Spreading processes are often modelled as a stochastic dynamics occurring on top of a given network with edge weights corresponding to the transmission probabilities. Knowledge of veracious transmission probabilities is essential for prediction, optimization, and control of diffusion dynamics. Unfortunately, in most cases the transmission rates are unknown and need to be reconstructed from the spreading data. Moreover, in realistic settings it is impossible to monitor the state of each node at every time, and thus the data is highly incomplete. We introduce an efficient dynamic message-passing algorithm, which is able to reconstruct parameters of the spreading model given only partial information on the activation times of nodes in the network. The method is generalizable to a large class of dynamic models, as well to the case of temporal graphs.

Markov Chain Monte Carlo (MCMC) and Belief Propagation (BP) are the most popular algorithms for computational inference in Graphical Models (GM). In principle, MCMC is an exact probabilistic method which, however, often suffers from exponentially slow mixing. In contrast, BP is a deterministic method, which is typically fast, empirically very successful, however in general lacking control of accuracy over loopy graphs. In this paper, we introduce MCMC algorithms correcting the approximation error of BP, i.e., we provide a way to compensate for BP errors via a consecutive BP-aware MCMC. Our framework is based on the Loop Calculus approach which allows to express the BP error as a sum of weighted generalized loops. Although the full series is computationally intractable, it is known that a truncated series, summing up all 2-regular loops, is computable in polynomial-time for planar pair-wise binary GMs and it also provides a highly accurate approximation empirically. Motivated by this, we first propose a polynomial-time approximation MCMC scheme for the truncated series of general (non-planar) pair-wise binary models. Our main idea here is to use the Worm algorithm, known to provide fast mixing in other (related) problems, and then design an appropriate rejection scheme to sample 2-regular loops.

An augmented Lagrangian (AL) can convert a constrained optimization problem into a sequence of simpler (e.g., unconstrained) problems, which are then usually solved with local solvers. Recently, surrogate-based Bayesian optimization (BO) sub-solvers have been successfully deployed in the AL framework for a more global search in the presence of inequality constraints; however, a drawback was that expected improvement (EI) evaluations relied on Monte Carlo. Here we introduce an alternative slack variable AL, and show that in this formulation the EI may be evaluated with library routines. The slack variables furthermore facilitate equality as well as inequality constraints, and mixtures thereof. We show our new slack "ALBO" compares favorably to the original. Its superiority over conventional alternatives is reinforced on several mixed constraint examples.

Three approaches for adaptively tuning diagonal scale matrices for HMC are discussed and compared. The common practice of scaling according to estimated marginal standard deviations is taken as a benchmark. Scaling according to the mean log-target gradient (ISG), and a scaling method targeting that the frequency of when the underlying Hamiltonian dynamics crosses the respective medians should be uniform across dimensions, are taken as alternatives. Numerical studies suggest that the ISG method leads in many cases to more efficient sampling than the benchmark, in particular in cases with strong correlations or non-linear dependencies. The ISG method is also easy to implement, computationally cheap and would be relatively simple to include in automatically tuned codes as an alternative to the benchmark practice.

We propose an operator learning approach to accelerate geometric Markov chain Monte Carlo (MCMC) for solving infinite-dimensional nonlinear Bayesian inverse problems. While geometric MCMC employs high-quality proposals that adapt to posterior local geometry, it requires computing local gradient and Hessian information of the log-likelihood, incurring a high cost when the parameter-to-observable (PtO) map is defined through expensive model simulations. We consider a delayed-acceptance geometric MCMC method driven by a neural operator surrogate of the PtO map, where the proposal is designed to exploit fast surrogate approximations of the log-likelihood and, simultaneously, its gradient and Hessian. To achieve a substantial speedup, the surrogate needs to be accurate in predicting both the observable and its parametric derivative (the derivative of the observable with respect to the parameter). Training such a surrogate via conventional operator learning using input--output samples often demands a prohibitively large number of model simulations. In this work, we present an extension of derivative-informed operator learning [O'Leary-Roseberry et al., J. Comput. Phys., 496 (2024)] using input--output--derivative training samples. Such a learning method leads to derivative-informed neural operator (DINO) surrogates that accurately predict the observable and its parametric derivative at a significantly lower training cost than the conventional method. Cost and error analysis for reduced basis DINO surrogates are provided. Numerical studies on PDE-constrained Bayesian inversion demonstrate that DINO-driven MCMC generates effective posterior samples 3--9 times faster than geometric MCMC and 60--97 times faster than prior geometry-based MCMC. Furthermore, the training cost of DINO surrogates breaks even after collecting merely 10--25 effective posterior samples compared to geometric MCMC.

The ionosphere is a vitally dynamic charged particle region in the Earth's upper atmosphere, playing a crucial role in applications such as radio communication and satellite navigation. The Slant Total Electron Contents (STEC) is an important parameter for characterizing wave propagation, representing the integrated electron density along the ray of radio signals passing through the ionosphere. The accurate prediction of STEC is essential for mitigating the ionospheric impact particularly on Global Navigation Satellite Systems (GNSS). In this work, we propose a high-precision STEC prediction model named DeepONet-STEC, which learns nonlinear operators to predict the 4D temporal-spatial integrated parameter for specified ground station - satellite ray path globally. As a demonstration, we validate the performance of the model based on GNSS observation data for global and US-CORS regimes under ionospheric quiet and storm conditions. The DeepONet-STEC model results show that the three-day 72 hour prediction in quiet periods could achieve high accuracy using observation data by the Precise Point Positioning (PPP) with temporal resolution 30s. Under active solar magnetic storm periods, the DeepONet-STEC also demonstrated its robustness and superiority than traditional deep learning methods. This work presents a neural operator regression architecture for predicting the 4D temporal-spatial ionospheric parameter for satellite navigation system performance, which may be further extended for various space applications and beyond.

Automated hand gesture recognition has long been a focal point in the AI community. Traditionally, research in this field has predominantly focused on scenarios with access to a continuous flow of hand's images. This focus has been driven by the widespread use of cameras and the abundant availability of image data. However, there is an increasing demand for gesture recognition technologies that operate on low-power sensor devices. This is due to the rising concerns for data leakage and end-user privacy, as well as the limited battery capacity and the computing power in low-cost devices. Moreover, the challenge in data collection for individually designed hardware also hinders the generalisation of a gesture recognition model. In this study, we unveil a novel methodology for pattern recognition systems using adaptive and agile error correction, designed to enhance the performance of legacy gesture recognition models on devices with limited battery capacity and computing power. This system comprises a compact Support Vector Machine as the base model for live gesture recognition. Additionally, it features an adaptive agile error corrector that employs few-shot learning within the feature space induced by high-dimensional kernel mappings. The error corrector can be customised for each user, allowing for dynamic adjustments to the gesture prediction based on their movement patterns while maintaining the agile performance of its base model on a low-cost and low-power micro-controller. This proposed system is distinguished by its compact size, rapid processing speed, and low power consumption, making it ideal for a wide range of embedded systems.

In the context of advancing 6G, a substantial paradigm shift is anticipated, highlighting comprehensive everything-to-everything interactions characterized by numerous connections and stringent adherence to Quality of Service/Experience (QoS/E) prerequisites. The imminent challenge stems from resource scarcity, prompting a deliberate transition to Computing-Network Convergence (CNC) as an auspicious approach for joint resource orchestration. While CNC-based mechanisms have garnered attention, their effectiveness in realizing future services, particularly in use cases like the Metaverse, may encounter limitations due to the continually changing nature of users, services, and resources. Hence, this paper presents the concept of Adaptable CNC (ACNC) as an autonomous Machine Learning (ML)-aided mechanism crafted for the joint orchestration of computing and network resources, catering to dynamic and voluminous user requests with stringent requirements. ACNC encompasses two primary functionalities: state recognition and context detection. Given the intricate nature of the user-service-computing-network space, the paper employs dimension reduction to generate live, holistic, abstract system states in a hierarchical structure. To address the challenges posed by dynamic changes, Continual Learning (CL) is employed, classifying the system state into contexts controlled by dedicated ML agents, enabling them to operate efficiently. These two functionalities are intricately linked within a closed loop overseen by the End-to-End (E2E) orchestrator to allocate resources. The paper introduces the components of ACNC, proposes a Metaverse scenario to exemplify ACNC's role in resource provisioning with Segment Routing v6 (SRv6), outlines ACNC's workflow, details a numerical analysis for efficiency assessment, and concludes with discussions on relevant challenges and potential avenues for future research.

This paper explores the application of deep learning techniques, particularly focusing on BERT models, in sentiment analysis. It begins by introducing the fundamental concept of sentiment analysis and how deep learning methods are utilized in this domain. Subsequently, it delves into the architecture and characteristics of BERT models. Through detailed explanation, it elucidates the application effects and optimization strategies of BERT models in sentiment analysis, supported by experimental validation. The experimental findings indicate that BERT models exhibit robust performance in sentiment analysis tasks, with notable enhancements post fine-tuning. Lastly, the paper concludes by summarizing the potential applications of BERT models in sentiment analysis and suggests directions for future research and practical implementations.

Efficiently solving unbalanced three-phase power flow in distribution grids is pivotal for grid analysis and simulation. There is a pressing need for scalable algorithms capable of handling large-scale unbalanced power grids that can provide accurate and fast solutions. To address this, deep learning techniques, especially Graph Neural Networks (GNNs), have emerged. However, existing literature primarily focuses on balanced networks, leaving a critical gap in supporting unbalanced three-phase power grids. This letter introduces PowerFlowMultiNet, a novel multigraph GNN framework explicitly designed for unbalanced three-phase power grids. The proposed approach models each phase separately in a multigraph representation, effectively capturing the inherent asymmetry in unbalanced grids. A graph embedding mechanism utilizing message passing is introduced to capture spatial dependencies within the power system network. PowerFlowMultiNet outperforms traditional methods and other deep learning approaches in terms of accuracy and computational speed. Rigorous testing reveals significantly lower error rates and a notable hundredfold increase in computational speed for large power networks compared to model-based methods.