Forecasting dynamical systems is of importance to numerous real-world applications. When possible, dynamical systems forecasts are constructed based on first-principles-based models such as through the use of differential equations. When these equations are unknown, non-intrusive techniques must be utilized to build predictive models from data alone. Machine learning (ML) methods have recently been used for such tasks. Moreover, ML methods provide the added advantage of significant reductions in time-to-solution for predictions in contrast with first-principle based models. However, many state-of-the-art ML-based methods for forecasting rely on neural networks, which may be expensive to train and necessitate requirements for large amounts of memory. In this work, we propose a quantum mechanics inspired ML modeling strategy for learning nonlinear dynamical systems that provides data-driven forecasts for complex dynamical systems with reduced training time and memory costs. This approach, denoted the quantum reservoir computing technique (QRC), is a hybrid quantum-classical framework employing an ensemble of interconnected small quantum systems via classical linear feedback connections. By mapping the dynamical state to a suitable quantum representation amenable to unitary operations, QRC is able to predict complex nonlinear dynamical systems in a stable and accurate manner. We demonstrate the efficacy of this framework through benchmark forecasts of the NOAA Optimal Interpolation Sea Surface Temperature dataset and compare the performance of QRC to other ML methods.

翻译：预测动力系统对众多实际应用具有重要意义。在可能的情况下，动力系统预测通常基于第一性原理模型构建，例如通过微分方程实现。当这些方程未知时，必须采用非侵入式技术仅从数据中建立预测模型。机器学习方法近年来已被用于此类任务。此外，与基于第一性原理的模型相比，机器学习方法还具有显著缩短预测求解时间的优势。然而，许多最先进的基于机器学习的预测方法依赖于神经网络，其训练成本可能较高且需要大量内存。在本工作中，我们提出一种受量子力学启发的机器学习建模策略，用于学习非线性动力系统，该策略能以更短的训练时间和更低的内存成本为复杂动力系统提供数据驱动的预测。该方法称为量子储层计算技术，是一种混合量子-经典框架，通过经典线性反馈连接集成多个相互关联的小型量子系统。通过将动力系统状态映射到适合酉操作的量子表示，QRC能够以稳定且准确的方式预测复杂非线性动力系统。我们通过NOAA最优插值海面温度数据集的基准预测验证了该框架的有效性，并将QRC的性能与其他机器学习方法进行了比较。