arXiv subjects

Filippo Maria Bianchi

Publications and source records attributed to Filippo Maria Bianchi.

At least 37 records · Page 2Linked to original sources

arXiv2023

Probabilistic load forecasting with Reservoir Computing

Some applications of deep learning require not only to provide accurate results but also to quantify the amount of confidence in their prediction. The management of an electric power grid is one of these cases: to avoid risky scenarios, decision-makers need both precise and reliable forecasts of, for example, power loads. For this reason, point forecasts are not enough hence it is necessary to adopt methods that provide an uncertainty quantification. This work focuses on reservoir computing as the core time series forecasting method, due to its computational efficiency and effectiveness in predicting time series. While the RC literature mostly focused on point forecasting, this work explores the compatibility of some popular uncertainty quantification methods with the reservoir setting. Both Bayesian and deterministic approaches to uncertainty assessment are evaluated and compared in terms of their prediction accuracy, computational resource efficiency and reliability of the estimated uncertainty, based on a set of carefully chosen performance metrics.

cs.LG↗

arXiv2023

Total Variation Graph Neural Networks

Recently proposed Graph Neural Networks (GNNs) for vertex clustering are trained with an unsupervised minimum cut objective, approximated by a Spectral Clustering (SC) relaxation. However, the SC relaxation is loose and, while it offers a closed-form solution, it also yields overly smooth cluster assignments that poorly separate the vertices. In this paper, we propose a GNN model that computes cluster assignments by optimizing a tighter relaxation of the minimum cut based on graph total variation (GTV). The cluster assignments can be used directly to perform vertex clustering or to implement graph pooling in a graph classification framework. Our model consists of two core components: i) a message-passing layer that minimizes the $\ell_1$ distance in the features of adjacent vertices, which is key to achieving sharp transitions between clusters; ii) an unsupervised loss function that minimizes the GTV of the cluster assignments while ensuring balanced partitions. Experimental results show that our model outperforms other GNNs for vertex clustering and graph classification.

cs.LG↗

arXiv2023

Combining Stochastic Explainers and Subgraph Neural Networks can Increase Expressivity and Interpretability

Subgraph-enhanced graph neural networks (SGNN) can increase the expressive power of the standard message-passing framework. This model family represents each graph as a collection of subgraphs, generally extracted by random sampling or with hand-crafted heuristics. Our key observation is that by selecting "meaningful" subgraphs, besides improving the expressivity of a GNN, it is also possible to obtain interpretable results. For this purpose, we introduce a novel framework that jointly predicts the class of the graph and a set of explanatory sparse subgraphs, which can be analyzed to understand the decision process of the classifier. We compare the performance of our framework against standard subgraph extraction policies, like random node/edge deletion strategies. The subgraphs produced by our framework allow to achieve comparable performance in terms of accuracy, with the additional benefit of providing explanations.

cs.LG↗

arXiv2023

Scalable Spatiotemporal Graph Neural Networks

Neural forecasting of spatiotemporal time series drives both research and industrial innovation in several relevant application domains. Graph neural networks (GNNs) are often the core component of the forecasting architecture. However, in most spatiotemporal GNNs, the computational complexity scales up to a quadratic factor with the length of the sequence times the number of links in the graph, hence hindering the application of these models to large graphs and long temporal sequences. While methods to improve scalability have been proposed in the context of static graphs, few research efforts have been devoted to the spatiotemporal case. To fill this gap, we propose a scalable architecture that exploits an efficient encoding of both temporal and spatial dynamics. In particular, we use a randomized recurrent neural network to embed the history of the input time series into high-dimensional state representations encompassing multi-scale temporal dynamics. Such representations are then propagated along the spatial dimension using different powers of the graph adjacency matrix to generate node embeddings characterized by a rich pool of spatiotemporal features. The resulting node embeddings can be efficiently pre-computed in an unsupervised manner, before being fed to a feed-forward decoder that learns to map the multi-scale spatiotemporal representations to predictions. The training procedure can then be parallelized node-wise by sampling the node embeddings without breaking any dependency, thus enabling scalability to large networks. Empirical results on relevant datasets show that our approach achieves results competitive with the state of the art, while dramatically reducing the computational burden.

cs.LG↗

arXiv2023

Power Availability of PV plus Thermal Batteries in real-world electric power grids

As variable renewable energy sources comprise a growing share of total electricity generation, energy storage technologies are becoming increasingly critical for balancing energy generation and demand. In this study, we modeled an existing thermal energy storage unit with estimated capital costs that are sufficiently low to enable large-scale deployment in the electric power system. Our analysis emphasizes the value of using such units to cost-effectively improve renewable energy dispatchability. This study modeled an existing real-world grid rather than simulating hypothetical future electric power systems. The storage unit coupled with a photovoltaic (PV) system was modeled with different storage capacities, whereas each storage unit size had various discharge capacities. The modeling was performed under a baseline case with no emission constraints and under hypothetical scenarios in which CO$_2$ emissions were reduced. The results show that power availability increases with increasing storage size and vastly increases in the hypothetical CO$_2$ reduction scenarios, as the storage unit is utilized differently. When CO$_2$ emissions are reduced, the power system must be less dependent on fossil fuel technologies that currently serve the grid, and thus rely more on the power that is served from the PV + storage unit. The proposed approach can provide increased knowledge to power system planners regarding how adding PV + storage systems to existing grids can contribute to the efficient stepwise decarbonization of electric power systems.

math.DS↗

arXiv2023

Explainability in subgraphs-enhanced Graph Neural Networks

Recently, subgraphs-enhanced Graph Neural Networks (SGNNs) have been introduced to enhance the expressive power of Graph Neural Networks (GNNs), which was proved to be not higher than the 1-dimensional Weisfeiler-Leman isomorphism test. The new paradigm suggests using subgraphs extracted from the input graph to improve the model's expressiveness, but the additional complexity exacerbates an already challenging problem in GNNs: explaining their predictions. In this work, we adapt PGExplainer, one of the most recent explainers for GNNs, to SGNNs. The proposed explainer accounts for the contribution of all the different subgraphs and can produce a meaningful explanation that humans can interpret. The experiments that we performed both on real and synthetic datasets show that our framework is successful in explaining the decision process of an SGNN on graph classification tasks.

cs.LG↗

arXiv2022

Simplifying Clustering with Graph Neural Networks

The objective functions used in spectral clustering are usually composed of two terms: i) a term that minimizes the local quadratic variation of the cluster assignments on the graph and; ii) a term that balances the clustering partition and helps avoiding degenerate solutions. This paper shows that a graph neural network, equipped with suitable message passing layers, can generate good cluster assignments by optimizing only a balancing term. Results on attributed graph datasets show the effectiveness of the proposed approach in terms of clustering performance and computation time.

cs.LG↗

arXiv2022

Ensemble Conformalized Quantile Regression for Probabilistic Time Series Forecasting

This paper presents a novel probabilistic forecasting method called ensemble conformalized quantile regression (EnCQR). EnCQR constructs distribution-free and approximately marginally valid prediction intervals (PIs), which are suitable for nonstationary and heteroscedastic time series data. EnCQR can be applied on top of a generic forecasting model, including deep learning architectures. EnCQR exploits a bootstrap ensemble estimator, which enables the use of conformal predictors for time series by removing the requirement of data exchangeability. The ensemble learners are implemented as generic machine learning algorithms performing quantile regression, which allow the length of the PIs to adapt to local variability in the data. In the experiments, we predict time series characterized by a different amount of heteroscedasticity. The results demonstrate that EnCQR outperforms models based only on quantile regression or conformal prediction, and it provides sharper, more informative, and valid PIs.

cs.LG↗

arXiv2022

Recognition of polar lows in Sentinel-1 SAR images with deep learning

In this paper, we explore the possibility of detecting polar lows in C-band SAR images by means of deep learning. Specifically, we introduce a novel dataset consisting of Sentinel-1 images divided into two classes, representing the presence and absence of a maritime mesocyclone, respectively. The dataset is constructed using the ERA5 dataset as baseline and it consists of 2004 annotated images. To our knowledge, this is the first dataset of its kind to be publicly released. The dataset is used to train a deep learning model to classify the labeled images. Evaluated on an independent test set, the model yields an F-1 score of 0.95, indicating that polar lows can be consistently detected from SAR images. Interpretability techniques applied to the deep learning model reveal that atmospheric fronts and cyclonic eyes are key features in the classification. Moreover, experimental results show that the model is accurate even if: (i) such features are significantly cropped due to the limited swath width of the SAR, (ii) the features are partly covered by sea ice and (iii) land is covering significant parts of the images. By evaluating the model performance on multiple input image resolutions (pixel sizes of 500m, 1km and 2km), it is found that higher resolution yield the best performance. This emphasises the potential of using high resolution sensors like SAR for detecting polar lows, as compared to conventionally used sensors such as scatterometers.

cs.CV↗

arXiv2022

Power Flow Balancing with Decentralized Graph Neural Networks

We propose an end-to-end framework based on a Graph Neural Network (GNN) to balance the power flows in energy grids. The balancing is framed as a supervised vertex regression task, where the GNN is trained to predict the current and power injections at each grid branch that yield a power flow balance. By representing the power grid as a line graph with branches as vertices, we can train a GNN that is accurate and robust to changes in topology. In addition, by using specialized GNN layers, we are able to build a very deep architecture that accounts for large neighborhoods on the graph, while implementing only localized operations. We perform three different experiments to evaluate: i) the benefits of using localized rather than global operations and the tendency of deep GNN models to oversmooth the quantities on the nodes; ii) the resilience to perturbations in the graph topology; and iii) the capability to train the model simultaneously on multiple grid topologies and the consequential improvement in generalization to new, unseen grids. The proposed framework is efficient and, compared to other solvers based on deep learning, is robust to perturbations not only to the physical quantities on the grid components, but also to the topology.

cs.LG↗

arXiv2022

Probabilistic forecasts of wind power generation in regions with complex topography using deep learning methods: An Arctic case

The energy market relies on forecasting capabilities of both demand and power generation that need to be kept in dynamic balance. Today, when it comes to renewable energy generation, such decisions are increasingly made in a liberalized electricity market environment, where future power generation must be offered through contracts and auction mechanisms, hence based on forecasts. The increased share of highly intermittent power generation from renewable energy sources increases the uncertainty about the expected future power generation. Point forecast does not account for such uncertainties. To account for these uncertainties, it is possible to make probabilistic forecasts. This work first presents important concepts and approaches concerning probabilistic forecasts with deep learning. Then, deep learning models are used to make probabilistic forecasts of day-ahead power generation from a wind power plant located in Northern Norway. The performance in terms of obtained quality of the prediction intervals is compared for different deep learning models and sets of covariates. The findings show that the accuracy of the predictions improves when historical data on measured weather and numerical weather predictions (NWPs) were included as exogenous variables. This allows the model to auto-correct systematic biases in the NWPs using the historical measurement data. Using only NWPs, or only measured weather as exogenous variables, worse prediction performances were obtained.

cs.LG↗

arXiv2021

Understanding Pooling in Graph Neural Networks

Inspired by the conventional pooling layers in convolutional neural networks, many recent works in the field of graph machine learning have introduced pooling operators to reduce the size of graphs. The great variety in the literature stems from the many possible strategies for coarsening a graph, which may depend on different assumptions on the graph structure or the specific downstream task. In this paper we propose a formal characterization of graph pooling based on three main operations, called selection, reduction, and connection, with the goal of unifying the literature under a common framework. Following this formalization, we introduce a taxonomy of pooling operators and categorize more than thirty pooling methods proposed in recent literature. We propose criteria to evaluate the performance of a pooling operator and use them to investigate and contrast the behavior of different classes of the taxonomy on a variety of tasks.

cs.LG↗

arXiv2021

Detecting and interpreting faults in vulnerable power grids with machine learning

Unscheduled power disturbances cause severe consequences both for customers and grid operators. To defend against such events, it is necessary to identify the causes of interruptions in the power distribution network. In this work, we focus on the power grid of a Norwegian community in the Arctic that experiences several faults whose sources are unknown. First, we construct a data set consisting of relevant meteorological data and information about the current power quality logged by power-quality meters. Then, we adopt machine-learning techniques to predict the occurrence of faults. Experimental results show that both linear and non-linear classifiers achieve good classification performance. This indicates that the considered power-quality and weather variables explain well the power disturbances. Interpreting the decision process of the classifiers provides valuable insights to understand the main causes of disturbances. Traditional features selection methods can only indicate which are the variables that, on average, mostly explain the fault occurrences in the dataset. Besides providing such a global interpretation, it is also important to identify the specific set of variables that explain each individual fault. To address this challenge, we adopt a recent technique to interpret the decision process of a deep learning model, called Integrated Gradients. The proposed approach allows to gain detailed insights on the occurrence of a specific fault, which are valuable for the distribution system operators to implement strategies to prevent and mitigate power disturbances.

cs.LG↗

arXiv2021

Uncovering contributing factors to interruptions in the power grid: An Arctic case

Electric failures are a problem for customers and grid operators. Identifying causes and localizing the source of failures in the grid is critical. Here, we focus on a specific power grid in the Arctic region of North Norway. First, we collect data pertaining to the grid topology, the topography of the area, the historical meteorological data, and the historical energy consumption/production data. Then, we exploit statistical and machine-learning techniques to predict the occurrence of failures. We interpret the variables that mostly explain the classification results to be the main driving factors of power interruption. We are able to predict 57% (F1-score 0.53) of all failures reported over a period of 1 year with a weighted support-vector machine model. Wind speed and local industry activity are found to be the main controlling parameters where the location of exposed power lines is a likely trigger. In summary, we discuss causing factors for failures in the power grid and enable the distribution system operators to implement strategies to prevent and mitigate incoming failures.

physics.soc-ph↗

arXiv2021

Pyramidal Reservoir Graph Neural Network

We propose a deep Graph Neural Network (GNN) model that alternates two types of layers. The first type is inspired by Reservoir Computing (RC) and generates new vertex features by iterating a non-linear map until it converges to a fixed point. The second type of layer implements graph pooling operations, that gradually reduce the support graph and the vertex features, and further improve the computational efficiency of the RC-based GNN. The architecture is, therefore, pyramidal. In the last layer, the features of the remaining vertices are combined into a single vector, which represents the graph embedding. Through a mathematical derivation introduced in this paper, we show formally how graph pooling can reduce the computational complexity of the model and speed-up the convergence of the dynamical updates of the vertex features. Our proposed approach to the design of RC-based GNNs offers an advantageous and principled trade-off between accuracy and complexity, which we extensively demonstrate in experiments on a large set of graph datasets.

cs.LG↗

arXiv2021

Deep Image Translation with an Affinity-Based Change Prior for Unsupervised Multimodal Change Detection

Image translation with convolutional neural networks has recently been used as an approach to multimodal change detection. Existing approaches train the networks by exploiting supervised information of the change areas, which, however, is not always available. A main challenge in the unsupervised problem setting is to avoid that change pixels affect the learning of the translation function. We propose two new network architectures trained with loss functions weighted by priors that reduce the impact of change pixels on the learning objective. The change prior is derived in an unsupervised fashion from relational pixel information captured by domain-specific affinity matrices. Specifically, we use the vertex degrees associated with an absolute affinity difference matrix and demonstrate their utility in combination with cycle consistency and adversarial training. The proposed neural networks are compared with state-of-the-art algorithms. Experiments conducted on three real datasets show the effectiveness of our methodology.

cs.LG↗

arXiv2021

Graph Neural Networks with convolutional ARMA filters

Popular graph neural networks implement convolution operations on graphs based on polynomial spectral filters. In this paper, we propose a novel graph convolutional layer inspired by the auto-regressive moving average (ARMA) filter that, compared to polynomial ones, provides a more flexible frequency response, is more robust to noise, and better captures the global graph structure. We propose a graph neural network implementation of the ARMA filter with a recursive and distributed formulation, obtaining a convolutional layer that is efficient to train, localized in the node space, and can be transferred to new graphs at test time. We perform a spectral analysis to study the filtering effect of the proposed ARMA layer and report experiments on four downstream tasks: semi-supervised node classification, graph signal classification, graph classification, and graph regression. Results show that the proposed ARMA layer brings significant improvements over graph neural networks based on polynomial filters.

cs.LG↗

arXiv2020

Spectral Clustering with Graph Neural Networks for Graph Pooling

Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster. However, the eigendecomposition of the Laplacian is expensive and, since clustering results are graph-specific, pooling methods based on SC must perform a new optimization for each new sample. In this paper, we propose a graph clustering approach that addresses these limitations of SC. We formulate a continuous relaxation of the normalized minCUT problem and train a GNN to compute cluster assignments that minimize this objective. Our GNN-based implementation is differentiable, does not require to compute the spectral decomposition, and learns a clustering function that can be quickly evaluated on out-of-sample graphs. From the proposed clustering method, we design a graph pooling operator that overcomes some important limitations of state-of-the-art graph pooling techniques and achieves the best performance in several supervised and unsupervised tasks.

cs.LG↗