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We consider the problem of blob detection for uncertain images, such as images that have to be inferred from noisy measurements. Extending recent work motivated by astronomical applications, we propose an approach that represents the uncertainty in the position and size of a blob by a region in a three-dimensional scale space. Motivated by classic tube methods such as the taut-string algorithm, these regions are obtained from level sets of the minimizer of a total variation functional within a high-dimensional tube. The resulting non-smooth optimization problem is challenging to solve, and we compare various numerical approaches for its solution and relate them to the literature on constrained total variation denoising. Finally, the proposed methodology is illustrated on numerical experiments for deconvolution and models related to astrophysics, where it is demonstrated that it allows to represent the uncertainty in the detected blobs in a precise and physically interpretable way.

Operator learning frameworks, because of their ability to learn nonlinear maps between two infinite dimensional functional spaces and utilization of neural networks in doing so, have recently emerged as one of the more pertinent areas in the field of applied machine learning. Although these frameworks are extremely capable when it comes to modeling complex phenomena, they require an extensive amount of data for successful training which is often not available or is too expensive. However, this issue can be alleviated with the use of multi-fidelity learning, where a model is trained by making use of a large amount of inexpensive low-fidelity data along with a small amount of expensive high-fidelity data. To this end, we develop a new framework based on the wavelet neural operator which is capable of learning from a multi-fidelity dataset. The developed model's excellent learning capabilities are demonstrated by solving different problems which require effective correlation learning between the two fidelities for surrogate construction. Furthermore, we also assess the application of the developed framework for uncertainty quantification. The results obtained from this work illustrate the excellent performance of the proposed framework.

We use a combination of unsupervised clustering and sparsity-promoting inference algorithms to learn locally dominant force balances that explain macroscopic pattern formation in self-organized active particle systems. The self-organized emergence of macroscopic patterns from microscopic interactions between self-propelled particles can be widely observed nature. Although hydrodynamic theories help us better understand the physical basis of this phenomenon, identifying a sufficient set of local interactions that shape, regulate, and sustain self-organized structures in active particle systems remains challenging. We investigate a classic hydrodynamic model of self-propelled particles that produces a wide variety of patterns, like asters and moving density bands. Our data-driven analysis shows that propagating bands are formed by local alignment interactions driven by density gradients, while steady-state asters are shaped by a mechanism of splay-induced negative compressibility arising from strong particle interactions. Our method also reveals analogous physical principles of pattern formation in a system where the speed of the particle is influenced by local density. This demonstrates the ability of our method to reveal physical commonalities across models. The physical mechanisms inferred from the data are in excellent agreement with analytical scaling arguments and experimental observations.

There is a growing trend of cyberattacks against Internet of Things (IoT) devices; moreover, the sophistication and motivation of those attacks is increasing. The vast scale of IoT, diverse hardware and software, and being typically placed in uncontrolled environments make traditional IT security mechanisms such as signature-based intrusion detection and prevention systems challenging to integrate. They also struggle to cope with the rapidly evolving IoT threat landscape due to long delays between the analysis and publication of the detection rules. Machine learning methods have shown faster response to emerging threats; however, model training architectures like cloud or edge computing face multiple drawbacks in IoT settings, including network overhead and data isolation arising from the large scale and heterogeneity that characterizes these networks. This work presents an architecture for training unsupervised models for network intrusion detection in large, distributed IoT and Industrial IoT (IIoT) deployments. We leverage Federated Learning (FL) to collaboratively train between peers and reduce isolation and network overhead problems. We build upon it to include an unsupervised device clustering algorithm fully integrated into the FL pipeline to address the heterogeneity issues that arise in FL settings. The architecture is implemented and evaluated using a testbed that includes various emulated IoT/IIoT devices and attackers interacting in a complex network topology comprising 100 emulated devices, 30 switches and 10 routers. The anomaly detection models are evaluated on real attacks performed by the testbed's threat actors, including the entire Mirai malware lifecycle, an additional botnet based on the Merlin command and control server and other red-teaming tools performing scanning activities and multiple attacks targeting the emulated devices.

The ever-growing use of wind energy makes necessary the optimization of turbine operations through pitch angle controllers and their maintenance with early fault detection. It is crucial to have accurate and robust models imitating the behavior of wind turbines, especially to predict the generated power as a function of the wind speed. Existing empirical and physics-based models have limitations in capturing the complex relations between the input variables and the power, aggravated by wind variability. Data-driven methods offer new opportunities to enhance wind turbine modeling of large datasets by improving accuracy and efficiency. In this study, we used physics-informed neural networks to reproduce historical data coming from 4 turbines in a wind farm, while imposing certain physical constraints to the model. The developed models for regression of the power, torque, and power coefficient as output variables showed great accuracy for both real data and physical equations governing the system. Lastly, introducing an efficient evidential layer provided uncertainty estimations of the predictions, proved to be consistent with the absolute error, and made possible the definition of a confidence interval in the power curve.

Neural network (NN) potentials promise highly accurate molecular dynamics (MD) simulations within the computational complexity of classical MD force fields. However, when applied outside their training domain, NN potential predictions can be inaccurate, increasing the need for Uncertainty Quantification (UQ). Bayesian modeling provides the mathematical framework for UQ, but classical Bayesian methods based on Markov chain Monte Carlo (MCMC) are computationally intractable for NN potentials. By training graph NN potentials for coarse-grained systems of liquid water and alanine dipeptide, we demonstrate here that scalable Bayesian UQ via stochastic gradient MCMC (SG-MCMC) yields reliable uncertainty estimates for MD observables. We show that cold posteriors can reduce the required training data size and that for reliable UQ, multiple Markov chains are needed. Additionally, we find that SG-MCMC and the Deep Ensemble method achieve comparable results, despite shorter training and less hyperparameter tuning of the latter. We show that both methods can capture aleatoric and epistemic uncertainty reliably, but not systematic uncertainty, which needs to be minimized by adequate modeling to obtain accurate credible intervals for MD observables. Our results represent a step towards accurate UQ that is of vital importance for trustworthy NN potential-based MD simulations required for decision-making in practice.

Machine learning models often need to be robust to noisy input data. The effect of real-world noise (which is often random) on model predictions is captured by a model's local robustness, i.e., the consistency of model predictions in a local region around an input. However, the na\"ive approach to computing local robustness based on Monte-Carlo sampling is statistically inefficient, leading to prohibitive computational costs for large-scale applications. In this work, we develop the first analytical estimators to efficiently compute local robustness of multi-class discriminative models using local linear function approximation and the multivariate Normal CDF. Through the derivation of these estimators, we show how local robustness is connected to concepts such as randomized smoothing and softmax probability. We also confirm empirically that these estimators accurately and efficiently compute the local robustness of standard deep learning models. In addition, we demonstrate these estimators' usefulness for various tasks involving local robustness, such as measuring robustness bias and identifying examples that are vulnerable to noise perturbation in a dataset. By developing these analytical estimators, this work not only advances conceptual understanding of local robustness, but also makes its computation practical, enabling the use of local robustness in critical downstream applications.

Physics-informed neural networks (PINNs) offer a novel and efficient approach to solving partial differential equations (PDEs). Their success lies in the physics-informed loss, which trains a neural network to satisfy a given PDE at specific points and to approximate the solution. However, the solutions to PDEs are inherently infinite-dimensional, and the distance between the output and the solution is defined by an integral over the domain. Therefore, the physics-informed loss only provides a finite approximation, and selecting appropriate collocation points becomes crucial to suppress the discretization errors, although this aspect has often been overlooked. In this paper, we propose a new technique called good lattice training (GLT) for PINNs, inspired by number theoretic methods for numerical analysis. GLT offers a set of collocation points that are effective even with a small number of points and for multi-dimensional spaces. Our experiments demonstrate that GLT requires 2--20 times fewer collocation points (resulting in lower computational cost) than uniformly random sampling or Latin hypercube sampling, while achieving competitive performance.

Graph Neural Networks (GNNs) have been successfully used in many problems involving graph-structured data, achieving state-of-the-art performance. GNNs typically employ a message-passing scheme, in which every node aggregates information from its neighbors using a permutation-invariant aggregation function. Standard well-examined choices such as the mean or sum aggregation functions have limited capabilities, as they are not able to capture interactions among neighbors. In this work, we formalize these interactions using an information-theoretic framework that notably includes synergistic information. Driven by this definition, we introduce the Graph Ordering Attention (GOAT) layer, a novel GNN component that captures interactions between nodes in a neighborhood. This is achieved by learning local node orderings via an attention mechanism and processing the ordered representations using a recurrent neural network aggregator. This design allows us to make use of a permutation-sensitive aggregator while maintaining the permutation-equivariance of the proposed GOAT layer. The GOAT model demonstrates its increased performance in modeling graph metrics that capture complex information, such as the betweenness centrality and the effective size of a node. In practical use-cases, its superior modeling capability is confirmed through its success in several real-world node classification benchmarks.

Vast amount of data generated from networks of sensors, wearables, and the Internet of Things (IoT) devices underscores the need for advanced modeling techniques that leverage the spatio-temporal structure of decentralized data due to the need for edge computation and licensing (data access) issues. While federated learning (FL) has emerged as a framework for model training without requiring direct data sharing and exchange, effectively modeling the complex spatio-temporal dependencies to improve forecasting capabilities still remains an open problem. On the other hand, state-of-the-art spatio-temporal forecasting models assume unfettered access to the data, neglecting constraints on data sharing. To bridge this gap, we propose a federated spatio-temporal model -- Cross-Node Federated Graph Neural Network (CNFGNN) -- which explicitly encodes the underlying graph structure using graph neural network (GNN)-based architecture under the constraint of cross-node federated learning, which requires that data in a network of nodes is generated locally on each node and remains decentralized. CNFGNN operates by disentangling the temporal dynamics modeling on devices and spatial dynamics on the server, utilizing alternating optimization to reduce the communication cost, facilitating computations on the edge devices. Experiments on the traffic flow forecasting task show that CNFGNN achieves the best forecasting performance in both transductive and inductive learning settings with no extra computation cost on edge devices, while incurring modest communication cost.