A methodology is developed, based on nonparametric Bayesian dictionary learning, for joint space-time wind field data extrapolation and estimation of related statistics by relying on limited/incomplete measurements. Specifically, utilizing sparse/incomplete measured data, a time-dependent optimization problem is formulated for determining the expansion coefficients of an associated low-dimensional representation of the stochastic wind field. Compared to an alternative, standard, compressive sampling treatment of the problem, the developed methodology exhibits the following advantages. First, the Bayesian formulation enables also the quantification of the uncertainty in the estimates. Second, the requirement in standard CS-based applications for an a priori selection of the expansion basis is circumvented. Instead, this is done herein in an adaptive manner based on the acquired data. Overall, the methodology exhibits enhanced extrapolation accuracy, even in cases of high-dimensional data of arbitrary form, and of relatively large extrapolation distances. Thus, it can be used, potentially, in a wide range of wind engineering applications where various constraints dictate the use of a limited number of sensors. The efficacy of the methodology is demonstrated by considering two case studies. The first relates to the extrapolation of simulated wind velocity records consistent with a prescribed joint wavenumber-frequency power spectral density in a three-dimensional domain (2D and time). The second pertains to the extrapolation of four-dimensional (3D and time) boundary layer wind tunnel experimental data that exhibit significant spatial variability and non-Gaussian characteristics.

Understanding the training dynamics of quantum neural networks is a fundamental task in quantum information science with wide impact in physics, chemistry and machine learning. In this work, we show that the late-time training dynamics of quantum neural networks can be described by the generalized Lotka-Volterra equations, which lead to a dynamical phase transition. When the targeted value of cost function crosses the minimum achievable value from above to below, the dynamics evolve from a frozen-kernel phase to a frozen-error phase, showing a duality between the quantum neural tangent kernel and the total error. In both phases, the convergence towards the fixed point is exponential, while at the critical point becomes polynomial. Via mapping the Hessian of the training dynamics to a Hamiltonian in the imaginary time, we reveal the nature of the phase transition to be second-order with the exponent $\nu=1$, where scale invariance and closing gap are observed at critical point. We also provide a non-perturbative analytical theory to explain the phase transition via a restricted Haar ensemble at late time, when the output state approaches the steady state. The theory findings are verified experimentally on IBM quantum devices.

Producing high-quality forecasts of key climate variables such as temperature and precipitation on subseasonal time scales has long been a gap in operational forecasting. Recent studies have shown promising results using machine learning (ML) models to advance subseasonal forecasting (SSF), but several open questions remain. First, several past approaches use the average of an ensemble of physics-based forecasts as an input feature of these models. However, ensemble forecasts contain information that can aid prediction beyond only the ensemble mean. Second, past methods have focused on average performance, whereas forecasts of extreme events are far more important for planning and mitigation purposes. Third, climate forecasts correspond to a spatially-varying collection of forecasts, and different methods account for spatial variability in the response differently. Trade-offs between different approaches may be mitigated with model stacking. This paper describes the application of a variety of ML methods used to predict monthly average precipitation and two meter temperature using physics-based predictions (ensemble forecasts) and observational data such as relative humidity, pressure at sea level, or geopotential height, two weeks in advance for the whole continental United States. Regression, quantile regression, and tercile classification tasks using linear models, random forests, convolutional neural networks, and stacked models are considered. The proposed models outperform common baselines such as historical averages (or quantiles) and ensemble averages (or quantiles). This paper further includes an investigation of feature importance, trade-offs between using the full ensemble or only the ensemble average, and different modes of accounting for spatial variability.

Variational quantum circuits (VQCs) [1] are candidates for achieving practical quantum advantages in the noisy intermediate-scale quantum (NISQ) era [2], when scalable error-corrected quantum computers are not yet available. VQCs utilize classical control to optimize a quantum circuit to solve computation problems, including optimization [3], eigen-system problem [4-10], partial-differential equations [11], quantum simulation [12-14] and machine learning [15-23]. As a general approach of designing quantum circuits, it has also found applications in the approximation [24], preparation [25, 26], classification [27-31] and tomography [32] of quantum states. Initial works on VQCs concern discrete-variable (DV) finite-dimensional systems of qubits, which are natural for computation; while continous-variable (CV) systems of bosonic qumodes are less explored. Yet, many important quantum systems are modelled by qumodes. For example, quantum communication and networking [33-37] rely on photons--the only flying quantum information carrier. In this regard, quantum transduction and entanglement distillation are shown to be enhanced by CV VQCs [38]; Photonic quantum computers [39, 40] are also relying on bosonic encoding such as the cat code and Gottesman-Kitaev-Preskill (GKP) code [41], which has shown great promise [42, 43]. The engineering of such code states are greatly boosted by CV VQCs [44-47]; Finally, distributed entangled sensor networks ubiquitously rely on CV VQCs to achieve quantum advantages in sensing [48-51] and data classification [52, 53]. Different from traditional algorithms, the runtime of VQCs is characterized by the time necessary to train the variational parameters to optimize a cost function.

The inverse Potts problem to infer the Boltzmann distribution for homologous protein sequences from their single-site and pairwise frequencies recently attracts a great deal of attention due to its capacity to accurately predict residue-residue contacts in a 3D protein complex. A Boltzmann machine for the accurate estimation of the field and coupling interactions, which is required for other studies in protein evolution and folding, is studied about learning methods, regularization models and a tuning method of regularization parameters in order to infer the interactions with reasonable characteristics. Using $L_2$ regularization for fields, group $L_1$ for couplings is shown to be very effective for parse couplings in comparison with $L_2$ and with $L_1$. Two regularization parameters for fields and couplings are tuned to yield equal values for both the sample average and the ensemble average of evolutionary energies of natural proteins. Both the averages along a learning process smoothly change and converge, but their profiles are very different between the learning methods. Most per-parameter adaptive learning methods invented for machine learning cannot learn reasonable parameters for sparse-interaction systems. A modified Adam (ModAdam) method is invented to make step-size proportional to the partial derivative for sparse couplings and to use a soft thresholding function for group $L_1$. It is shown by first inferring interactions from protein sequences and then from Monte Carlo samples that the fields and couplings can be well recovered by the group $L_1$ and the ModAdam method. However, the distribution of evolutionary energies over natural proteins is shifted towards lower energies from that of Monte Carlo samples, indicating that there may be higher-order interactions to favor natural sequences.

This report describes the suicidality prediction models created under the DARPA DCAPS program in association with the Durkheim Project [http://durkheimproject.org/]. The models were built primarily from unstructured text (free-format clinician notes) for several hundred patient records obtained from the Veterans Health Administration (VHA). The models were constructed using a genetic programming algorithm applied to bag-of-words and bag-of-phrases datasets. The influence of additional structured data was explored but was found to be minor. Given the small dataset size, classification between cohorts was high fidelity (98%). Cross-validation suggests these models are reasonably predictive, with an accuracy of 50% to 69% on five rotating folds, with ensemble averages of 58% to 67%. One particularly noteworthy result is that word-pairs can dramatically improve classification accuracy; but this is the case only when one of the words in the pair is already known to have a high predictive value. By contrast, the set of all possible word-pairs does not improve on a simple bag-of-words model.