Explicitly accounting for uncertainties is paramount to the safety of engineering structures. Optimization which is often carried out at the early stage of the structural design offers an ideal framework for this task. When the uncertainties are mainly affecting the objective function, robust design optimization is traditionally considered. This work further assumes the existence of multiple and competing objective functions that need to be dealt with simultaneously. The optimization problem is formulated by considering quantiles of the objective functions which allows for the combination of both optimality and robustness in a single metric. By introducing the concept of common random numbers, the resulting nested optimization problem may be solved using a general-purpose solver, herein the non-dominated sorting genetic algorithm (NSGA-II). The computational cost of such an approach is however a serious hurdle to its application in real-world problems. We therefore propose a surrogate-assisted approach using Kriging as an inexpensive approximation of the associated computational model. The proposed approach consists of sequentially carrying out NSGA-II while using an adaptively built Kriging model to estimate the quantiles. Finally, the methodology is adapted to account for mixed categorical-continuous parameters as the applications involve the selection of qualitative design parameters as well. The methodology is first applied to two analytical examples showing its efficiency. The third application relates to the selection of optimal renovation scenarios of a building considering both its life cycle cost and environmental impact. It shows that when it comes to renovation, the heating system replacement should be the priority.

Accurate PhotoVoltaic (PV) power generation forecasting is vital for the efficient operation of Smart Grids. The automated design of such accurate forecasting models for individual PV plants includes two challenges: First, information about the PV mounting configuration (i.e. inclination and azimuth angles) is often missing. Second, for new PV plants, the amount of historical data available to train a forecasting model is limited (cold-start problem). We address these two challenges by proposing a new method for day-ahead PV power generation forecasts called AutoPV. AutoPV is a weighted ensemble of forecasting models that represent different PV mounting configurations. This representation is achieved by pre-training each forecasting model on a separate PV plant and by scaling the model's output with the peak power rating of the corresponding PV plant. To tackle the cold-start problem, we initially weight each forecasting model in the ensemble equally. To tackle the problem of missing information about the PV mounting configuration, we use new data that become available during operation to adapt the ensemble weights to minimize the forecasting error. AutoPV is advantageous as the unknown PV mounting configuration is implicitly reflected in the ensemble weights, and only the PV plant's peak power rating is required to re-scale the ensemble's output. AutoPV also allows to represent PV plants with panels distributed on different roofs with varying alignments, as these mounting configurations can be reflected proportionally in the weighting. Additionally, the required computing memory is decoupled when scaling AutoPV to hundreds of PV plants, which is beneficial in Smart Grids with limited computing capabilities. For a real-world data set with 11 PV plants, the accuracy of AutoPV is comparable to a model trained on two years of data and outperforms an incrementally trained model.

We present a method for providing statistical guarantees on runtime safety and goal reachability for integrated planning and control of a class of systems with unknown nonlinear stochastic underactuated dynamics. Specifically, given a dynamics dataset, our method jointly learns a mean dynamics model, a spatially-varying disturbance bound that captures the effect of noise and model mismatch, and a feedback controller based on contraction theory that stabilizes the learned dynamics. We propose a sampling-based planner that uses the mean dynamics model and simultaneously bounds the closed-loop tracking error via a learned disturbance bound. We employ techniques from Extreme Value Theory (EVT) to estimate, to a specified level of confidence, several constants which characterize the learned components and govern the size of the tracking error bound. This ensures plans are guaranteed to be safely tracked at runtime. We validate that our guarantees translate to empirical safety in simulation on a 10D quadrotor, and in the real world on a physical CrazyFlie quadrotor and Clearpath Jackal robot, whereas baselines that ignore the model error and stochasticity are unsafe.

In the field of derivative-free optimization, both of its main branches, the deterministic and nature-inspired techniques, experienced in recent years substantial advancement. In this paper, we provide an extensive computational comparison of selected methods from each of these branches. The chosen representatives were either standard and well-utilized methods, or the best-performing methods from recent numerical comparisons. The computational comparison was performed on five different benchmark sets and the results were analyzed in terms of performance, time complexity, and convergence properties of the selected methods. The results showed that, when dealing with situations where the objective function evaluations are relatively cheap, the nature-inspired methods have a significantly better performance than their deterministic counterparts. However, in situations when the function evaluations are costly or otherwise prohibited, the deterministic methods might provide more consistent and overall better results.

Many commodity crops have growth stages during which they are particularly vulnerable to stress-induced yield loss. In-season crop progress information is useful for quantifying crop risk, and satellite remote sensing (RS) can be used to track progress at regional scales. At present, all existing RS-based crop progress estimation (CPE) methods which target crop-specific stages rely on ground truth data for training/calibration. This reliance on ground survey data confines CPE methods to surveyed regions, limiting their utility. In this study, a new method is developed for conducting RS-based in-season CPE in unsurveyed regions by combining data from surveyed regions with synthetic crop progress data generated for an unsurveyed region. Corn-growing zones in Argentina were used as surrogate 'unsurveyed' regions. Existing weather generation, crop growth, and optical radiative transfer models were linked to produce synthetic weather, crop progress, and canopy reflectance data. A neural network (NN) method based upon bi-directional Long Short-Term Memory was trained separately on surveyed data, synthetic data, and two different combinations of surveyed and synthetic data. A stopping criterion was developed which uses the weighted divergence of surveyed and synthetic data validation loss. Net F1 scores across all crop progress stages increased by 8.7% when trained on a combination of surveyed region and synthetic data, and overall performance was only 21% lower than when the NN was trained on surveyed data and applied in the US Midwest. Performance gain from synthetic data was greatest in zones with dual planting windows, while the inclusion of surveyed region data from the US Midwest helped mitigate NN sensitivity to noise in NDVI data. Overall results suggest in-season CPE in other unsurveyed regions may be possible with increased quantity and variety of synthetic crop progress data.

Experimental sciences have come to depend heavily on our ability to organize and interpret high-dimensional datasets. Natural laws, conservation principles, and inter-dependencies among observed variables yield geometric structure, with fewer degrees of freedom, on the dataset. We introduce the frameworks of semiclassical and microlocal analysis to data analysis and develop a novel, yet natural uncertainty principle for extracting fine-scale features of this geometric structure in data, crucially dependent on data-driven approximations to quantum mechanical processes underlying geometric optics. This leads to the first tractable algorithm for approximation of wave dynamics and geodesics on data manifolds with rigorous probabilistic convergence rates under the manifold hypothesis. We demonstrate our algorithm on real-world datasets, including an analysis of population mobility information during the COVID-19 pandemic to achieve four-fold improvement in dimensionality reduction over existing state-of-the-art and reveal anomalous behavior exhibited by less than 1.2% of the entire dataset. Our work initiates the study of data-driven quantum dynamics for analyzing datasets, and we outline several future directions for research.

Discriminative features extracted from the sparse coding model have been shown to perform well for classification. Recent deep learning architectures have further improved reconstruction in inverse problems by considering new dense priors learned from data. We propose a novel dense and sparse coding model that integrates both representation capability and discriminative features. The model studies the problem of recovering a dense vector $\mathbf{x}$ and a sparse vector $\mathbf{u}$ given measurements of the form $\mathbf{y} = \mathbf{A}\mathbf{x}+\mathbf{B}\mathbf{u}$. Our first analysis proposes a geometric condition based on the minimal angle between spanning subspaces corresponding to the matrices $\mathbf{A}$ and $\mathbf{B}$ that guarantees unique solution to the model. The second analysis shows that, under mild assumptions, a convex program recovers the dense and sparse components. We validate the effectiveness of the model on simulated data and propose a dense and sparse autoencoder (DenSaE) tailored to learning the dictionaries from the dense and sparse model. We demonstrate that (i) DenSaE denoises natural images better than architectures derived from the sparse coding model ($\mathbf{B}\mathbf{u}$), (ii) in the presence of noise, training the biases in the latter amounts to implicitly learning the $\mathbf{A}\mathbf{x} + \mathbf{B}\mathbf{u}$ model, (iii) $\mathbf{A}$ and $\mathbf{B}$ capture low- and high-frequency contents, respectively, and (iv) compared to the sparse coding model, DenSaE offers a balance between discriminative power and representation.

Generating power system states that have similar distribution and dependency to the historical ones is essential for the tasks of system planning and security assessment, especially when the historical data is insufficient. In this paper, we described a generative model for load profiles of industrial and commercial customers, based on the conditional variational autoencoder (CVAE) neural network architecture, which is challenging due to the highly variable nature of such profiles. Generated contextual load profiles were conditioned on the month of the year and typical power exchange with the grid. Moreover, the quality of generations was both visually and statistically evaluated. The experimental results demonstrate our proposed CVAE model can capture temporal features of historical load profiles and generate `realistic' data with satisfying univariate distributions and multivariate dependencies.

Risk management in many environmental settings requires an understanding of the mechanisms that drive extreme events. Useful metrics for quantifying such risk are extreme quantiles of response variables conditioned on predictor variables that describe, e.g., climate, biosphere and environmental states. Typically these quantiles lie outside the range of observable data and so, for estimation, require specification of parametric extreme value models within a regression framework. Classical approaches in this context utilise linear or additive relationships between predictor and response variables and suffer in either their predictive capabilities or computational efficiency; moreover, their simplicity is unlikely to capture the truly complex structures that lead to the creation of extreme wildfires. In this paper, we propose a new methodological framework for performing extreme quantile regression using artificial neutral networks, which are able to capture complex non-linear relationships and scale well to high-dimensional data. The ``black box" nature of neural networks means that they lack the desirable trait of interpretability often favoured by practitioners; thus, we unify linear, and additive, regression methodology with deep learning to create partially-interpretable neural networks that can be used for statistical inference but retain high prediction accuracy. To complement this methodology, we further propose a novel point process model for extreme values which overcomes the finite lower-endpoint problem associated with the generalised extreme value class of distributions. Efficacy of our unified framework is illustrated on U.S. wildfire data with a high-dimensional predictor set and we illustrate vast improvements in predictive performance over linear and spline-based regression techniques.

The fast development of renewable energies is a necessity to mitigate climate changes [22]. Wind energy has developed rapidly over the past three decades, with an average annual growth rate of 23.6% between 1990 and 2016 [17], and is now considered as a mature technology. The share of renewable energies in global electricity generation reached 29% in 2020, and is expected to keep growing fast in coming years [18] which raises a number of challenges, stemming from the variability and spatial distribution of the resource. Then, in order to facilitate the dynamic management of electricity networks, forecasts of wind energy require continual improvement. Short timescales, from a few minutes to a few hours, are of particular importance for operations. To produce forecasts, one can rely on several distinct sources of information. On timescales of half a day to about a week, deterministic weather forecasts provide a representation on a grid of the atmospheric state, including wind speed near the surface. The skill of such numerical weather forecasts (NWP) models has continually increased over the past decades [2], while their spatial resolution has also grown finer (down to few km).