A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the physical processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have demonstrated promising results for forecasting chaotic systems purely from past time series measurements of system state variables (training data), without prior knowledge of the system dynamics. The motivation for this paper is the potential of machine learning for filling in the gaps in our underlying mechanistic knowledge that cause widely-used knowledge-based models to be inaccurate. Thus we here propose a general method that leverages the advantages of these two approaches by combining a knowledge-based model and a machine learning technique to build a hybrid forecasting scheme. Potential applications for such an approach are numerous (e.g., improving weather forecasting). We demonstrate and test the utility of this approach using a particular illustrative version of a machine learning known as reservoir computing, and we apply the resulting hybrid forecaster to a low-dimensional chaotic system, as well as to a high-dimensional spatiotemporal chaotic system. These tests yield extremely promising results in that our hybrid technique is able to accurately predict for a much longer period of time than either its machine-learning component or its model-based component alone. Prediction of dynamical system states (e.g., as in weather forecasting) is a common and essential task with many applications in science and technology. This task is often carried out via a system of dynamical equations derived to model the process to be predicted. Due to deficiencies in knowledge or computational capacity, application of these models will generally be imperfect and may give unacceptably inaccurate results. On the other hand data-driven methods, independent of derived knowledge of the system, can be computationally intensive and require unreasonably large amounts of data. In this paper we consider a particular hybridization technique for combining these two approaches. Our tests of this hybrid technique suggest that it can be extremely effective and widely applicable.

The paper investigates the applicability of machine learning (ML) to weather prediction by building a reservoir computing-based, low-resolution, global prediction model. The model is designed to take advantage of the massively parallel architecture of a modern supercomputer. The forecast performance of the model is assessed by comparing it to that of daily climatology, persistence, and a numerical (physics-based) model of identical prognostic state variables and resolution. Hourly resolution 20-day forecasts with the model predict realistic values of the atmospheric state variables at all forecast times for the entire globe. The ML model outperforms both climatology and persistence for the first three forecast days in the midlatitudes, but not in the tropics. Compared to the numerical model, the ML model performs best for the state variables most affected by parameterized processes in the numerical model. a computationally efficient hybrid modeling approach. The present paper implements the parallel ML technique of Pathak, Wikner, et al. (2018) to build a model that predicts the weather in the same format as a global numerical model. We train and verify the model on hourly ERA5 reanalysis data from the European Centre for Medium-Range Weather Forecasts (Hersbach et al., 2019).The work presented here can also be considered an attempt to develop a ML model that can predict the evolution of the three-dimensional, multivariate, global atmospheric state. To the best of our knowledge, the only similar prior attempts were those by Scher (2018) and Scher and Messori (2019), but they trained their three-dimensional multivariate ML model on data that were produced by low-resolution numerical model simulations. In addition, Dueben and Bauer (2018) and Weyn et al., 2019Weyn et al., (2020 designed ML models to predict two-dimensional, horizontal fields of select atmospheric state variables. Similar to our verification strategy, they also verified the ML forecasts against reanalysis data. Compared to all of the aforementioned studies, an important new aspect of our work is that we employ reservoir computing (RC) (Jaeger, 2001;Lukoševičius & Jaeger, 2009;Lukoševičius, 2012;Maass et al., 2002) rather than deep learning (e.g., Goodfellow et al., 2016), which is primarily motivated by the significantly lower computer wall clock time required to train an RC-based model. This difference in training efficiency would allow for a larger number of experiments to tune the ML model at higher resolutions.The structure of the paper is as follows. Section 2 describes the ML model, while section 3 presents the results of the forecast experiments, using as benchmarks persistence of the atmospheric state, daily climatology, and numerical forecasts from a physics-based model of identical prognostic state variables and resolution. Section 4 summarizes our conclusions.

We consider the commonly encountered situation (e.g., in weather forecast) where the goal is to predict the time evolution of a large, spatiotemporally chaotic dynamical system when we have access to both time series data of previous system states and an imperfect model of the full system dynamics. Specifically, we attempt to utilize machine learning as the essential tool for integrating the use of past data into predictions. In order to facilitate scalability to the common scenario of interest where the spatiotemporally chaotic system is very large and complex, we propose combining two approaches: (i) a parallel machine learning prediction scheme and (ii) a hybrid technique for a composite prediction system composed of a knowledge-based component and a machine learning-based component. We demonstrate that not only can this method combining (i) and (ii) be scaled to give excellent performance for very large systems but also that the length of time series data needed to train our multiple, parallel machine learning components is dramatically less than that necessary without parallelization. Furthermore, considering cases where computational realization of the knowledge-based component does not resolve subgrid-scale processes, our scheme is able to use training data to incorporate the effect of the unresolved short-scale dynamics upon the resolved longer-scale dynamics (subgrid-scale closure).

This paper describes an implementation of the combined hybrid‐parallel prediction (CHyPP) approach of Wikner et al. (2020), https://doi.org/10.1063/5.0005541 on a low‐resolution atmospheric global circulation model (AGCM). The CHyPP approach combines a physics‐based numerical model of a dynamical system (e.g., the atmosphere) with a computationally efficient type of machine learning (ML) called reservoir computing to construct a hybrid model. This hybrid atmospheric model produces more accurate forecasts of most atmospheric state variables than the host AGCM for the first 7–8 forecast days, and for even longer times for the temperature and humidity near the earth's surface. It also produces more accurate forecasts than a model based only on ML, or a model that combines linear regression, rather than ML, with the AGCM. The potential of the CHyPP approach for climate research is demonstrated by a 10‐year long hybrid model simulation of the atmospheric general circulation, which shows that the hybrid model can simulate the general circulation with substantially smaller systematic errors and more realistic variability than the host AGCM.

Arcomano et al. (2022) (AEA22 hereafter) described a hybrid atmospheric modeling approach that combines machine learning (ML) with an atmospheric general circulation model (AGCM). They showed that, when the hybrid model was used for weather prediction, it provided more accurate short and medium range (1-7 days) forecasts than either the AGCM or the ML-only component of the model (Arcomano et al., 2020) acting alone. They also showed that when the model was used for climate simulations, it greatly reduced the systematic errors (biases) of the model climate compared to that of the AGCM. In the present study, we further explore the potential of the approach of AEA22 for climate modeling, and describe methods that significantly extends its utility and scope. The results we report are in accord with the idea that the inaccuracies of an AGCM could potentially be mitigated by utilization of information in time series of past observational data via the ML component of the hybrid.The approach of AEA22 is an implementation of the combined hybrid/parallel prediction (CHyPP) scheme of Wikner et al. ( 2020) on an AGCM. CHyPP itself is an adaptation of the hybrid modeling approach of Pathak, Wikner, et al. (2018) to large dynamical systems, using the parallel reservoir computing (RC) algorithm of Pathak,