Higher order quantum reservoir computing for non-intrusive reduced-order models

TL;DR

The paper tackles forecasting dynamical systems when governing equations are unavailable by introducing Higher Order Quantum Reservoir Computing (HQRC), an ensemble of quantum reservoirs with temporal multiplexing and linear readouts. It applies HQRC to non-intrusive reduced-order modeling by forecasting POD-coefficient trajectories of NOAA SST data, achieving competitive accuracy with reduced training time and memory compared to deep learning baselines. HQRC outperforms GRU, LSTM, and ESN on test RMSE for autoregressive SST forecasts and demonstrates robustness across ensemble models, while revealing sensitivity to state-space dimensionality and compression. The work suggests HQRC as a practical quantum-inspired tool for efficient data-driven forecasting, with future directions including modal selection and multimodal data integration to scale to higher-dimensional problems.

Abstract

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.

Figures (12)

• Figure 1: Average prediction and corresponding ensemble standard deviations for the top 5 HQRC models over train (left) and test (right) dataset predictions.
• Figure 2: Best-case reconstruction error (i.e., using ground truth POD-coefficients) (top) and model-based prediction error of top 5 models of HQRC (bottom) for 300 averaged timesteps of predictions.
• Figure 3: Average prediction and corresponding ensemble standard deviations for the top 5 GRU models over train (left) and test (right) dataset predictions.
• Figure 4: Model-based prediction error of top 5 GRU models for 300 averaged timesteps of predictions.
• Figure 5: Average prediction and corresponding ensemble standard deviations for the top 5 LSTM models over train (left) and test (right) dataset predictions.