Machine learning (ML) models can be effective for forecasting the dynamics of unknown systems from time-series data, but they often require large amounts of data and struggle to generalize across systems with varying dynamics. Combined, these issues make forecasting from short time series particularly challenging. To address this problem, we introduce Meta-learning for Tailored Forecasting from Related Time Series (METAFORS), which uses related systems with longer time-series data to supplement limited data from the system of interest. By leveraging a library of models trained on related systems, METAFORS builds tailored models to forecast system evolution with limited data. Using a reservoir computing implementation and testing on simulated chaotic systems, we demonstrate METAFORS' ability to predict both short-term dynamics and long-term statistics, even when test and related systems exhibit significantly different behaviors and the available data are scarce, highlighting its robustness and versatility in data-limited scenarios.

Reservoir computers (RCs) are powerful machine learning architectures for time series prediction. Recently, next generation reservoir computers (NGRCs) have been introduced, offering distinct advantages over RCs, such as reduced computational expense and lower training data requirements. However, NGRCs have their own practical difficulties, including sensitivity to sampling time and type of nonlinearities in the data. Here, we introduce a hybrid RC-NGRC approach for time series forecasting of dynamical systems. We show that our hybrid approach can produce accurate short term predictions and capture the long term statistics of chaotic dynamical systems in situations where the RC and NGRC components alone are insufficient, e.g., due to constraints from limited computational resources, sub-optimal hyperparameters, sparsely-sampled training data, etc. Under these conditions, we show for multiple model chaotic systems that the hybrid RC-NGRC method with a small reservoir can achieve prediction performance approaching that of a traditional RC with a much larger reservoir, illustrating that the hybrid approach can offer significant gains in computational efficiency over traditional RCs while simultaneously addressing some of the limitations of NGRCs. Our results suggest that hybrid RC-NGRC approach may be particularly beneficial in cases when computational efficiency is a high priority and an NGRC alone is not adequate.

Recent work has shown that machine learning (ML) models can be trained to accurately forecast the dynamics of unknown chaotic dynamical systems. Short-term predictions of the state evolution and long-term predictions of the statistical patterns of the dynamics (``climate'') can be produced by employing a feedback loop, whereby the model is trained to predict forward one time step, then the model output is used as input for multiple time steps. In the absence of mitigating techniques, however, this technique can result in artificially rapid error growth. In this article, we systematically examine the technique of adding noise to the ML model input during training to promote stability and improve prediction accuracy. Furthermore, we introduce Linearized Multi-Noise Training (LMNT), a regularization technique that deterministically approximates the effect of many small, independent noise realizations added to the model input during training. Our case study uses reservoir computing, a machine-learning method using recurrent neural networks, to predict the spatiotemporal chaotic Kuramoto-Sivashinsky equation. We find that reservoir computers trained with noise or with LMNT produce climate predictions that appear to be indefinitely stable and have a climate very similar to the true system, while reservoir computers trained without regularization are unstable. Compared with other regularization techniques that yield stability in some cases, we find that both short-term and climate predictions from reservoir computers trained with noise or with LMNT are substantially more accurate. Finally, we show that the deterministic aspect of our LMNT regularization facilitates fast hyperparameter tuning when compared to training with noise.

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.

There is a large amount of interest in understanding users of social media in order to predict their behavior in this space. Despite this interest, user predictability in social media is not well-understood. To examine this question, we consider a network of fifteen thousand users on Twitter over a seven week period. We apply two contrasting modeling paradigms: computational mechanics and echo state networks. Both methods attempt to model the behavior of users on the basis of their past behavior. We demonstrate that the behavior of users on Twitter can be well-modeled as processes with self-feedback. We find that the two modeling approaches perform very similarly for most users, but that they differ in performance on a small subset of the users. By exploring the properties of these performance-differentiated users, we highlight the challenges faced in applying predictive models to dynamic social data.