E. Isufi
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102 records found
1
Flood hazard maps are essential for protection and emergency plans, yet their probabilistic application is constrained by the computational cost of numerical models. Deep learning surrogates can provide orders of magnitude faster predictions, but their use for uncertainty quantification in realistic settings and their ability to incorporate hydraulic structures remain largely unexplored. Studying deep learning surrogates for probabilistic flood maps is non-trivial because of the lack of reference ground-truth data that might lead to misleading confidence in predictions. Moreover, hydraulic structures are challenging to include due to their generally unidimensional nature. In this work, we investigate the use of deep learning surrogates for realistic, large-scale flood simulations in case studies with hydraulic structures under diverse boundary conditions. To this end, we employ the multi-scale shallow-water-equations graph neural network (mSWE-GNN) that enjoys transferability to different boundary conditions and locations and whose graph-based architecture allows to represent structures such as canals, underpasses, and elevated elements as inputs. To address the lack of reference ground-truth data, we further introduce the average relative mass error (ARME), a mass-conservation-based criterion that helps identify physically plausible simulations. We applied the model on dike ring 41 in the Netherlands, generating probabilistic flood maps that account for uncertainties in breach location and breach outflow hydrographs. The model was trained on 30 simulations, generated with Delft3D, and evaluated against unseen benchmark simulations from the Dutch national flood catalogue, achieving a critical success index (CSI) of 73.6 % while running 10 000 times faster than the numerical simulator. The proposed ARME is negatively correlated with the CSI, with a Spearman correlation coefficient of -0.7, making it a useful indicator of simulation plausibility when evaluating unseen case studies. We obtained probabilistic flood maps by running 10 000 different flooding scenarios on a computational mesh of 180 000 cells in approximately 10 h, with about half of the simulations classified as plausible based on the mass-conservation check. This framework offers a practical tool for rapid probabilistic flood hazard assessment and a way to prioritize detailed physical simulations, supporting more efficient and robust flood risk management.
Topological signal processing and learning
Recent advances and future challenges
Developing methods to process irregularly structured data is crucial in applications like gene-regulatory, brain, power, and socioeconomic networks. Graphs have been the go-to algebraic tool for modeling the structure via nodes and edges capturing their interactions, leading to the establishment of the fields of graph signal processing (GSP) and graph machine learning (GML). Key graph-aware methods include Fourier transform, filtering, sampling, as well as topology identification and spatiotemporal processing. Although versatile, graphs can model only pairwise dependencies in the data. To this end, topological structures such as simplicial and cell complexes have emerged as algebraic representations for more intricate structure modeling in data-driven systems, fueling the rapid development of novel topological-based processing and learning methods. This paper first presents the core principles of topological signal processing through the Hodge theory, a framework instrumental in propelling the field forward thanks to principled connections with GSP-GML. It then outlines advances in topological signal representation, filtering, and sampling, as well as inferring topological structures from data, processing spatiotemporal topological signals, and connections with topological machine learning. The impact of topological signal processing and learning is finally highlighted in applications dealing with flow data over networks, geometric processing, statistical ranking, biology, and semantic communication.
In urban centers, cycling is increasingly popular as an eco-friendly transportation mode and a short-distance transport option, driving higher demand for accurate bicycle travel time estimation. Policymakers need to understand bicycle traffic for urban traffic management and sustainable transport promotion, while cyclists benefit from better route planning and improved network efficiency. However, urban bicycle travel time estimation has not received as much attention as car traffic estimation and presents several challenges: 1) Limited availability of structural cycling data, which can be inaccessible due to privacy concerns and/or severely biased by user demographics. 2) The diverse and complex behaviors of cyclists. 3) The lack of strict road constraints for cyclists and frequent rule violations, complicating the model definition of a comprehensive cycling infrastructure network. This paper presents the first study on urban bicycle travel time estimation using GPS tracking data. Leveraging graph-based deep learning's ability to learn from topological network information, we introduce the Dual Graph-based approach for bicycles (DG4b), which employs two parallel encode-process-decode pipelines: one for a shared undirected road network graph to capture intrinsic road characteristics, and another for a directed trip-specific graph reflecting unique trip features. The outputs are combined to estimate road segment speeds and overall trip travel time. When applied to a real-world dataset from Berlin, our method shows superior accuracy and reliability compared to baseline models, while maintaining low complexity. Our approach provides a novel perspective on integrating bicycling-specific characteristics and aims to inspire more future research in bicycle-related traffic estimation.
Neural networks on simplicial complexes (SCs) can learn representations from data residing on simplices such as nodes, edges, triangles, etc. However, existing works often overlook the Hodge theorem that decomposes simplicial data into three orthogonal characteristic subspaces, such as the identifiable gradient, curl and harmonic components of edge flows. This provides a universal tool to understand the machine learning models on SCs, thus, allowing for better principled and effective learning. In this paper, we study the effect of this data inductive bias on learning on SCs via the principle of convolutions. Particularly, we present a general convolutional architecture that respects the three key principles of uncoupling the lower and upper simplicial adjacencies, accounting for the inter-simplicial couplings, and performing higher-order convolutions. To understand these principles, we first use Dirichlet energy minimizations on SCs to interpret their effects on mitigating simplicial oversmoothing. Then, we show the three principles promote the Hodge-aware learning of this architecture, through the lens of spectral simplicial theory, in the sense that the three Hodge subspaces are invariant under its learnable functions and the learning in two nontrivial subspaces is independent and expressive. Third, we investigate the learning ability of this architecture in optic of perturbation theory on simplicial topologies and prove that the convolutional architecture is stable to small perturbations. Finally, we corroborate the three principles by comparing with methods that either violate or do not respect them. Overall, this paper bridges learning on SCs with the Hodge theorem, highlighting its importance for rational and effective learning from simplicial data, and provides theoretical insights to convolutional learning on SCs.
This paper proposes a scalable method for identifying interactions in higher-order networks from observations of nodal processes. Finding such dependencies is important in many disciplines, including neuroscience, social influence modeling, and beyond. However, current approaches are either limited to extracting pairwise dependencies or struggle with scalability, as estimating higher-order dependencies becomes computationally prohibitive. To overcome these challenges, we introduce a tensorbased graph Volterra model that leverages low-rank decomposition techniques to estimate higher-order interactions efficiently. Our approach not only reduces computational and storage complexity but also acts as an implicit regularizer, improving network estimation in ill-posed settings. We validate our method through simulations and real data experiments, demonstrating competitive performance and enhanced scalability compared to existing techniques.
Graph filters are a staple tool for processing signals over graphs in a multitude of downstream tasks. However, they are commonly designed for graphs with a fixed number of nodes, despite real-world networks typically grow over time. This topological evolution is often known up to a stochastic model, thus, making conventional graph filters ill-equipped to withstand such topological changes, their uncertainty, as well as the dynamic nature of the incoming data. To tackle these issues, we propose an online graph filtering framework by relying on online learning principles. We design filters for scenarios where the topology is both known and unknown, including a learner adaptive to such evolution. We conduct a regret analysis to highlight the role played by the different components such as the online algorithm, the filter order, and the growing graph model. Numerical experiments with synthetic and real data corroborate the proposed approach for graph signal inference tasks and show a competitive performance w.r.t. baselines and state-of-the-art alternatives.
Inference of time varying data over graphs is of importance in real-world applications such as urban water networks, economics, and brain recordings. It typically relies on identifying a computationally affordable joint spatiotemporal method that can leverage the patterns in the data. While this per se is a challenging task, it becomes even more so when the network comes with uncertainties, which, if not accounted for, can lead to unpredictable consequences. To target this setting, we model graph uncertainties as Gaussian noise on the edges and design a stochastic partial differential equation (SPDE) based on it. We use this SPDE as a state equation to model the time varying signal evolution and extend it further to a state-space model where the observations are graph-filtered versions of the state. This allows us to have a joint spatiotemporal expressive kernel that can be estimated online via Kalman filtering and which parameters can also be estimated online via maximum likelihood principles, ultimately, reducing the computational cost. We corroborate the proposed approach on numerical experiments, showing a superior performance to approaches ignoring either the uncertainty or considering a separable spatiotemporal kernel.