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.
A Non-Intrusive Neural Quality Assessment Model for Surface Electromyography Signals
National Yang Ming Chiao Tung University（国立阳明交通大学）；National Taiwan University（国立台湾大学）；University of Massachusetts（马萨诸塞大学）；National Institute of Information and Communications Technology（信息通信研究机构）；Academia Sinica（中央研究院）
Discrete-time signatures and randomness in reservoir computing
University of Vienna（维也纳大学）；Ludwig-Maximilians-Universität München（路德维希-马克西米利安慕尼黑大学）；Universität Konstanz（康斯坦茨大学）；Universität Sankt Gallen（圣加仑大学）；Centre National de la Recherche Scientifique (CNRS)（法国国家科学研究中心）；ETH Zürich（苏黎世联邦理工学院）
Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations
Courant Institute of Mathematical Sciences, New York University（纽约大学柯朗数学科学研究所）
Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation
Argonne Leadership Computing Facility（阿贡领导力计算设施）；Argonne National Laboratory（阿贡国家实验室）；The Alan Turing Institute（艾伦·图灵研究所）；Imperial College London（帝国理工学院）
A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling
Cornell University（康奈尔大学）；ANSYS Inc.（ANSYS公司）；Korea Institute for Advanced Study（韩国高等研究院）；University of Arizona（亚利桑那大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；North Carolina State University（北卡罗来纳州立大学）；Pohang University of Science and Technology（浦项科技大学）；University of California, San Diego（加利福尼亚大学圣迭戈分校）
Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniques
Cornell University（康奈尔大学）；Catholic University of the Sacred Heart（圣心天主教大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Sandia National Laboratories（桑迪亚国家实验室）
Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms
Max Planck Institute for Dynamics of Complex Technical Systems（马克斯·普朗克复杂技术系统动力学研究所）；University of California San Diego（加利福尼亚大学圣地亚哥分校）；New York University（纽约大学）；The University of Texas at Austin（得克萨斯大学奥斯汀分校）
Scientific Machine Learning Based Reduced-Order Models for Plasma Turbulence Simulations
Max Planck Institute for Plasma Physics（马克斯·普朗克等离子体物理研究所）；Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校奥登计算工程与科学研究所）；Virginia Tech（弗吉尼亚理工大学）
