We develop parallel predictive entropy search (PPES), a novel algorithm for Bayesian optimization of expensive black-box objective functions. At each iteration, PPES aims to select a batch of points which will maximize the information gain about the global maximizer of the objective. Well known strategies exist for suggesting a single evaluation point based on previous observations, while far fewer are known for selecting batches of points to evaluate in parallel. The few batch selection schemes that have been studied all resort to greedy methods to compute an optimal batch. To the best of our knowledge, PPES is the first non-greedy batch Bayesian optimization strategy. We demonstrate the benefit of this approach in optimization performance on both synthetic and real world applications, including problems in machine learning, rocket science and robotics.

In this study, we demonstrate that the linear combination of atomic orbitals (LCAO), an approximation introduced by Pauling and Lennard-Jones in the 1920s, corresponds to graph convolutional networks (GCNs) for molecules. However, GCNs involve unnecessary nonlinearity and deep architecture. We also verify that molecular GCNs are based on a poor basis function set compared with the standard one used in theoretical calculations or quantum chemical simulations. From these observations, we describe the quantum deep field (QDF), a machine learning (ML) model based on an underlying quantum physics, in particular the density functional theory (DFT). We believe that the QDF model can be easily understood because it can be regarded as a single linear layer GCN. Moreover, it uses two vanilla feedforward neural networks to learn an energy functional and a Hohenberg-Kohn map that have nonlinearities inherent in quantum physics and the DFT. For molecular energy prediction tasks, we demonstrated the viability of an "extrapolation," in which we trained a QDF model with small molecules, tested it with large molecules, and achieved high extrapolation performance. We believe that we should move away from the competition of interpolation accuracy within benchmark datasets and evaluate ML models based on physics using an extrapolation setting; this will lead to reliable and practical applications, such as fast, large-scale molecular screening for discovering effective materials.

Super-resolution is the problem of recovering a superposition of point sources using bandlimited measurements, which may be corrupted with noise. This signal processing problem arises in numerous imaging problems, ranging from astronomy to biology to spectroscopy, where it is common to take (coarse) Fourier measurements of an object. Of particular interest is in obtaining estimation procedures which are robust to noise, with the following desirable statistical and computational properties: we seek to use coarse Fourier measurements (bounded by some cutoff frequency); we hope to take a (quantifiably) small number of measurements; we desire our algorithm to run quickly. Suppose we have k point sources in d dimensions, where the points are separated by at least from each other (in Euclidean distance). This work provides an algorithm with the following favorable guarantees: The algorithm uses Fourier measurements, whose frequencies are bounded by O (1 /) (up to log factors).

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

The majority of LiRP A-based methods focus on simple feed-forward networks and need particular manual derivations and implementations when extended to other architectures. In this paper, we develop an automatic framework to enable perturbation analysis on any neural network structures, by generalizing existing LiRP A algorithms such as CROWN to operate on general computational graphs.

This paper presents a Bayesian optimization method with exponential convergence without the need of auxiliary optimization and without the δ -cover sampling. Most Bayesian optimization methods require auxiliary optimization: an additional non-convex global optimization problem, which can be time-consuming and hard to implement in practice. Also, the existing Bayesian optimization method with exponential convergence [ 1] requires access to the δ -cover sampling, which was considered to be impractical [ 1, 2]. Our approach eliminates both requirements and achieves an exponential convergence rate.

Wind farm placement arranges the size and the location of multiple wind farms within a given region. The power output is highly related to the wind speed on spatial and temporal levels, which can be modeled by advanced data-driven approaches. To this end, we use a probabilistic neural network as a surrogate that accounts for the spatiotemporal correlations of wind speed. This neural network uses ReLU activation functions so that it can be reformulated as mixed-integer linear set of constraints (constraint learning). We embed these constraints into the placement decision problem, formulated as a two-stage stochastic optimization problem. Specifically, conditional quantiles of the total electricity production are regarded as recursive decisions in the second stage. We use real high-resolution regional data from a northern region in Spain. We validate that the constraint learning approach outperforms the classical bilinear interpolation method. Numerical experiments are implemented on risk-averse investors. The results indicate that risk-averse investors concentrate on dominant sites with strong wind, while exhibiting spatial diversification and sensitive capacity spread in non-dominant sites. Furthermore, we show that if we introduce transmission line costs in the problem, risk-averse investors favor locations closer to the substations. On the contrary, risk-neutral investors are willing to move to further locations to achieve higher expected profits. Our results conclude that the proposed novel approach is able to tackle a portfolio of regional wind farm placements and further provide guidance for risk-averse investors.

The increasing integration of distributed energy resources (DERs), particularly renewables, poses significant challenges for power system protection, with fault classification (FC) and fault localization (FL) being among the most critical tasks. Conventional protection schemes, based on fixed thresholds, cannot reliably identify and localize short circuits with the increasing complexity of the grid under dynamic conditions. Machine learning (ML) offers a promising alternative; however, systematic benchmarks across models and settings remain limited. This work presents, for the first time, a comparative benchmarking study of classical ML models for FC and FL in power system protection based on EMT data. Using voltage and current waveforms segmented into sliding windows of 10 ms to 50 ms, we evaluate models under realistic real-time constraints. Performance is assessed in terms of accuracy, robustness to window size, and runtime efficiency. The best-performing FC model achieved an F1 score of 0.992$\pm$0.001, while the top FL model reached an R2 of 0.806$\pm$0.008 with a mean processing time of 0.563 ms.