arXiv subjects

Alessandro Lonardi

Publications and source records attributed to Alessandro Lonardi.

12 recordsLinked to original sources

arXiv2026

High-fidelity inference of power grid frequency distributions

Precision measurements of power grid frequency track energy supply-demand imbalances, with persistent fluctuations indicating strain that can lead to outages. Characterizing the statistical properties of grid frequency fluctuations is therefore essential to achieve efficient control and stable operations. Existing models had limited success in reconstructing the complex non-Gaussian features of observed frequency distributions. Here, we introduce a method for statistical inference of an interpretable stochastic process governing frequency fluctuations, modeling frequency through a coarse-grained power imbalance signal combined with nonlinear generator control and Gaussian white noise. We develop an efficient algorithm to infer these latent variables via maximum likelihood estimation, combined with superstatistics. We test our method on a large dataset of new measurements from Great Britain and South Africa. Although these grids have markedly different properties, our predictions for frequency distributions match measurements excellently. Our method uses only frequency data for inference, thus offering an alternative to data-intensive approaches.

physics.soc-ph↗

arXiv2026

Stochastic Modeling of Power-Grid Frequency Fluctuations in Low-Inertia Systems via a Gaussian-Core Potential and Superstatistics

Power grid frequency stability is fundamental to the secure operation of modern energy systems, yet the growing penetration of renewables and the associated reduction of system inertia have made frequency fluctuations increasingly non-Gaussian and difficult to model. Existing stochastic models based on standard Ornstein--Uhlenbeck-type restoring terms yield a unimodal frequency distribution and therefore fail to reproduce the bimodal structure, central suppression, and heavy tails widely observed in empirical data. Here, we propose a data-driven stochastic process that combines a Gaussian-core potential with superstatistical modeling, assuming slowly fluctuating coefficients for the grid dynamics. The Gaussian-core potential captures the potential barrier that gives rise to the characteristic double-peak structure of frequency distributions. Fitting the model to frequency data resolved at one-second intervals from the Great Britain grid, we find that the central barrier parameter increases substantially from 2020 to 2025 as the grid inertia progressively decreases. To simulate superstatistics, we use an Euler--Maruyama discretization and sample the drift amplitude from a lognormal distribution, thereby successfully reproducing empirical bimodality and heavy tails, as well as the autocorrelation decay. Our results establish a compact and interpretable model for characterizing the evolving complexity of low-inertia grid frequency dynamics.

physics.soc-ph↗

arXiv2026

Understanding the complexity of frequency and phase angle fluctuations in power grids

Power grids must modernize to meet climate goals while maintaining reliable and stable operating conditions. Yet progress is hindered by a limited understanding of the stochastic processes underlying grid frequency and phase-angle fluctuations, which are induced by the growing penetration of renewable generation, consumer demand fluctuations, and market trading. This issue is particularly acute in Africa, where grids often face weak investment. Here, we present results from a newly collected, large-scale, high-resolution dataset of grid frequency and phase angles for the United Kingdom and South Africa, comprising close to one billion data points. Using superstatistical modeling, we treat market-driven power fluctuations as a slowly varying parameter driving grid dynamics and incorporate nonlinear frequency control. As a result, we derive an analytical model that reproduces multimodal frequency distributions previously obtained from numerical simulations, as well as heavy-tailed fluctuations and double-exponential frequency autocorrelation decays, all in excellent agreement with experimental measurements. Beyond frequency, we also address the so far largely overlooked problem of characterizing spatial phase-angle fluctuations. By comparing our predictions with measurement data, we demonstrate that a low-dimensional effective grid model accurately fits South African data despite the grid's complexity. We also highlight significant differences between the grids of South Africa and the United Kingdom. Our results clarify how energy markets and control policies shape grid dynamics across countries with contrasting infrastructure maturity.

physics.soc-ph↗

arXiv2025

Unifying Post-hoc Explanations of Knowledge Graph Completions

Knowledge Graphs organize information as entity-relation-entity triples, enabling machine learning models to predict plausible missing triples in a task known as Knowledge Graph Completion (KGC). Post-hoc explainability for KGC addresses the problem of identifying which triples most influence the predictions of machine learning models. Currently, the field lacks formalization and consistent evaluations, hindering reproducibility and cross-study comparisons. This paper argues for a unified taxonomy for post-hoc explainability in KGC. First, we propose a characterization of post-hoc explanations via multi-objective optimization that unifies existing post-hoc explainability algorithms in KGC and the explanations they produce, balancing explanation effectiveness and conciseness. Next, we examine improved evaluation protocols based on popular metrics, such as Mean Reciprocal Rank and Hits@k, through illustrative experiments. Finally, we stress the importance of interpretability as the ability of explanations to address queries meaningful to end users. By unifying methods and discussing evaluation standards, this work puts forward a case for more reproducible and impactful research in KGC explainability.

cs.AI↗

arXiv2024

Cohesive urban bicycle infrastructure design through optimal transport routing in multilayer networks

Bicycle infrastructure networks must meet the needs of cyclists to position cycling as a viable transportation choice in cities. In particular, protected infrastructure should be planned cohesively for the whole city and spacious enough to accommodate all cyclists safely and prevent cyclist congestion -- a common problem in cycling cities like Copenhagen. Here, we devise an adaptive method for optimal bicycle network design and for evaluating congestion criticalities on bicycle paths. The method goes beyond static network measures, using computationally efficient adaptation rules inspired by Optimal Transport on the dynamically updating multilayer network of roads and protected bicycle lanes. Street capacities and cyclist flows reciprocally control each other to optimally accommodate cyclists on streets with one control parameter that dictates the preference of bicycle infrastructure over roads. Applying our method to Copenhagen confirms that the city's bicycle network is generally well-developed. However, we are able to identify the network's bottlenecks, and we find, at a finer scale, disparities in network accessibility and criticalities between different neighborhoods. Our model and results are generalizable beyond this particular case study to serve as a scalable and versatile tool for aiding urban planners in designing cycling-friendly cities.

physics.soc-ph↗

arXiv2023

Message-Passing on Hypergraphs: Detectability, Phase Transitions and Higher-Order Information

Hypergraphs are widely adopted tools to examine systems with higher-order interactions. Despite recent advancements in methods for community detection in these systems, we still lack a theoretical analysis of their detectability limits. Here, we derive closed-form bounds for community detection in hypergraphs. Using a Message-Passing formulation, we demonstrate that detectability depends on hypergraphs' structural properties, such as the distribution of hyperedge sizes or their assortativity. Our formulation enables a characterization of the entropy of a hypergraph in relation to that of its clique expansion, showing that community detection is enhanced when hyperedges highly overlap on pairs of nodes. We develop an efficient Message-Passing algorithm to learn communities and model parameters on large systems. Additionally, we devise an exact sampling routine to generate synthetic data from our probabilistic model. With these methods, we numerically investigate the boundaries of community detection in synthetic datasets, and extract communities from real systems. Our results extend the understanding of the limits of community detection in hypergraphs and introduce flexible mathematical tools to study systems with higher-order interactions.

cs.SI↗

arXiv2023

Bilevel Optimization for Traffic Mitigation in Optimal Transport Networks

Global infrastructure robustness and local transport efficiency are critical requirements for transportation networks. However, since passengers often travel greedily to maximize their own benefit and trigger traffic jams, overall transportation performance can be heavily disrupted. We develop adaptation rules that leverage Optimal Transport theory to effectively route passengers along their shortest paths while also strategically tuning edge weights to optimize traffic. As a result, we enforce both global and local optimality of transport. We prove the efficacy of our approach on synthetic networks and on real data. Our findings on the International European highways suggest that thoughtfully devised routing schemes might help to lower car-produced carbon emissions.

nlin.AO↗

arXiv2023

Immiscible Color Flows in Optimal Transport Networks for Image Classification

In classification tasks, it is crucial to meaningfully exploit the information contained in data. While much of the work in addressing these tasks is devoted to building complex algorithmic infrastructures to process inputs in a black-box fashion, less is known about how to exploit the various facets of the data, before inputting this into an algorithm. Here, we focus on this latter perspective, by proposing a physics-inspired dynamical system that adapts Optimal Transport principles to effectively leverage color distributions of images. Our dynamics regulates immiscible fluxes of colors traveling on a network built from images. Instead of aggregating colors together, it treats them as different commodities that interact with a shared capacity on edges. The resulting optimal flows can then be fed into standard classifiers to distinguish images in different classes. We show how our method can outperform competing approaches on image classification tasks in datasets where color information matters.

cs.CV↗

arXiv2023

Infrastructure adaptation and emergence of loops in network routing with time-dependent loads

Network routing approaches are widely used to study the evolution in time of self-adapting systems. However, few advances have been made for problems where adaptation is governed by time-dependent inputs. In this work we study a dynamical system where the edge conductivities of a network are regulated by time-varying mass loads injected on nodes. Motivated by empirical observations, we assume that conductivities adapt slowly with respect to the characteristic time of the loads. Furthermore, assuming the loads to be periodic, we derive a dynamics where the evolution of the system is controlled by a matrix obtained with the Fourier coefficients of the input loads. Remarkably, we find a sufficient condition on these coefficients that determines when the resulting network topologies are trees. We show an example of this on the Bordeaux bus network where we tune the input loads to interpolate between loopy and tree topologies. We validate our model on several synthetic networks and provide an expression for long-time solutions of the original conductivities.

physics.soc-ph↗

arXiv2022

Optimal transport in multilayer networks for traffic flow optimization

Modeling traffic distribution and extracting optimal flows in multilayer networks is of utmost importance to design efficient multi-modal network infrastructures. Recent results based on optimal transport theory provide powerful and computationally efficient methods to address this problem, but they are mainly focused on modeling single-layer networks. Here we adapt these results to study how optimal flows distribute on multilayer networks. We propose a model where optimal flows on different layers contribute differently to the total cost to be minimized. This is done by means of a parameter that varies with layers, which allows to flexibly tune the sensitivity to traffic congestion of the various layers. As an application, we consider transportation networks, where each layer is associated to a different transportation system and show how the traffic distribution varies as we tune this parameter across layers. We show an example of this result on the real 2-layer network of the city of Bordeaux with bus and tram, where we find that in certain regimes the presence of the tram network significantly unburdens the traffic on the road network. Our model paves the way to further analysis of optimal flows and navigability strategies in real multilayer networks.

physics.soc-ph↗

arXiv2022

Multicommodity routing optimization for engineering networks

Optimizing passengers routes is crucial to design efficient transportation networks. Recent results show that optimal transport provides an efficient alternative to standard optimization methods. However, it is not yet clear if this formalism has empirical validity on engineering networks. We address this issue by considering different response functions -- quantities determining the interaction between passengers -- in the dynamics implementing the optimal transport formulation. Particularly, we couple passengers' fluxes by taking their sum or the sum of their squares. The first choice naturally reflects edges occupancy in transportation networks, however the second guarantees convergence to an optimal configuration of flows. Both modeling choices are applied to the Paris metro. We measure the extent of traffic bottlenecks and infrastructure resilience to node removal, showing that the two settings are equivalent in the congested transport regime, but different in the branched one. In the latter, the two formulations differ on how fluxes are distributed, with one function favoring routes consolidation, thus potentially being prone to generate traffic overload. Additionally, we compare our method to Dijkstra's algorithm to show its capacity to efficiently recover shortest-path-like graphs. Finally, we observe that optimal transport networks lie in the Pareto front drawn by the energy dissipated by passengers, and the cost to build the infrastructure.

physics.soc-ph↗

arXiv2021

Designing optimal networks for multi-commodity transport problem

Designing and optimizing different flows in networks is a relevant problem in many contexts. While a number of methods have been proposed in the physics and optimal transport literature for the one-commodity case, we lack similar results for the multi-commodity scenario. In this paper we present a model based on optimal transport theory for finding optimal multi-commodity flow configurations on networks. This model introduces a dynamics that regulates the edge conductivities to achieve, at infinite times, a minimum of a Lyapunov functional given by the sum of a convex transport cost and a concave infrastructure cost. We show that the long time asymptotics of this dynamics are the solutions of a standard constrained optimization problem that generalizes the one-commodity framework. Our results provide new insights into the nature and properties of optimal network topologies. In particular, they show that loops can arise as a consequence of distinguishing different flow types, complementing previous results where loops, in the one-commodity case, were obtained as a consequence of imposing dynamical rules to the sources and sinks or when enforcing robustness to damage. Finally, we provide an efficient implementation of our model which convergences faster than standard optimization methods based on gradient descent.

physics.soc-ph↗