Theoretical models of spins coupled to bosons provide a simple setting for studying a broad range of important phenomena in many-body physics, from virtually mediated interactions to decoherence and thermalization. In many atomic, molecular, and optical systems, such models also underlie the most successful attempts to engineer strong, long-ranged interactions for the purpose of entanglement generation. Especially when the coupling between the spins and bosons is strong-such that it cannot be treated perturbatively-the properties of such models are extremely challenging to calculate theoretically. Here, exact analytical expressions for nonequilibrium spin-spin correlation functions are derived for a specific model of spins coupled to bosons. The spatial structure of the coupling between spins and bosons is completely arbitrary, and thus the solution can be applied to systems in any number of dimensions. The explicit and nonperturbative inclusion of the bosons enables the study of entanglement generation (in the form of spin squeezing) even when the bosons are driven strongly and near-resonantly, and thus provides a quantitative view of the breakdown of adiabatic elimination that inevitably occurs as one pushes towards the fastest entanglement generation possible. The solution also helps elucidate the effect of finite temperature on spin squeezing. The model considered is relevant to a variety of atomic, molecular, and optical systems, such as atoms in cavities or trapped ions. As an explicit example, the results are used to quantify phonon effects in trapped ion quantum simulators, which are expected to become increasingly important as these experiments push towards larger numbers of ions.

We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed subsets of the data, and dominant time scales are discovered using spectral clustering on their eigenvalues. This approach produces time series data for each identified component, which sum to a faithful reconstruction of the input signal. It differs from most other methods in the field of multiresolution analysis (MRA) in that it 1) accounts for spatial and temporal coherencies simultaneously, making it more robust to scale overlap between components, and 2) yields a closed-form expression for local dynamics at each scale, which can be used for short-term prediction of any or all components. Our technique is an extension of multi-resolution dynamic mode decomposition (mrDMD), generalized to treat a broader variety of multiscale systems and more faithfully reconstruct their isolated components. In this paper we present an overview of our algorithm and its results on two example physical systems, and briefly discuss some advantages and potential forecasting applications for the technique.

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Time series forecasting remains a central challenge problem in almost all scientific disciplines, including load modeling in power systems engineering. The ability to produce accurate forecasts has major implications for real-time control, pricing, maintenance, and security decisions. We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system using Dynamic Mode Decomposition (DMD) in time delay coordinates. Central to this approach is the insight that grid load, like many observables on complex real-world systems, has an "almost-periodic" character, i.e., a continuous Fourier spectrum punctuated by dominant peaks, which capture regular (e.g., daily or weekly) recurrences in the dynamics. The forecasting method presented takes advantage of this property by (i) regressing to a deterministic linear model whose eigenspectrum maps onto those peaks, and (ii) simultaneously learning a stochastic Gaussian process regression (GPR) process to actuate this system. Our forecasting algorithm is compared against state-of-the-art forecasting techniques not using additional explanatory variables and is shown to produce superior performance. Moreover, its use of linear intrinsic dynamics offers a number of desirable properties in terms of interpretability and parsimony.