瓶颈，从而同时提升了速度与能效。我们通过构建HP忆阻器的数字孪生对方法进行了实验验证，该孪生体能够准确外推其非线性动力学特性，在保持可接受误差范围的前提下，相较于最先进的数字硬件实现了4.2倍的预期加速和41.4倍的预期能耗降低。此外，我们通过基于实验的Lorenz96动力学仿真证明了该方法的可扩展性，相较于传统数字方法展现出12.6倍的速度提升和189.7倍的能效提升预期。通过充分发挥全模拟计算的优势，我们的突破性成果加速了数字孪生的发展，为满足工业4.0的需求提供了高效快速的解决方案。