In multivariate time series systems, key insights can be obtained by discovering lead-lag relationships inherent in the data, which refer to the dependence between two time series shifted in time relative to one another, and which can be leveraged for the purposes of control, forecasting or clustering. We develop a clustering-driven methodology for robust detection of lead-lag relationships in lagged multi-factor models. Within our framework, the envisioned pipeline takes as input a set of time series, and creates an enlarged universe of extracted subsequence time series from each input time series, via a sliding window approach. This is then followed by an application of various clustering techniques, (such as k-means++ and spectral clustering), employing a variety of pairwise similarity measures, including nonlinear ones. Once the clusters have been extracted, lead-lag estimates across clusters are robustly aggregated to enhance the identification of the consistent relationships in the original universe. We establish connections to the multireference alignment problem for both the homogeneous and heterogeneous settings. Since multivariate time series are ubiquitous in a wide range of domains, we demonstrate that our method is not only able to robustly detect lead-lag relationships in financial markets, but can also yield insightful results when applied to an environmental data set.

In real-world scenarios like traffic and energy, massive time-series data with missing values and noises are widely observed, even sampled irregularly. While many imputation methods have been proposed, most of them work with a local horizon, which means models are trained by splitting the long sequence into batches of fit-sized patches. This local horizon can make models ignore global trends or periodic patterns. More importantly, almost all methods assume the observations are sampled at regular time stamps, and fail to handle complex irregular sampled time series arising from different applications. Thirdly, most existing methods are learned in an offline manner. Thus, it is not suitable for many applications with fast-arriving streaming data. To overcome these limitations, we propose BayOTIDE: Bayesian Online Multivariate Time series Imputation with functional decomposition. We treat the multivariate time series as the weighted combination of groups of low-rank temporal factors with different patterns. We apply a group of Gaussian Processes (GPs) with different kernels as functional priors to fit the factors. For computational efficiency, we further convert the GPs into a state-space prior by constructing an equivalent stochastic differential equation (SDE), and developing a scalable algorithm for online inference. The proposed method can not only handle imputation over arbitrary time stamps, but also offer uncertainty quantification and interpretability for the downstream application. We evaluate our method on both synthetic and real-world datasets.

The key assumption underlying linear Markov Decision Processes (MDPs) is that the learner has access to a known feature map $\phi(x, a)$ that maps state-action pairs to $d$-dimensional vectors, and that the rewards and transitions are linear functions in this representation. But where do these features come from? In the absence of expert domain knowledge, a tempting strategy is to use the ``kitchen sink" approach and hope that the true features are included in a much larger set of potential features. In this paper we revisit linear MDPs from the perspective of feature selection. In a $k$-sparse linear MDP, there is an unknown subset $S \subset [d]$ of size $k$ containing all the relevant features, and the goal is to learn a near-optimal policy in only poly$(k,\log d)$ interactions with the environment. Our main result is the first polynomial-time algorithm for this problem. In contrast, earlier works either made prohibitively strong assumptions that obviated the need for exploration, or required solving computationally intractable optimization problems. Along the way we introduce the notion of an emulator: a succinct approximate representation of the transitions that suffices for computing certain Bellman backups. Since linear MDPs are a non-parametric model, it is not even obvious whether polynomial-sized emulators exist. We show that they do exist and can be computed efficiently via convex programming. As a corollary of our main result, we give an algorithm for learning a near-optimal policy in block MDPs whose decoding function is a low-depth decision tree; the algorithm runs in quasi-polynomial time and takes a polynomial number of samples. This can be seen as a reinforcement learning analogue of classic results in computational learning theory. Furthermore, it gives a natural model where improving the sample complexity via representation learning is computationally feasible.

Machine-learning-based parameterizations (i.e. representation of sub-grid processes) of global climate models or turbulent simulations have recently been proposed as a powerful alternative to physical, but empirical, representations, offering a lower computational cost and higher accuracy. Yet, those approaches still suffer from a lack of generalization and extrapolation beyond the training data, which is however critical to projecting climate change or unobserved regimes of turbulence. Here we show that a multi-fidelity approach, which integrates datasets of different accuracy and abundance, can provide the best of both worlds: the capacity to extrapolate leveraging the physically-based parameterization and a higher accuracy using the machine-learning-based parameterizations. In an application to climate modeling, the multi-fidelity framework yields more accurate climate projections without requiring major increase in computational resources. Our multi-fidelity randomized prior networks (MF-RPNs) combine physical parameterization data as low-fidelity and storm-resolving historical run's data as high-fidelity. To extrapolate beyond the training data, the MF-RPNs are tested on high-fidelity warming scenarios, $+4K$, data. We show the MF-RPN's capacity to return much more skillful predictions compared to either low- or high-fidelity (historical data) simulations trained only on one regime while providing trustworthy uncertainty quantification across a wide range of scenarios. Our approach paves the way for the use of machine-learning based methods that can optimally leverage historical observations or high-fidelity simulations and extrapolate to unseen regimes such as climate change.

The modeling of multistage manufacturing systems (MMSs) has attracted increased attention from both academia and industry. Recent advancements in deep learning methods provide an opportunity to accomplish this task with reduced cost and expertise. This study introduces a stochastic deep Koopman (SDK) framework to model the complex behavior of MMSs. Specifically, we present a novel application of Koopman operators to propagate critical quality information extracted by variational autoencoders. Through this framework, we can effectively capture the general nonlinear evolution of product quality using a transferred linear representation, thus enhancing the interpretability of the data-driven model. To evaluate the performance of the SDK framework, we carried out a comparative study on an open-source dataset. The main findings of this paper are as follows. Our results indicate that SDK surpasses other popular data-driven models in accuracy when predicting stagewise product quality within the MMS. Furthermore, the unique linear propagation property in the stochastic latent space of SDK enables traceability for quality evolution throughout the process, thereby facilitating the design of root cause analysis schemes. Notably, the proposed framework requires minimal knowledge of the underlying physics of production lines. It serves as a virtual metrology tool that can be applied to various MMSs, contributing to the ultimate goal of Zero Defect Manufacturing.

Event identification is increasingly recognized as crucial for enhancing the reliability, security, and stability of the electric power system. With the growing deployment of Phasor Measurement Units (PMUs) and advancements in data science, there are promising opportunities to explore data-driven event identification via machine learning classification techniques. However, obtaining accurately-labeled eventful PMU data samples remains challenging due to its labor-intensive nature and uncertainty about the event type (class) in real-time. Thus, it is natural to use semi-supervised learning techniques, which make use of both labeled and unlabeled samples. %We propose a novel semi-supervised framework to assess the effectiveness of incorporating unlabeled eventful samples to enhance existing event identification methodologies. We evaluate three categories of classical semi-supervised approaches: (i) self-training, (ii) transductive support vector machines (TSVM), and (iii) graph-based label spreading (LS) method. Our approach characterizes events using physically interpretable features extracted from modal analysis of synthetic eventful PMU data. In particular, we focus on the identification of four event classes whose identification is crucial for grid operations. We have developed and publicly shared a comprehensive Event Identification package which consists of three aspects: data generation, feature extraction, and event identification with limited labels using semi-supervised methodologies. Using this package, we generate and evaluate eventful PMU data for the South Carolina synthetic network. Our evaluation consistently demonstrates that graph-based LS outperforms the other two semi-supervised methods that we consider, and can noticeably improve event identification performance relative to the setting with only a small number of labeled samples.

Batteries are an essential component in a deeply decarbonized future. Understanding battery performance and "useful life" as a function of design and use is of paramount importance to accelerating adoption. Historically, battery state of health (SOH) was summarized by a single parameter, the fraction of a battery's capacity relative to its initial state. A more useful approach, however, is a comprehensive characterization of its state and complexities, using an interrelated set of descriptors including capacity, energy, ionic and electronic impedances, open circuit voltages, and microstructure metrics. Indeed, predicting across an extensive suite of properties as a function of battery use is a "holy grail" of battery science; it can provide unprecedented insights toward the design of better batteries with reduced experimental effort, and de-risking energy storage investments that are necessary to meet CO2 reduction targets. In this work, we present a first step in that direction via deep transformer networks for the prediction of 28 battery state of health descriptors using two cycling datasets representing six lithium-ion cathode chemistries (LFP, NMC111, NMC532, NMC622, HE5050, and 5Vspinel), multiple electrolyte/anode compositions, and different charge-discharge scenarios. The accuracy of these predictions versus battery life (with an unprecedented mean absolute error of 19 cycles in predicting end of life for an LFP fast-charging dataset) illustrates the promise of deep learning towards providing deeper understanding and control of battery health.

Unmanned aerial vehicles (UAVs) are capable of surveying expansive areas, but their operational range is constrained by limited battery capacity. The deployment of mobile recharging stations using unmanned ground vehicles (UGVs) significantly extends the endurance and effectiveness of UAVs. However, optimizing the routes of both UAVs and UGVs, known as the UAV-UGV cooperative routing problem, poses substantial challenges, particularly with respect to the selection of recharging locations. Here in this paper, we leverage reinforcement learning (RL) for the purpose of identifying optimal recharging locations while employing constraint programming to determine cooperative routes for the UAV and UGV. Our proposed framework is then benchmarked against a baseline solution that employs Genetic Algorithms (GA) to select rendezvous points. Our findings reveal that RL surpasses GA in terms of reducing overall mission time, minimizing UAV-UGV idle time, and mitigating energy consumption for both the UAV and UGV. These results underscore the efficacy of incorporating heuristics to assist RL, a method we refer to as heuristics-assisted RL, in generating high-quality solutions for intricate routing problems.

Precise and timely fault diagnosis is a prerequisite for a distribution system to ensure minimum downtime and maintain reliable operation. This necessitates access to a comprehensive procedure that can provide the grid operators with insightful information in the case of a fault event. In this paper, we propose a heterogeneous multi-task learning graph neural network (MTL-GNN) capable of detecting, locating and classifying faults in addition to providing an estimate of the fault resistance and current. Using a graph neural network (GNN) allows for learning the topological representation of the distribution system as well as feature learning through a message-passing scheme. We investigate the robustness of our proposed model using the IEEE-123 test feeder system. This work also proposes a novel GNN-based explainability method to identify key nodes in the distribution system which then facilitates informed sparse measurements. Numerical tests validate the performance of the model across all tasks.

In the era of information explosion, spatio-temporal data mining serves as a critical part of urban management. Considering the various fields demanding attention, e.g., traffic state, human activity, and social event, predicting multiple spatio-temporal attributes simultaneously can alleviate regulatory pressure and foster smart city construction. However, current research can not handle the spatio-temporal multi-attribute prediction well due to the complex relationships between diverse attributes. The key challenge lies in how to address the common spatio-temporal patterns while tackling their distinctions. In this paper, we propose an effective solution for spatio-temporal multi-attribute prediction, PromptST. We devise a spatio-temporal transformer and a parameter-sharing training scheme to address the common knowledge among different spatio-temporal attributes. Then, we elaborate a spatio-temporal prompt tuning strategy to fit the specific attributes in a lightweight manner. Through the pretrain and prompt tuning phases, our PromptST is able to enhance the specific spatio-temoral characteristic capture by prompting the backbone model to fit the specific target attribute while maintaining the learned common knowledge. Extensive experiments on real-world datasets verify that our PromptST attains state-of-the-art performance. Furthermore, we also prove PromptST owns good transferability on unseen spatio-temporal attributes, which brings promising application potential in urban computing. The implementation code is available to ease reproducibility.