Unveiling feeder topologies from data is of paramount importance to advance situational awareness and proper utilization of smart resources in power distribution grids. This tutorial summarizes, contrasts, and establishes useful links between recent works on topology identification and detection schemes that have been proposed for power distribution grids. The primary focus is to highlight methods that overcome the limited availability of measurement devices in distribution grids, while enhancing topology estimates using conservation laws of power-flow physics and structural properties of feeders. Grid data from phasor measurement units or smart meters can be collected either passively in the traditional way, or actively, upon actuating grid resources and measuring the feeder's voltage response. Analytical claims on feeder identifiability and detectability are reviewed under disparate meter placement scenarios. Such topology learning claims can be attained exactly or approximately so via algorithmic solutions with various levels of computational complexity, ranging from least-squares fits to convex optimization problems, and from polynomial-time searches over graphs to mixed-integer programs. Although the emphasis is on radial single-phase feeders, extensions to meshed and/or multiphase circuits are sometimes possible and discussed. This tutorial aspires to provide researchers and engineers with knowledge of the current state-of-the-art in tractable distribution grid learning and insights into future directions of work.

Ensemble forecast post-processing is a necessary step in producing accurate probabilistic forecasts. Conventional post-processing methods operate by estimating the parameters of a parametric distribution, frequently on a perlocation or per-lead-time basis, which limits their expressive power. We propose a novel, neural network-based method, which produces forecasts for all locations and lead times, jointly. To relax the distributional assumption made by many post-processing methods, our approach incorporates normalizing flows as flexible parametric distribution estimators. This enables us to model varying forecast distributions in a mathematically exact way. We demonstrate the effectiveness of our method in the context of the EUPPBench benchmark, where we conduct temperature forecast post-processing for stations in a sub-region of western Europe. We show that our novel method exhibit state-of-the-art performance on the benchmark, outclassing our previous, well-performing entry. Additionally, by providing a detailed comparison of three variants of our novel post-processing method, we elucidate the reasons why our method outperforms per-lead-time-based approaches and approaches with distributional assumptions.

The concept of integrating physics-based and data-driven approaches has become popular for modeling sustainable energy systems. However, the existing literature mainly focuses on the data-driven surrogates generated to replace physics-based models. These models often trade accuracy for speed but lack the generalisability, adaptability, and interpretability inherent in physics-based models, which are often indispensable in the modeling of real-world dynamic systems for optimization and control purposes. In this work, we propose a novel architecture for generating model-integrated neural networks (MINN) to allow integration on the level of learning physics-based dynamics of the system. The obtained hybrid model solves an unsettled research problem in control-oriented modeling, i.e., how to obtain an optimally simplified model that is physically insightful, numerically accurate, and computationally tractable simultaneously. We apply the proposed neural network architecture to model the electrochemical dynamics of lithium-ion batteries and show that MINN is extremely data-efficient to train while being sufficiently generalizable to previously unseen input data, owing to its underlying physical invariants. The MINN battery model has an accuracy comparable to the first principle-based model in predicting both the system outputs and any locally distributed electrochemical behaviors but achieves two orders of magnitude reduction in the solution time.

Experimental data is often comprised of variables measured independently, at different sampling rates (non-uniform ${\Delta}$t between successive measurements); and at a specific time point only a subset of all variables may be sampled. Approaches to identifying dynamical systems from such data typically use interpolation, imputation or subsampling to reorganize or modify the training data $\textit{prior}$ to learning. Partial physical knowledge may also be available $\textit{a priori}$ (accurately or approximately), and data-driven techniques can complement this knowledge. Here we exploit neural network architectures based on numerical integration methods and $\textit{a priori}$ physical knowledge to identify the right-hand side of the underlying governing differential equations. Iterates of such neural-network models allow for learning from data sampled at arbitrary time points $\textit{without}$ data modification. Importantly, we integrate the network with available partial physical knowledge in "physics informed gray-boxes"; this enables learning unknown kinetic rates or microbial growth functions while simultaneously estimating experimental parameters.

Poverty is a multifaceted phenomenon linked to the lack of capabilities of households to earn a sustainable livelihood, increasingly being assessed using multidimensional indicators. Its spatial pattern depends on social, economic, political, and regional variables. Artificial intelligence has shown immense scope in analyzing the complexities and nuances of poverty. The proposed project aims to examine the poverty situation of rural India for the period of 1990-2022 based on the quality of life and livelihood indicators. The districts will be classified into `advanced', `catching up', `falling behind', and `lagged' regions. The project proposes to integrate multiple data sources, including conventional national-level large sample household surveys, census surveys, and proxy variables like daytime, and nighttime data from satellite images, and communication networks, to name a few, to provide a comprehensive view of poverty at the district level. The project also intends to examine causation and longitudinal analysis to examine the reasons for poverty. Poverty and inequality could be widening in developing countries due to demographic and growth-agglomerating policies. Therefore, targeting the lagging regions and the vulnerable population is essential to eradicate poverty and improve the quality of life to achieve the goal of `zero poverty'. Thus, the study also focuses on the districts with a higher share of the marginal section of the population compared to the national average to trace the performance of development indicators and their association with poverty in these regions.

Understanding the structure, quantity, and type of snow in mountain landscapes is crucial for assessing avalanche safety, interpreting satellite imagery, building accurate hydrology models, and choosing the right pair of skis for your weekend trip. Currently, such characteristics of snowpack are measured using a combination of remote satellite imagery, weather stations, and laborious point measurements and descriptions provided by local forecasters, guides, and backcountry users. Here, we explore how characteristics of the top layer of snowpack could be estimated while skiing using strain sensors mounted to the top surface of an alpine ski. We show that with two strain gauges and an inertial measurement unit it is feasible to correctly assign one of three qualitative labels (powder, slushy, or icy/groomed snow) to each 10 second segment of a trajectory with 97% accuracy, independent of skiing style. Our algorithm uses a combination of a data-driven linear model of the ski-snow interaction, dimensionality reduction, and a Naive Bayes classifier. Comparisons of classifier performance between strain gauges suggest that the optimal placement of strain gauges is halfway between the binding and the tip/tail of the ski, in the cambered section just before the point where the unweighted ski would touch the snow surface. The ability to classify snow, potentially in real-time, using skis opens the door to applications that range from citizen science efforts to map snow surface characteristics in the backcountry, and develop skis with automated stiffness tuning based on the snow type.

We present a computationally-efficient strategy to initialise the hyperparameters of a Gaussian process (GP) avoiding the computation of the likelihood function. Our strategy can be used as a pretraining stage to find initial conditions for maximum-likelihood (ML) training, or as a standalone method to compute hyperparameters values to be plugged in directly into the GP model. Motivated by the fact that training a GP via ML is equivalent (on average) to minimising the KL-divergence between the true and learnt model, we set to explore different metrics/divergences among GPs that are computationally inexpensive and provide hyperparameter values that are close to those found via ML. In practice, we identify the GP hyperparameters by projecting the empirical covariance or (Fourier) power spectrum onto a parametric family, thus proposing and studying various measures of discrepancy operating on the temporal and frequency domains. Our contribution extends the variogram method developed by the geostatistics literature and, accordingly, it is referred to as the generalised variogram method (GVM). In addition to the theoretical presentation of GVM, we provide experimental validation in terms of accuracy, consistency with ML and computational complexity for different kernels using synthetic and real-world data.

We apply the Physics Informed Neural Network (PINN) to the problem of wildfire fire-front modelling. We use the PINN to solve the level-set equation, which is a partial differential equation that models a fire-front through the zero-level-set of a level-set function. The result is a PINN that simulates a fire-front as it propagates through the spatio-temporal domain. We show that popular optimisation cost functions used in the literature can result in PINNs that fail to maintain temporal continuity in modelled fire-fronts when there are extreme changes in exogenous forcing variables such as wind direction. We thus propose novel additions to the optimisation cost function that improves temporal continuity under these extreme changes. Furthermore, we develop an approach to perform data assimilation within the PINN such that the PINN predictions are drawn towards observations of the fire-front. Finally, we incorporate our novel approaches into a Bayesian PINN (B-PINN) to provide uncertainty quantification in the fire-front predictions. This is significant as the standard solver, the level-set method, does not naturally offer the capability for data assimilation and uncertainty quantification. Our results show that, with our novel approaches, the B-PINN can produce accurate predictions with high quality uncertainty quantification on real-world data.

ChatGPT is a large language model recently released by the OpenAI company. In this technical report, we explore for the first time the capability of ChatGPT for programming numerical algorithms. Specifically, we examine the capability of GhatGPT for generating codes for numerical algorithms in different programming languages, for debugging and improving written codes by users, for completing missed parts of numerical codes, rewriting available codes in other programming languages, and for parallelizing serial codes. Additionally, we assess if ChatGPT can recognize if given codes are written by humans or machines. To reach this goal, we consider a variety of mathematical problems such as the Poisson equation, the diffusion equation, the incompressible Navier-Stokes equations, compressible inviscid flow, eigenvalue problems, solving linear systems of equations, storing sparse matrices, etc. Furthermore, we exemplify scientific machine learning such as physics-informed neural networks and convolutional neural networks with applications to computational physics. Through these examples, we investigate the successes, failures, and challenges of ChatGPT. Examples of failures are producing singular matrices, operations on arrays with incompatible sizes, programming interruption for relatively long codes, etc. Our outcomes suggest that ChatGPT can successfully program numerical algorithms in different programming languages, but certain limitations and challenges exist that require further improvement of this machine learning model.

Deep reinforcement learning (RL) has been endowed with high expectations in tackling challenging manipulation tasks in an autonomous and self-directed fashion. Despite the significant strides made in the development of reinforcement learning, the practical deployment of this paradigm is hindered by at least two barriers, namely, the engineering of a reward function and ensuring the safety guaranty of learning-based controllers. In this paper, we address these challenging limitations by proposing a framework that merges a reinforcement learning \lstinline[columns=fixed]{planner} that is trained using sparse rewards with a model predictive controller (MPC) \lstinline[columns=fixed]{actor}, thereby offering a safe policy. On the one hand, the RL \lstinline[columns=fixed]{planner} learns from sparse rewards by selecting intermediate goals that are easy to achieve in the short term and promising to lead to target goals in the long term. On the other hand, the MPC \lstinline[columns=fixed]{actor} takes the suggested intermediate goals from the RL \lstinline[columns=fixed]{planner} as the input and predicts how the robot's action will enable it to reach that goal while avoiding any obstacles over a short period of time. We evaluated our method on four challenging manipulation tasks with dynamic obstacles and the results demonstrate that, by leveraging the complementary strengths of these two components, the agent can solve manipulation tasks in complex, dynamic environments safely with a $100\%$ success rate. Videos are available at \url{https://videoviewsite.wixsite.com/mpc-hgg}.