Weight-sharing Neural Architecture Search (WS-NAS) provides an efficient mechanism for developing end-to-end deep recommender models. However, in complex search spaces, distinguishing between superior and inferior architectures (or paths) is challenging. This challenge is compounded by the limited coverage of the supernet and the co-adaptation of subnet weights, which restricts the exploration and exploitation capabilities inherent to weight-sharing mechanisms. To address these challenges, we introduce Farthest Greedy Path Sampling (FGPS), a new path sampling strategy that balances path quality and diversity. FGPS enhances path diversity to facilitate more comprehensive supernet exploration, while emphasizing path quality to ensure the effective identification and utilization of promising architectures. By incorporating FGPS into a Two-shot NAS (TS-NAS) framework, we derive high-performance architectures. Evaluations on three Click-Through Rate (CTR) prediction benchmarks demonstrate that our approach consistently achieves superior results, outperforming both manually designed and most NAS-based models.

Data assimilation, in its most comprehensive form, addresses the Bayesian inverse problem of identifying plausible state trajectories that explain noisy or incomplete observations of stochastic dynamical systems. Various approaches have been proposed to solve this problem, including particle-based and variational methods. However, most algorithms depend on the transition dynamics for inference, which becomes intractable for long time horizons or for high-dimensional systems with complex dynamics, such as oceans or atmospheres. In this work, we introduce score-based data assimilation for trajectory inference. We learn a score-based generative model of state trajectories based on the key insight that the score of an arbitrarily long trajectory can be decomposed into a series of scores over short segments. After training, inference is carried out using the score model, in a non-autoregressive manner by generating all states simultaneously. Quite distinctively, we decouple the observation model from the training procedure and use it only at inference to guide the generative process, which enables a wide range of zero-shot observation scenarios. We present theoretical and empirical evidence supporting the effectiveness of our method.

We study pointwise estimation and uncertainty quantification for a sparse variational Gaussian process method with eigenvector inducing variables. For a rescaled Brownian motion prior, we derive theoretical guarantees and limitations for the frequentist size and coverage of pointwise credible sets. For sufficiently many inducing variables, we precisely characterize the asymptotic frequentist coverage, deducing when credible sets from this variational method are conservative and when overconfident/misleading. We numerically illustrate the applicability of our results and discuss connections with other common Gaussian process priors.

We propose principled Gaussian processes (GPs) for modeling functions defined over the edge set of a simplicial 2-complex, a structure similar to a graph in which edges may form triangular faces. This approach is intended for learning flow-type data on networks where edge flows can be characterized by the discrete divergence and curl. Drawing upon the Hodge decomposition, we first develop classes of divergence-free and curl-free edge GPs, suitable for various applications. We then combine them to create \emph{Hodge-compositional edge GPs} that are expressive enough to represent any edge function. These GPs facilitate direct and independent learning for the different Hodge components of edge functions, enabling us to capture their relevance during hyperparameter optimization. To highlight their practical potential, we apply them for flow data inference in currency exchange, ocean flows and water supply networks, comparing them to alternative models.

This book aims to provide an introduction to the topic of deep learning algorithms. We review essential components of deep learning algorithms in full mathematical detail including different artificial neural network (ANN) architectures (such as fully-connected feedforward ANNs, convolutional ANNs, recurrent ANNs, residual ANNs, and ANNs with batch normalization) and different optimization algorithms (such as the basic stochastic gradient descent (SGD) method, accelerated methods, and adaptive methods). We also cover several theoretical aspects of deep learning algorithms such as approximation capacities of ANNs (including a calculus for ANNs), optimization theory (including Kurdyka-{\L}ojasiewicz inequalities), and generalization errors. In the last part of the book some deep learning approximation methods for PDEs are reviewed including physics-informed neural networks (PINNs) and deep Galerkin methods. We hope that this book will be useful for students and scientists who do not yet have any background in deep learning at all and would like to gain a solid foundation as well as for practitioners who would like to obtain a firmer mathematical understanding of the objects and methods considered in deep learning.

Abstract--Mobile robots often have limited battery life and need to recharge periodically. This paper presents an RRTbased path-planning algorithm that addresses battery power management. A path is generated continuously from the robot's current position to its recharging station. The robot decides if a recharge is needed based on the energy required to travel on that path and the robot's current power. RRT* is used to generate the first path, and then subsequent paths are made using information from previous trees. Finally, the presented algorithm was compared with Extended Rate Random Tree (ERRT) algorithm [4].

A thorough regulation of building energy systems translates in relevant energy savings and in a better comfort for the occupants. Algorithms to predict the thermal state of a building on a certain time horizon with a good confidence are essential for the implementation of effective control systems. This work presents a global Transformer architecture for indoor temperature forecasting in multi-room buildings, aiming at optimizing energy consumption and reducing greenhouse gas emissions associated with HVAC systems. Recent advancements in deep learning have enabled the development of more sophisticated forecasting models compared to traditional feedback control systems. The proposed global Transformer architecture can be trained on the entire dataset encompassing all rooms, eliminating the need for multiple room-specific models, significantly improving predictive performance, and simplifying deployment and maintenance. Notably, this study is the first to apply a Transformer architecture for indoor temperature forecasting in multi-room buildings. The proposed approach provides a novel solution to enhance the accuracy and efficiency of temperature forecasting, serving as a valuable tool to optimize energy consumption and decrease greenhouse gas emissions in the building sector.

Load shapes derived from smart meter data are frequently employed to analyze daily energy consumption patterns, particularly in the context of applications like Demand Response (DR). Nevertheless, one of the most important challenges to this endeavor lies in identifying the most suitable consumer clusters with similar consumption behaviors. In this paper, we present a novel machine learning based framework in order to achieve optimal load profiling through a real case study, utilizing data from almost 5000 households in London. Four widely used clustering algorithms are applied specifically K-means, K-medoids, Hierarchical Agglomerative Clustering and Density-based Spatial Clustering. An empirical analysis as well as multiple evaluation metrics are leveraged to assess those algorithms. Following that, we redefine the problem as a probabilistic classification one, with the classifier emulating the behavior of a clustering algorithm,leveraging Explainable AI (xAI) to enhance the interpretability of our solution. According to the clustering algorithm analysis the optimal number of clusters for this case is seven. Despite that, our methodology shows that two of the clusters, almost 10\% of the dataset, exhibit significant internal dissimilarity and thus it splits them even further to create nine clusters in total. The scalability and versatility of our solution makes it an ideal choice for power utility companies aiming to segment their users for creating more targeted Demand Response programs.

Coverage path planning is a fundamental challenge in robotics, with diverse applications in aerial surveillance, manufacturing, cleaning, inspection, agriculture, and more. The main objective is to devise a trajectory for an agent that efficiently covers a given area, while minimizing time or energy consumption. Existing practical approaches often lack a solid theoretical foundation, relying on purely heuristic methods, or overly abstracting the problem to a simple Traveling Salesman Problem in Grid Graphs. Moreover, the considered cost functions only rarely consider turn cost, prize-collecting variants for uneven cover demand, or arbitrary geometric regions. In this paper, we describe an array of systematic methods for handling arbitrary meshes derived from intricate, polygonal environments. This adaptation paves the way to compute efficient coverage paths with a robust theoretical foundation for real-world robotic applications. Through comprehensive evaluations, we demonstrate that the algorithm also exhibits low optimality gaps, while efficiently handling complex environments. Furthermore, we showcase its versatility in handling partial coverage and accommodating heterogeneous passage costs, offering the flexibility to trade off coverage quality and time efficiency.

Food security, a global concern, necessitates precise and diverse data-driven solutions to address its multifaceted challenges. This paper explores the integration of AI foundation models across various food security applications, leveraging distinct data types, to overcome the limitations of current deep and machine learning methods. Specifically, we investigate their utilization in crop type mapping, cropland mapping, field delineation and crop yield prediction. By capitalizing on multispectral imagery, meteorological data, soil properties, historical records, and high-resolution satellite imagery, AI foundation models offer a versatile approach. The study demonstrates that AI foundation models enhance food security initiatives by providing accurate predictions, improving resource allocation, and supporting informed decision-making. These models serve as a transformative force in addressing global food security limitations, marking a significant leap toward a sustainable and secure food future.