Three-Body and One-Body Channels of the Auger Core-Valence-Valence decay: Simplified Approach

We propose a computationally simple model of Auger and APECS line shapes from open-band solids. Part of the intensity comes from the decay of unscreened core-holes and is obtained by the two-body Green's function $G^{(2)}_{\omega}$, as in the case of filled bands. The rest of the intensity arises from screened core-holes and is derived using a variational description of the relaxed ground state; this involves the two-holes-one-electron propagator $G_{\omega}$, which also contains one-hole contributions. For many transition metals, the two-hole Green's function $G^{(2)}_{\omega}$ can be well described by the Ladder Approximation, but the three-body Green's function poses serious further problems. To calculate $G_{\omega}$, treating electrons and holes on equal footing, we propose a practical approach to sum the series to all orders. We achieve that by formally rewriting the problem in terms of a fictitious three-body interaction. Our method grants non-negative densities of states, explains the apparent negative-U behavior of the spectra of early transition metals and interpolates well between weak and strong coupling, as we demonstrate by test model calculations.Comment: AMS-LaTeX file, 23 pages, 8 eps and 3 ps figures embedded in the text with epsfig.sty and float.sty, submitted to Phys. Rev.

Sparse Graph Learning from Spatiotemporal Time Series

Outstanding achievements of graph neural networks for spatiotemporal time series analysis show that relational constraints introduce an effective inductive bias into neural forecasting architectures. Often, however, the relational information characterizing the underlying data-generating process is unavailable and the practitioner is left with the problem of inferring from data which relational graph to use in the subsequent processing stages. We propose novel, principled - yet practical - probabilistic score-based methods that learn the relational dependencies as distributions over graphs while maximizing end-to-end the performance at task. The proposed graph learning framework is based on consolidated variance reduction techniques for Monte Carlo score-based gradient estimation, is theoretically grounded, and, as we show, effective in practice. In this paper, we focus on the time series forecasting problem and show that, by tailoring the gradient estimators to the graph learning problem, we are able to achieve state-of-the-art performance while controlling the sparsity of the learned graph and the computational scalability. We empirically assess the effectiveness of the proposed method on synthetic and real-world benchmarks, showing that the proposed solution can be used as a stand-alone graph identification procedure as well as a graph learning component of an end-to-end forecasting architecture.Comment: updated and extended versio

Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations

Modeling multivariate time series as temporal signals over a (possibly dynamic) graph is an effective representational framework that allows for developing models for time series analysis. In fact, discrete sequences of graphs can be processed by autoregressive graph neural networks to recursively learn representations at each discrete point in time and space. Spatiotemporal graphs are often highly sparse, with time series characterized by multiple, concurrent, and long sequences of missing data, e.g., due to the unreliable underlying sensor network. In this context, autoregressive models can be brittle and exhibit unstable learning dynamics. The objective of this paper is, then, to tackle the problem of learning effective models to reconstruct, i.e., impute, missing data points by conditioning the reconstruction only on the available observations. In particular, we propose a novel class of attention-based architectures that, given a set of highly sparse discrete observations, learn a representation for points in time and space by exploiting a spatiotemporal propagation architecture aligned with the imputation task. Representations are trained end-to-end to reconstruct observations w.r.t. the corresponding sensor and its neighboring nodes. Compared to the state of the art, our model handles sparse data without propagating prediction errors or requiring a bidirectional model to encode forward and backward time dependencies. Empirical results on representative benchmarks show the effectiveness of the proposed method.Comment: Accepted at NeurIPS 202

Graph-based Time Series Clustering for End-to-End Hierarchical Forecasting

Existing relationships among time series can be exploited as inductive biases in learning effective forecasting models. In hierarchical time series, relationships among subsets of sequences induce hard constraints (hierarchical inductive biases) on the predicted values. In this paper, we propose a graph-based methodology to unify relational and hierarchical inductive biases in the context of deep learning for time series forecasting. In particular, we model both types of relationships as dependencies in a pyramidal graph structure, with each pyramidal layer corresponding to a level of the hierarchy. By exploiting modern - trainable - graph pooling operators we show that the hierarchical structure, if not available as a prior, can be learned directly from data, thus obtaining cluster assignments aligned with the forecasting objective. A differentiable reconciliation stage is incorporated into the processing architecture, allowing hierarchical constraints to act both as an architectural bias as well as a regularization element for predictions. Simulation results on representative datasets show that the proposed method compares favorably against the state of the art

Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks

Dealing with missing values and incomplete time series is a labor-intensive, tedious, inevitable task when handling data coming from real-world applications. Effective spatio-temporal representations would allow imputation methods to reconstruct missing temporal data by exploiting information coming from sensors at different locations. However, standard methods fall short in capturing the nonlinear time and space dependencies existing within networks of interconnected sensors and do not take full advantage of the available - and often strong - relational information. Notably, most state-of-the-art imputation methods based on deep learning do not explicitly model relational aspects and, in any case, do not exploit processing frameworks able to adequately represent structured spatio-temporal data. Conversely, graph neural networks have recently surged in popularity as both expressive and scalable tools for processing sequential data with relational inductive biases. In this work, we present the first assessment of graph neural networks in the context of multivariate time series imputation. In particular, we introduce a novel graph neural network architecture, named GRIN, which aims at reconstructing missing data in the different channels of a multivariate time series by learning spatio-temporal representations through message passing. Empirical results show that our model outperforms state-of-the-art methods in the imputation task on relevant real-world benchmarks with mean absolute error improvements often higher than 20%.Comment: Accepted at ICLR 202

Underactuated Attitude Control with Deep Reinforcement Learning

Autonomy is a key challenge for future space exploration endeavors. Deep Reinforcement Learning holds the promises for developing agents able to learn complex behaviors simply by interacting with their environment. This work investigates the use of Reinforcement Learning for satellite attitude control applied to two working conditions: the nominal case, in which all the actuators (a set of 3 reaction wheels) are working properly, and the underactuated case, where an actuator failure is simulated randomly along one of the axes. In particular, a control policy is implemented and evaluated to maneuver a small satellite from a random starting angle to a given pointing target. In the proposed approach, the control policies are implemented as Neural Networks trained with a custom version of the Proximal Policy Optimization algorithm, and they allow the designer to specify the desired control properties by simply shaping the reward function. The agents learn to effectively perform large-angle slew maneuvers with fast convergence and industry-standard pointing accuracy

Deep Reinforcement Learning with Weighted Q-Learning

Overestimation of the maximum action-value is a well-known problem that hinders Q-Learning performance, leading to suboptimal policies and unstable learning. Among several Q-Learning variants proposed to address this issue, Weighted Q-Learning (WQL) effectively reduces the bias and shows remarkable results in stochastic environments. WQL uses a weighted sum of the estimated action-values, where the weights correspond to the probability of each action-value being the maximum; however, the computation of these probabilities is only practical in the tabular settings. In this work, we provide the methodological advances to benefit from the WQL properties in Deep Reinforcement Learning (DRL), by using neural networks with Dropout Variational Inference as an effective approximation of deep Gaussian processes. In particular, we adopt the Concrete Dropout variant to obtain calibrated estimates of epistemic uncertainty in DRL. We show that model uncertainty in DRL can be useful not only for action selection, but also action evaluation. We analyze how the novel Weighted Deep Q-Learning algorithm reduces the bias w.r.t. relevant baselines and provide empirical evidence of its advantages on several representative benchmarks.Comment: Corrected typo

Graph Deep Learning for Time Series Forecasting

Graph-based deep learning methods have become popular tools to process collections of correlated time series. Differently from traditional multivariate forecasting methods, neural graph-based predictors take advantage of pairwise relationships by conditioning forecasts on a (possibly dynamic) graph spanning the time series collection. The conditioning can take the form of an architectural inductive bias on the neural forecasting architecture, resulting in a family of deep learning models called spatiotemporal graph neural networks. Such relational inductive biases enable the training of global forecasting models on large time-series collections, while at the same time localizing predictions w.r.t. each element in the set (i.e., graph nodes) by accounting for local correlations among them (i.e., graph edges). Indeed, recent theoretical and practical advances in graph neural networks and deep learning for time series forecasting make the adoption of such processing frameworks appealing and timely. However, most of the studies in the literature focus on proposing variations of existing neural architectures by taking advantage of modern deep learning practices, while foundational and methodological aspects have not been subject to systematic investigation. To fill the gap, this paper aims to introduce a comprehensive methodological framework that formalizes the forecasting problem and provides design principles for graph-based predictive models and methods to assess their performance. At the same time, together with an overview of the field, we provide design guidelines, recommendations, and best practices, as well as an in-depth discussion of open challenges and future research directions

Taming Local Effects in Graph-based Spatiotemporal Forecasting

Spatiotemporal graph neural networks have shown to be effective in time series forecasting applications, achieving better performance than standard univariate predictors in several settings. These architectures take advantage of a graph structure and relational inductive biases to learn a single (global) inductive model to predict any number of the input time series, each associated with a graph node. Despite the gain achieved in computational and data efficiency w.r.t. fitting a set of local models, relying on a single global model can be a limitation whenever some of the time series are generated by a different spatiotemporal stochastic process. The main objective of this paper is to understand the interplay between globality and locality in graph-based spatiotemporal forecasting, while contextually proposing a methodological framework to rationalize the practice of including trainable node embeddings in such architectures. We ascribe to trainable node embeddings the role of amortizing the learning of specialized components. Moreover, embeddings allow for 1) effectively combining the advantages of shared message-passing layers with node-specific parameters and 2) efficiently transferring the learned model to new node sets. Supported by strong empirical evidence, we provide insights and guidelines for specializing graph-based models to the dynamics of each time series and show how this aspect plays a crucial role in obtaining accurate predictions.Comment: Accepted at NeurIPS 202