Edward Ott’s research while affiliated with Loyola University Maryland and other places

This paper explores the potential of a hybrid modeling approach that combines machine learning (ML) with conventional physics-based modeling for weather prediction beyond the medium range. It extends the work of Arcomano et al. (2022), which tested the approach for short- and medium-range weather prediction, and the work of Arcomano et al. (2023), which investigated its potential for climate modeling. The hybrid model used for the forecast experiments of the paper is based on the low-resolution, simplified parameterization atmospheric general circulation model (AGCM) SPEEDY. In addition to the hybridized prognostic variables of SPEEDY, the current version of the model has three purely ML-based prognostic variables. One of these is 6~h cumulative precipitation, another is the sea surface temperature, while the third is the heat content of the top 300 m deep layer of the ocean. The model has skill in predicting the El Ni\~no cycle and its global teleconnections with precipitation for 3-7 months depending on the season. The model captures equatorial variability of the precipitation associated with Kelvin and Rossby waves and MJO. Predictions of the precipitation in the equatorial region have skill for 15 days in the East Pacific and 11.5 days in the West Pacific. Though the model has low spatial resolution, for these tasks it has prediction skill comparable to what has been published for high-resolution, purely physics-based, conventional operational forecast models.

It is shown that a recently developed hybrid modeling approach that combines machine learning (ML) with an atmospheric global circulation model (AGCM) can serve as a basis for capturing atmospheric processes not captured by the AGCM. This power of the approach is illustrated by three examples from a decades‐long climate simulation experiment. The first example demonstrates that the hybrid model can produce sudden stratospheric warming, a dynamical process of nature not resolved by the low resolution AGCM component of the hybrid model. The second and third example show that introducing 6‐hr cumulative precipitation and sea surface temperature (SST) as ML‐based prognostic variables improves the precipitation climatology and leads to a realistic ENSO signal in the SST and atmospheric surface pressure.

Wave energy distribution within enclosures with irregular boundaries is a common phenomenon in many branches of electromagnetics. If the wavelength of the injected wave is small compared with the structure size, the scattering properties of the enclosure will be extremely sensitive to small changes in geometry or wave frequency. In this case, statistical models are sought. The random coupling model (RCM) is one such model that has been explored through experiments and theory. Previous studies were conducted by injecting waves into high Q cavities in a nearly omnidirectional manner. In this article, a directed beam approach is taken, and relatively low Q cavities are considered. The goal is to determine when the so-called “random plane wave hypothesis,” a fundamental basis of the RCM formulation, breaks down. Results show that injecting such directed beams leads to large deviations in the wave statistics for single realizations of the enclosure geometry. The expected statistics are restored to some degree when multiple realizations are considered.

Network link inference from measured time series data of the behavior of dynamically interacting network nodes is an important problem with wide-ranging applications, e.g., estimating synaptic connectivity among neurons from measurements of their calcium fluorescence. Network inference methods typically begin by using the measured time series to assign to any given ordered pair of nodes a numerical score reflecting the likelihood of a directed link between those two nodes. In typical cases, the measured time series data may be subject to limitations, including limited duration, low sampling rate, observational noise, and partial nodal state measurement. However, it is unknown how the performance of link inference techniques on such datasets depends on these experimental limitations of data acquisition. Here, we utilize both synthetic data generated from coupled chaotic systems as well as experimental data obtained from Caenorhabditis elegans neural activity to systematically assess the influence of data limitations on the character of scores reflecting the likelihood of a directed link between a given node pair. We do this for three network inference techniques: Granger causality, transfer entropy, and, a machine learning-based method. Furthermore, we assess the ability of appropriate surrogate data to determine statistical confidence levels associated with the results of link-inference techniques.

The ability of machine learning (ML) models to “extrapolate” to situations outside of the range spanned by their training data is crucial for predicting the long-term behavior of non-stationary dynamical systems (e.g., prediction of terrestrial climate change), since the future trajectories of such systems may (perhaps after crossing a tipping point) explore regions of state space which were not explored in past time-series measurements used as training data. We investigate the extent to which ML methods can yield useful results by extrapolation of such training data in the task of forecasting non-stationary dynamics, as well as conditions under which such methods fail. In general, we find that ML can be surprisingly effective even in situations that might appear to be extremely challenging, but do (as one would expect) fail when “too much” extrapolation is required. For the latter case, we show that good results can potentially be obtained by combining the ML approach with an available inaccurate conventional model based on scientific knowledge.

Recent work has shown that machine learning (ML) models can be trained to accurately forecast the dynamics of unknown chaotic dynamical systems. Such ML models can be used to produce both short-term predictions of the state evolution and long-term predictions of the statistical patterns of the dynamics (``climate''). Both of these tasks can be accomplished by employing a feedback loop, whereby the model is trained to predict forward one time step, then the trained model is iterated for multiple time steps with its output used as the input. In the absence of mitigating techniques, however, this technique can result in artificially rapid error growth, leading to inaccurate predictions and/or climate instability. In this article, we systematically examine the technique of adding noise to the ML model input during training as a means 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 types of regularization 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.

Electromagnetic (EM) wave scattering in electrically large, irregularly shaped, environments is a common phenomenon. The deterministic, or first principles, study of this process is usually computationally expensive and the results exhibit extreme sensitivity to scattering details. For this reason, the deterministic approach is often dropped in favor of a statistical one. The Random Coupling Model (RCM) is one such approach that has found great success in providing a statistical characterization for wave chaotic systems in the frequency domain. Here we aim to transform the RCM into the time domain and generalize it to new situations. The proposed time-domain RCM (TD-RCM) method can treat a wave chaotic system with multiple ports and modes. Two features are now possible with the time-domain approach that are not possible in the frequency-domain RCM: the incorporation of early-time short-orbit transmission path effects between the ports, and the inclusion of arbitrary nonlinear or time-varying port load impedances. We have conducted short-pulse time-domain experiments in wave chaotic enclosures, and used the TD-RCM to simulate the corresponding experimental setup. We have also examined a diode-loaded port and compared experimental results with a numerical TD-RCM treatment and found agreement.

In this paper we consider the machine learning (ML) task of predicting tipping point transitions and long-term post-tipping-point behavior associated with the time evolution of an unknown (or partially unknown), non-stationary, potentially noisy and chaotic, dynamical system. We focus on the particularly challenging situation where the past dynamical state time series that is available for ML training predominantly lies in a restricted region of the state space, while the behavior to be predicted evolves on a larger state space set not fully observed by the ML model during training. In this situation, it is required that the ML prediction system have the ability to extrapolate to different dynamics past that which is observed during training. We investigate the extent to which ML methods are capable of accomplishing useful results for this task, as well as conditions under which they fail. In general, we found that the ML methods were surprisingly effective even in situations that were extremely challenging, but do (as one would expect) fail when ``too much" extrapolation is required. For the latter case, we investigate the effectiveness of combining the ML approach with conventional modeling based on scientific knowledge, thus forming a hybrid prediction system which we find can enable useful prediction even when its ML-based and knowledge-based components fail when acting alone. We also found that achieving useful results may require using very carefully selected ML hyperparameters and we propose a hyperparameter optimization strategy to address this problem. The main conclusion of this paper is that ML-based approaches are promising tools for predicting the behavior of non-stationary dynamical systems even in the case where the future evolution (perhaps due to the crossing of a tipping point) includes dynamics on a set outside of that explored by the training data.