Weather-Informed Probabilistic Forecasting and Scenario Generation in Power Systems

The integration of renewable energy sources (RES) into power grids presents significant challenges due to their intrinsic stochasticity and uncertainty, necessitating the development of new techniques for reliable and efficient forecasting. This paper proposes a method combining probabilistic forecasting and Gaussian copula for day-ahead prediction and scenario generation of load, wind, and solar power in high-dimensional contexts. By incorporating weather covariates and restoring spatio-temporal correlations, the proposed method enhances the reliability of probabilistic forecasts in RES. Extensive numerical experiments compare the effectiveness of different time series models, with performance evaluated using comprehensive metrics on a real-world and high-dimensional dataset from Midcontinent Independent System Operator (MISO). The results highlight the importance of weather information and demonstrate the efficacy of the Gaussian copula in generating realistic scenarios, with the proposed weather-informed Temporal Fusion Transformer (WI-TFT) model showing superior performance.

Maximizing V-information for Pre-training Superior Foundation Models

Pre-training foundation models on large-scale datasets demonstrates exceptional performance. However, recent research questions this traditional notion, exploring whether an increase in pre-training data always leads to enhanced model performance. To address this issue, data-effective learning approaches have been introduced. However, current methods in this area lack a clear standard for sample selection. Our experiments reveal that by maximizing V-information, sample selection can be framed as an optimization problem, enabling effective improvement in model performance even with fewer samples. Under this guidance, we develop an optimal data-effective learning method (OptiDEL) to maximize V-information. The OptiDEL method generates hard samples to achieve or even exceed the performance of models trained on the full dataset while using substantially less data. We compare the OptiDEL method with state-of-the-art approaches finding that OptiDEL consistently outperforms existing approaches across different datasets, with foundation models trained on only 5% of the pre-training data surpassing the performance of those trained on the full dataset.

Manifold learning: what, how, and why

Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensional data is not merely a way to reduce the data; the new representations and descriptors obtained by ML reveal the geometric shape of high dimensional point clouds, and allow one to visualize, de-noise and interpret them. This survey presents the principles underlying ML, the representative methods, as well as their statistical foundations from a practicing statistician's perspective. It describes the trade-offs, and what theory tells us about the parameter and algorithmic choices we make in order to obtain reliable conclusions.

Asset Bundling for Wind Power Forecasting

The growing penetration of intermittent, renewable generation in US power grids, especially wind and solar generation, results in increased operational uncertainty. In that context, accurate forecasts are critical, especially for wind generation, which exhibits large variability and is historically harder to predict. To overcome this challenge, this work proposes a novel Bundle-Predict-Reconcile (BPR) framework that integrates asset bundling, machine learning, and forecast reconciliation techniques. The BPR framework first learns an intermediate hierarchy level (the bundles), then predicts wind power at the asset, bundle, and fleet level, and finally reconciles all forecasts to ensure consistency. This approach effectively introduces an auxiliary learning task (predicting the bundle-level time series) to help the main learning tasks. The paper also introduces new asset-bundling criteria that capture the spatio-temporal dynamics of wind power time series. Extensive numerical experiments are conducted on an industry-size dataset of 283 wind farms in the MISO footprint. The experiments consider short-term and day-ahead forecasts, and evaluates a large variety of forecasting models that include weather predictions as covariates. The results demonstrate the benefits of BPR, which consistently and significantly improves forecast accuracy over baselines, especially at the fleet level.

Optimization-based Learning for Dynamic Load Planning in Trucking Service Networks

The load planning problem is a critical challenge in service network design for parcel carriers: it decides how many trailers (or loads) to assign for dispatch over time between pairs of terminals. Another key challenge is to determine a flow plan, which specifies how parcel volumes are assigned to planned loads. This paper considers the Dynamic Load Planning Problem (DLPP) that considers both flow and load planning challenges jointly to adjust loads and flows as the demand forecast changes over time before the day of operations. The paper aims at developing a decision-support tool to inform planners making these decisions at terminals across the network. The paper formulates the DLPP as a MIP and shows that it admits a large number of symmetries in a network where each commodity can be routed through primary and alternate paths. As a result, an optimization solver may return fundamentally different solutions to closely related problems, confusing planners and reducing trust in optimization. To remedy this limitation, the paper proposes a Goal-Directed Optimization that eliminates those symmetries by generating optimal solutions staying close to a reference plan. The paper also proposes an optimization proxy to address the computational challenges of the optimization models. The proxy combines a machine learning model and a feasibility restoration model and finds solutions that satisfy real-time constraints imposed by planners-in-the-loop. An extensive computational study on industrial instances shows that the optimization proxy is around 10 times faster than the commercial solver in obtaining the same quality solutions and orders of magnitude faster for generating solutions that are consistent with each other. The proposed approach also demonstrates the benefits of the DLPP for load consolidation, and the significant savings obtained from combining machine learning and optimization.

Transfer Causal Learning: Causal Effect Estimation with Knowledge Transfer

A novel problem of improving causal effect estimation accuracy with the help of knowledge transfer under the same covariate (or feature) space setting, i.e., homogeneous transfer learning (TL), is studied, referred to as the Transfer Causal Learning (TCL) problem. While most recent efforts in adapting TL techniques to estimate average causal effect (ACE) have been focused on the heterogeneous covariate space setting, those methods are inadequate for tackling the TCL problem since their algorithm designs are based on the decomposition into shared and domain-specific covariate spaces. To address this issue, we propose a generic framework called $\ell_1$-TCL, which incorporates $\ell_1$ regularized TL for nuisance parameter estimation and downstream plug-in ACE estimators, including outcome regression, inverse probability weighted, and doubly robust estimators. Most importantly, with the help of Lasso for high-dimensional regression, we establish non-asymptotic recovery guarantees for the generalized linear model (GLM) under the sparsity assumption for the proposed $\ell_1$-TCL. From an empirical perspective, $\ell_1$-TCL is a generic learning framework that can incorporate not only GLM but also many recently developed non-parametric methods, which can enhance robustness to model mis-specification. We demonstrate this empirical benefit through extensive numerical simulation by incorporating both GLM and recent neural network-based approaches in $\ell_1$-TCL, which shows improved performance compared with existing TL approaches for ACE estimation. Furthermore, our $\ell_1$-TCL framework is subsequently applied to a real study, revealing that vasopressor therapy could prevent 28-day mortality within septic patients, which all baseline approaches fail to show.

Changes in Commuter Behavior from COVID-19 Lockdowns in the Atlanta Metropolitan Area

This paper analyzes the impact of COVID-19 related lockdowns in the Atlanta, Georgia metropolitan area by examining commuter patterns in three periods: prior to, during, and after the pandemic lockdown. A cellular phone location dataset is utilized in a novel pipeline to infer the home and work locations of thousands of users from the Density-based Spatial Clustering of Applications with Noise (DBSCAN) algorithm. The coordinates derived from the clustering are put through a reverse geocoding process from which word embeddings are extracted in order to categorize the industry of each work place based on the workplace name and Point of Interest (POI) mapping. Frequencies of commute from home locations to work locations are analyzed in and across all three time periods. Public health and economic factors are discussed to explain potential reasons for the observed changes in commuter patterns.

Dictionary-based Manifold Learning

We propose a paradigm for interpretable Manifold Learning for scientific data analysis, whereby we parametrize a manifold with $d$ smooth functions from a scientist-provided dictionary of meaningful, domain-related functions. When such a parametrization exists, we provide an algorithm for finding it based on sparse non-linear regression in the manifold tangent bundle, bypassing more standard manifold learning algorithms. We also discuss conditions for the existence of such parameterizations in function space and for successful recovery from finite samples. We demonstrate our method with experimental results from a real scientific domain.

The Parametric Stability of Well-separated Spherical Gaussian Mixtures

We quantify the parameter stability of a spherical Gaussian Mixture Model (sGMM) under small perturbations in distribution space. Namely, we derive the first explicit bound to show that for a mixture of spherical Gaussian $P$ (sGMM) in a pre-defined model class, all other sGMM close to $P$ in this model class in total variation distance has a small parameter distance to $P$. Further, this upper bound only depends on $P$. The motivation for this work lies in providing guarantees for fitting Gaussian mixtures; with this aim in mind, all the constants involved are well defined and distribution free conditions for fitting mixtures of spherical Gaussians. Our results tighten considerably the existing computable bounds, and asymptotically match the known sharp thresholds for this problem.

Risk-Aware Control and Optimization for High-Renewable Power Grids

The transition of the electrical power grid from fossil fuels to renewable sources of energy raises fundamental challenges to the market-clearing algorithms that drive its operations. Indeed, the increased stochasticity in load and the volatility of renewable energy sources have led to significant increases in prediction errors, affecting the reliability and efficiency of existing deterministic optimization models. The RAMC project was initiated to investigate how to move from this deterministic setting into a risk-aware framework where uncertainty is quantified explicitly and incorporated in the market-clearing optimizations. Risk-aware market-clearing raises challenges on its own, primarily from a computational standpoint. This paper reviews how RAMC approaches risk-aware market clearing and presents some of its innovations in uncertainty quantification, optimization, and machine learning. Experimental results on real networks are presented.