Accelerating Steady-State Analysis in Water Distribution Systems with Physics-informed Deep Learning and Topological Signal Processing

Water distribution systems (WDS) are an integral part of critical infrastructure which is pivotal to urban development. As 70% of the world's population will likely live in urban environments in 2050, efficient simulation and planning tools for WDS play a crucial role in reaching UN's sustainable developmental goal (SDG) 6 - "Clean water and sanitation for all". In this realm, we propose a novel and efficient machine learning emulator, more precisely, a physics-informed deep learning (DL) model, for hydraulic state estimation in WDS. Using a recursive approach, our model only needs a few graph convolutional neural network (GCN) layers and employs an innovative algorithm based on message passing. Unlike conventional machine learning tasks, the model uses hydraulic principles to infer two additional hydraulic state features in the process of reconstructing the available ground truth feature in an unsupervised manner. To the best of our knowledge, this is the first DL approach to emulate the popular hydraulic simulator EPANET, utilizing no additional information. Like most DL models and unlike the hydraulic simulator, our model demonstrates vastly faster emulation times that do not increase drastically with the size of the WDS. Moreover, we achieve high accuracy on the ground truth and very similar results compared to the hydraulic simulator as demonstrated through experiments on five real-world WDS datasets.

Graph neural networks (GNNs) is an information - processing system that uses message passing among graph nodes. In recent years, GNN variants including graph attention network (GAT), graph convolutional network (GCN), and graph recurrent network (GRN) have shown revolutionary performance in computer vision applications using deep learning and artificial intelligence. These neural network model extensions, collect information in the form of graphs. GNN may be divided into three groups based on the challenges it solves: link prediction, node classification, graph classification. Machines can differentiate and recognise objects in image and video using standard CNNs. Extensive amount of research work needs to be done before robots can have same visual intuition as humans. GNN architectures, on the other hand, may be used to solve various image categorization and video challenges. The number of GNN applications in computer vision not limited, continues to expand. Human-object interaction, actin understanding, image categorization from a few shots and many more. In this paper use of GNN in image and video understanding, design aspects, architecture, applications and implementation challenges towards computer vision is described. GNN is a strong tool for analysing graph data and is still a relatively active area that needs further researches attention to solve many computer vision applications.

<p>Water utilities tackle various problems in planning and operating their systems with complex and computationally expensive hydraulic models, i.e., maximizing system resilience, fault isolation, risk assessment, optimal pump scheduling, or water loss reduction via pressure management. To meet limited computational budgets, engineers employ less resource-intensive surrogate models. Current surrogate models based on artificial neural networks deliver similar accuracies as hydraulic models with lower computational costs. However, they require retraining when applied to an unknown water distribution system, which increases their computational load and limits their general applicability. Recent advancements in graph-based machine learning address these limitations. Graph neural networks (GNNs) naturally connect with the network elements (e.g., pipes and valves with edges, junctions, and tanks with vertices)  of water distribution systems, proving themselves to be a promising candidate for surrogate modeling. Once trained on a specific network to be a surrogate model, GNNs possess inductive biases that allow transferability to an unseen topology. In this work, we adopted a demand-driven simulation of a water distribution system in a graph machine learning setting. We built a synthetic dataset of demand-driven simulation with EPANET, founded on the example of real-world water distribution systems, and trained an attention-based GNN to emulate the hydraulic simulator. The accuracy was evaluated inductively on an unseen larger-sized water distribution network. We observed that the model showed promising transferability results to a larger network without the need for additional re-training on the unseen topology.</p>

This study introduces a novel approach to drug discovery in regenerative medicine through the utilization of a graph neural network (GNN). The research methodology integrates the development and training of the GNN with a subsequent evaluation of its performance metrics. The first phase involves the generation of synthetic data simulating a biological network, employing networkX and NumPy libraries to construct a random graph with Erdos-Renyi topology. The data, representing cellular responses to biomaterials, is then converted into PyTorch tensors for compatibility with the GNN architecture. The GNN model, characterized by two fully connected layers with ReLU and log-softmax activations, captures intricate relationships within the graph-structured data. The second phase employs a stochastic gradient descent algorithm, specifically the Adam optimizer, to train the GNN over 100 epochs using the cross-entropy loss for multi-class classification. The research methodology extends to the evaluation phase, producing three distinct output graphs for analysis: Visualization of the graph structure, a comparison between predicted and true labels, and a plot illustrating training loss over epochs. Performance metrics, including accuracy, precision, recall, and F1-score, are computed to assess the model’s predictive capabilities quantitatively. The study concludes with a discussion on the nuances revealed by each graph and their implications for refining GNN models in the context of drug discovery for regenerative medicine.

This study presents a novel approach that synergizes community detection algorithms with various Graph Neural Network (GNN) models to bolster link prediction in scientific literature networks. By integrating the Louvain community detection algorithm into our GNN frameworks, we consistently enhanced the performance across all models tested. For example, integrating the Louvain model with the GAT model resulted in an AUC score increase from 0.777 to 0.823, exemplifying the typical improvements observed. Similar gains were noted when the Louvain model was paired with other GNN architectures, confirming the robustness and effectiveness of incorporating community-level insights. This consistent increase in performance—reflected in our extensive experimentation on bipartite graphs of scientific collaborations and citations—highlights the synergistic potential of combining community detection with GNNs to overcome common link prediction challenges such as scalability and resolution limits. Our findings advocate for the integration of community structures as a significant step forward in the predictive accuracy of network science models, offering a comprehensive understanding of scientific collaboration patterns through the lens of advanced machine learning techniques.

The rapid advancements in machine learning have opened up new possibilities for solving complex problems, including in highly specialized applications with notable impact on relevant diseases, such as cancer. A critical aspect of cancer treatment is histopathological image analysis, a field that analyzes large zoomable images at a microscope level, to understand how the disease affected the patient, enabling patient-tailored treatment strategies. However, progress in this area relies heavily on interdisciplinary collaboration and the development of methods that utilize highquality annotated datasets effectively. In this thesis, we address these challenges by proposing a new collaborative annotation software for Whole Slides Images. Using the software, we aid in the construction of novel annotated datasets with application-specific goals. Then, inspired by the pathologist\'s work methodology, we develop a novel Graph Neural Network (GNN) technique based on activation maps that models neighborhood representation based on the presence or absence of features in the neighborhood. Our approach is based on the Message Passing architecture, which although very popular, may limit graph representation by suffering from issues such as limited injectability and oversquashing, depending on the GNN architecture and task. Moreover, increasing traditional GNN\'s receptive field requires deepening the neural network, which introduces additional challenges, such as higher computational requirements. In contrast, our approach projects the graph\'s features to a fixed-size map representation with Self-Organizing Maps, which are activated based on the presence and distance of features from the central node, within the model\'s configurable receptive field. Lastly, the activation map keeps the graph\'s features within their original domain during aggregation, which has benefits for interpretability. We conclude this work by training the proposed GNN on a novel annotated dataset developed with the proposed tool, and using its interpretability advantages to highlight the patterns it identifies, contrasting it with a pathologist\'s expectations. This work contributes to the advancement of histopathological image analysis by proposing novel research tools, annotated data, and methods, paving the way for more accurate and reliable AI-based personalized medicine.

A Novel Deep Learning Approach for Automated Rolling Bearing Fault Diagnosis (ARBFD) Using Graph Neural Networks and Physics Informed Deep Learning

In this paper we survey our recent results characterizing various graph neural network (GNN) architectures in terms of their ability to classify nodes over graphs, for classifiers based on unary logical formulas- or queries. We focus on the language FOC2, a well-studied fragment of FO. This choice is motivated by the fact that FOC2 is related to theWeisfeiler-Lehman (WL) test for checking graph isomorphism, which has the same ability as GNNs for distinguishing nodes on graphs. We unveil the exact relationship between FOC2 and GNNs in terms of node classification. To tackle this problem, we start by studying a popular basic class of GNNs, which we call AC-GNNs, in which the features of each node in a graph are updated, in successive layers, according only to the features of its neighbors. We prove that the unary FOC2 formulas that can be captured by an AC-GNN are exactly those that can be expressed in its guarded fragment, which in turn corresponds to graded modal logic. This result implies in particular that ACGNNs are too weak to capture all FOC2 formulas. We then seek for what needs to be added to AC-GNNs for capturing all FOC2. We show that it suffices to add readouts layers, which allow updating the node features not only in terms of its neighbors, but also in terms of a global attribute vector. We call GNNs with readouts ACR-GNNs. We also describe experiments that validate our findings by showing that, on synthetic data conforming to FOC2 but not to graded modal logic, AC-GNNs struggle to fit in while ACR-GNNs can generalise even to graphs of sizes not seen during training.

Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly focus on designing graph convolution operations. The graph pooling (or downsampling) operations, that play an important role in learning hierarchical representations, are usually overlooked. In this paper, we proposed a novel multi-view graph pooling operator dubbed as MVPool, which ranks nodes across different views with different contextual graph information. Meanwhile, attention mechanism is utilized to promote the collaboration of different views for generating robust node rankings. Then the pooling operation adaptively selects a subset of nodes to form an induced subgraph based on the ranking list. To preserve the underlying graph topological information, we further introduce a structure learning mechanism to learn a refined graph structure for the pooled graph at each layer. The proposed MVPool operator is a general strategy that can be integrated into various graph neural network architectures. By combining MVPool operator with graph neural networks, we perform hierarchical representation learning for both node and graph level classification as well as clustering tasks. Experimental results on nine widely used benchmarks demonstrate the effectiveness of our proposed model.

Ovonic threshold switching (OTS) selectors are pivotal in nonvolatile memory devices due to their nonlinear electrical characteristics and polarity-dependent threshold voltages. However, the atomic-scale origins of the defect states responsible for these behaviors remain unclear. In this study, we systematically investigate defects in amorphous GeSe using molecular dynamics simulations accelerated by machine learning interatomic potentials (MLIPs). We first benchmark several MLIP architectures, including descriptor-based potentials and graph neural network (GNN)-based potentials. Our results demonstrate that capturing higher-order interactions, at least four-body correlations, and medium-range structural order is essential for accurately representing amorphous GeSe structures. Our analysis indicates that GNN architectures with multiple interaction layers effectively capture higher-order correlations and medium-range order, thereby preventing spurious defects easily introduced by less descriptive MLIPs. Utilizing the optimized GNN model, we identify two distinct defect motifs across 20 independent 960-atom amorphous GeSe structures: aligned Ge chains associated with defect states near the conduction band, and overcoordinated Ge chains linked to defect states near the valence band. Moreover, we establish correlations between electronic defect levels and specific structural features─namely, the average alignment of bond angles in aligned chains and the degree of local Peierls distortion around overcoordinated Ge atoms. These insights provide a theoretical framework for interpreting experimental observations and deepening the understanding of defect-driven OTS phenomena in amorphous GeSe.

Chapter 2 - Machine learning for solid mechanics

The impingement of a round jet on a flat plate at an angle θ represents a basic model of jet mechanics (Fig. 5.1). To calculate the spreading of the water sheet on the plate surface, the mass, momentum, and energy conservation laws need to be used. Under the assumptions of frictionless deflection of the jet and frictionless spreading of the water sheet, it can be deduced from the conservation law of energy that the spreading speed of the water sheet on the plate surface is equal to the jet speed. The flow distribution along a periphery circle as well as in the radial extent can then be calculated by means of the law of momentum. The mass conservation law determines that the integrated mass flow along each periphery circle should reflect the mass flow of the jet. The first accurate calculation of such a flow distribution was conducted by Hasson and Peck (1964). The distribution of the water-sheet height along the periphery of an arbitrary circle is given by $$ \frac{2r\cdot h}{R^2}=\frac{{ \sin}^3\theta }{{\left(1- \cos \theta \cos \varphi \right)}^2}. $$ The center of the arbitrary circle coincides with the stagnation point of the round jet on the flat plate and is eccentric to the jet axis at a distance s which is given by $$ \frac{s}{R}= \cos \theta . $$ The interaction force between the jet at a speed C and the flat plate can be determined again by the law of momentum. Since the flow is assumed to be free of friction and hence no force component in the plane of the plate exists, the resulting interaction force is perpendicular to the flat plate. Using the momentum law in the normal direction of the flat plate, then it is calculated as $$ {F}_{\mathrm{jet}}=\pi {R}^2\cdot \rho {C}^2 \sin \theta . $$ This force is referred to as . Near the stagnation point beneath the water sheet, some overpressure exists. Its integration over the plate must be equal to the jet impact force from Eq. (5.3). The pressure distribution in the immediate vicinity of the stagnation point has been determined in a study by G.I. Taylor (1960), among others.

Graph Neural Networks (GNNs) have become indispensable tools for learning from graph-structured data, catering to various applications such as social network analysis and fraud detection for financial services. At the heart of these networks are the edges, which are crucial in guiding GNN models' predictions. In many scenarios, these edges represent sensitive information, such as personal associations or financial dealings, which require privacy assurance. However, their contributions to GNN model predictions may, in turn, be exploited by the adversary to compromise their privacy. Motivated by these conflicting requirements, this paper investigates edge privacy in contexts where adversaries possess only black-box access to the target GNN model, restricted further by access controls, preventing direct insights into arbitrary node outputs. Moreover, we are the first to extensively examine situations where the target graph continuously evolves—a common trait of many real-world graphs. In this setting, we present a range of attacks that leverage the message-passing mechanism of GNNs. We evaluated the effectiveness of our attacks using nine real-world datasets, encompassing both static and dynamic graphs, across four different GNN architectures. The results demonstrate that our attack outperforms existing methods across various GNN architectures, consistently achieving an F1 score of at least 0.8 in static scenarios. Furthermore, our attack retains robustness in dynamic graph scenarios, maintaining F1 scores up to 0.8, unlike previous methods that only achieve F1 scores around 0.2.

This research addresses the challenges of urban mobility and logistics by developing an AI-based system for intelligent route prediction and coordination. Using Graph Neural Networks and complementary AI methods, we intend to model heterogeneous fleets to optimize large-scale mobility with real-time decision-making and energy-aware trade-offs.

Uniqueness of solutions and conservation laws for the quasigeostrophic model