Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more classic explicit approximation approaches and others, which include variational inference, sequential monte carlo, and decoupled data consistency. We cover the extension to more challenging situations, including blind cases, high-dimensional data, and problems under data scarcity and distribution mismatch. More recent approaches that aim to leverage multimodal information through texts are covered. Through this chapter, we aim to (i) distill the common mathematical threads that connect these algorithms, (ii) systematically contrast their assumptions and performance trade-offs across representative inverse problems, and (iii) spotlight the open theoretical and practical challenges by clarifying the landscape of diffusion model based inverse problem solvers.

The performance of Bayesian optimization (BO), a highly sample-efficient method for expensive black-box problems, is critically governed by the selection of its hyperparameters, including the kernel and acquisition functions. This presents a challenge: an inappropriate combination of these can lead to poor performance and wasted evaluations. While individual improvements to kernel functions (e.g., tree-based kernels, deep kernel learning) and acquisition functions (e.g., multi-step lookahead, tree-based planning) have been explored, the joint and autonomous selection of the best pair of these fundamental hyperparameters has been overlooked. This forces practitioners to rely on heuristics or costly manual training. We propose a simple yet effective framework, BOOST (Bayesian Optimization with Optimal Kernel and Acquisition Function Selection Technique), that automates this selection. BOOST utilizes a lightweight, offline evaluation stage to predict the performance of various kernel-acquisition function pairs and identify the most suitable configuration before expensive evaluations. BOOST partitions data-in-hand into two subsets: a reference subset and a query subset, and it prepares all possible kernel-acquisition pairs from the user's chosen candidates. For each configuration, BOOST conducts internal BO runs using the reference subset, evaluating how effectively each pair guides the search toward the optimum in the unknown query subset, thereby identifying the configuration with the best retrospective performance for future optimization. Experiments on both synthetic benchmark functions and real-world hyperparameter optimization tasks demonstrate that BOOST consistently outperforms standard BO approaches with fixed hyperparameters, highlighting its effectiveness and robustness in diverse problem landscapes.

Generative artificial intelligence (AI) excels at producing complex data structures (text, images, videos) by learning patterns from training examples. Across scientific disciplines, researchers are now applying generative models to ``inverse problems'' to infer hidden parameters from observed data. While these methods can handle intractable models and large-scale studies, they can also produce biased or overconfident conclusions. We present a solution with Frequentist-Bayes (FreB), a mathematically rigorous protocol that reshapes AI-generated probability distributions into confidence regions that consistently include true parameters with the expected probability, while achieving minimum size when training and target data align. We demonstrate FreB's effectiveness by tackling diverse case studies in the physical sciences: identifying unknown sources under dataset shift, reconciling competing theoretical models, and mitigating selection bias and systematics in observational studies. By providing validity guarantees with interpretable diagnostics, FreB enables trustworthy scientific inference across fields where direct likelihood evaluation remains impossible or prohibitively expensive.

Laboratory of Computational Science and Modeling, Institut des Mat eriaux, Ecole Polytechnique F ed erale de Lausanne, 1015 Lausanne, Switzerland (Dated: August 5, 2025) The equations of classical mechanics can be used to model the time evolution of countless physical systems, from the astrophysical to the atomic scale. Accurate numerical integration requires small time steps, which limits the computational efficiency - especially in cases such as molecular dynamics that span wildly different time scales. Using machine-learning (ML) algorithms to predict trajectories allows one to greatly extend the integration time step, at the cost of introducing artifacts such as lack of energy conservation and loss of equipartition between different degrees of freedom of a system. We propose learning data-driven structure-preserving (symplectic and time-reversible) maps to generate long-time-step classical dynamics, showing that this method is equivalent to learning the mechanical action of the system of interest. We show that an action-derived ML integrator eliminates the pathological behavior of non-structure-preserving ML predictors, and that the method can be applied iteratively, serving as a correction to computationally cheaper direct predictors. Simulating classical mechanical systems with high accuracy and efficiency is a long-standing challenge in computational physics [31, 32]. Traditional numerical methods typically rely on small time steps to propagate the equations of motion for the dynamical system in order to provide accurate integration.

Accurate solar energy output prediction is key for integrating renewables into grids, maintaining stability, and improving energy management. However, standard error metrics such as Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Skill Scores (SS) fail to capture the multidimensional nature of solar irradiance forecasting. These metrics lack sensitivity to forecastability, rely on arbitrary baselines (e.g., clear-sky models), and are poorly suited for operational use. To address this, we introduce the NICEk framework (Normalized Informed Comparison of Errors, with k = 1, 2, 3, Sigma), offering a robust and interpretable evaluation of forecasting models. Each NICEk score corresponds to an Lk norm: NICE1 targets average errors, NICE2 emphasizes large deviations, NICE3 highlights outliers, and NICESigma combines all. Using Monte Carlo simulations and data from 68 stations in the Spanish SIAR network, we evaluated methods including autoregressive models, extreme learning, and smart persistence. Theoretical and empirical results align when assumptions hold (e.g., R^2 ~ 1.0 for NICE2). Most importantly, NICESigma consistently shows higher discriminative power (p < 0.05), outperforming traditional metrics (p > 0.05). The NICEk metrics exhibit stronger statistical significance (e.g., p-values from 10^-6 to 0.004 across horizons) and greater generalizability. They offer a unified and operational alternative to standard error metrics in deterministic solar forecasting.

The explosive growth of interactive Large Language Models (LLMs) has placed unprecedented demands for low latency on cloud GPUs, forcing them into high-power modes and causing escalating energy costs. Real-time inference workloads exhibit significant dynamic volatility, presenting substantial energy-saving opportunities. However, traditional static or rule-based power management strategies struggle to exploit these opportunities without compromising peak performance. To address this challenge, we propose AGFT (An Adaptive GPU Frequency Tuner), a framework that employs online reinforcement learning to autonomously learn an optimal frequency tuning policy. By monitoring real-time features like request load and latency, AGFT utilizes fine-grained frequency control for precise adjustments and intelligent action space pruning for stable, efficient decision-making. This creates a robust, automated energy management solution. We comprehensively evaluated AGFT in an environment simulating realistic, fluctuating inference requests. The experimental results demonstrate that AGFT successfully saves 44.3% of GPU energy consumption while introducing a minimal performance latency overhead of under 10%. This achievement translates into a comprehensive Energy-Delay Product (EDP) optimization of up to 40.3%, clearly showing that our framework can significantly enhance the energy efficiency and economic benefits of existing LLM inference clusters without compromising service quality.

Deep learning models have been widely adopted for False Data Injection Attack (FDIA) detection in smart grids due to their ability to capture unstructured and sparse features. However, the increasing system scale and data dimensionality introduce significant computational and memory burdens, particularly in large-scale industrial datasets, limiting detection efficiency. To address these issues, this paper proposes Rec-AD, a computationally efficient framework that integrates Tensor Train decomposition with the Deep Learning Recommendation Model (DLRM). Rec-AD enhances training and inference efficiency through embedding compression, optimized data access via index reordering, and a pipeline training mechanism that reduces memory communication overhead. Fully compatible with PyTorch, Rec-AD can be integrated into existing FDIA detection systems without code modifications. Experimental results show that Rec-AD significantly improves computational throughput and real-time detection performance, narrowing the attack window and increasing attacker cost. These advancements strengthen edge computing capabilities and scalability, providing robust technical support for smart grid security.

This paper introduces a novel simulation framework for evaluating motion control in tethered multi-robot systems within dynamic marine environments. Specifically, it focuses on the coordinated operation of an Autonomous Underwater Vehicle (AUV) and an Autonomous Surface Vehicle(ASV). The framework leverages GazeboSim, enhanced with realistic marine environment plugins and ArduPilots SoftwareIn-The-Loop (SITL) mode, to provide a high-fidelity simulation platform. A detailed tether model, combining catenary equations and physical simulation, is integrated to accurately represent the dynamic interactions between the vehicles and the environment. This setup facilitates the development and testing of advanced control strategies under realistic conditions, demonstrating the frameworks capability to analyze complex tether interactions and their impact on system performance.

Causal reasoning is essential for understanding decision-making about the behaviour of complex `ecosystems' of systems that underpin modern society, with security -- including issues around correctness, safety, resilience, etc. -- typically providing critical examples. We present a theory of strategic reasoning about system modelling based on minimal structural assumptions and employing the methods of transition systems, supported by a modal logic of system states in the tradition of van Benthem, Hennessy, and Milner, and validated through equivalence theorems. Our framework introduces an intervention operator and a separating conjunction to capture actual causal relationships between component systems of the ecosystem, aligning naturally with Halpern and Pearl's counterfactual approach based on Structural Causal Models. We illustrate the applicability through examples of of decision-making about microservices in distributed systems. We discuss localized decision-making through a separating conjunction. This work unifies a formal, minimalistic notion of system behaviour with a Halpern--Pearl-compatible theory of counterfactual reasoning, providing a logical foundation for studying decision making about causality in complex interacting systems.

The rise of Generative AI (GenAI) in recent years has catalyzed transformative advances in wireless communications and networks. Among the members of the GenAI family, Diffusion Models (DMs) have risen to prominence as a powerful option, capable of handling complex, high-dimensional data distribution, as well as consistent, noise-robust performance. In this survey, we aim to provide a comprehensive overview of the theoretical foundations and practical applications of DMs across future communication systems. We first provide an extensive tutorial of DMs and demonstrate how they can be applied to enhance optimizers, reinforcement learning and incentive mechanisms, which are popular approaches for problems in wireless networks. Then, we review and discuss the DM-based methods proposed for emerging issues in future networks and communications, including channel modeling and estimation, signal detection and data reconstruction, integrated sensing and communication, resource management in edge computing networks, semantic communications and other notable issues. We conclude the survey with highlighting technical limitations of DMs and their applications, as well as discussing future research directions.