The metaverse, envisioned as the next digital frontier for avatar-based virtual interaction, involves high-performance models. In this dynamic environment, users' tasks frequently shift, requiring fast model personalization despite limited data. This evolution consumes extensive resources and requires vast data volumes. To address this, meta-learning emerges as an invaluable tool for metaverse users, with federated meta-learning (FML), offering even more tailored solutions owing to its adaptive capabilities. However, the metaverse is characterized by users heterogeneity with diverse data structures, varied tasks, and uneven sample sizes, potentially undermining global training outcomes due to statistical difference. Given this, an urgent need arises for smart coalition formation that accounts for these disparities. This paper introduces a dual game-theoretic framework for metaverse services involving meta-learners as workers to manage FML. A blockchain-based cooperative coalition formation game is crafted, grounded on a reputation metric, user similarity, and incentives. We also introduce a novel reputation system based on users' historical contributions and potential contributions to present tasks, leveraging correlations between past and new tasks. Finally, a Stackelberg game-based incentive mechanism is presented to attract reliable workers to participate in meta-learning, minimizing users' energy costs, increasing payoffs, boosting FML efficacy, and improving metaverse utility. Results show that our dual game framework outperforms best-effort, random, and non-uniform clustering schemes - improving training performance by up to 10%, cutting completion times by as much as 30%, enhancing metaverse utility by more than 25%, and offering up to 5% boost in training efficiency over non-blockchain systems, effectively countering misbehaving users.

Cyber-Physical Systems (CPSs) are increasingly prevalent across various industrial and daily-life domains, with applications ranging from robotic operations to autonomous driving. With recent advancements in artificial intelligence (AI), learning-based components, especially AI controllers, have become essential in enhancing the functionality and efficiency of CPSs. However, the lack of interpretability in these AI controllers presents challenges to the safety and quality assurance of AI-enabled CPSs (AI-CPSs). Existing methods for improving the safety of AI controllers often involve neural network repair, which requires retraining with additional adversarial examples or access to detailed internal information of the neural network. Hence, these approaches have limited applicability for black-box policies, where only the inputs and outputs are accessible during operation. To overcome this, we propose MORTAR, a runtime action repair framework designed for AI-CPSs in this work. MORTAR begins by constructing a prediction model that forecasts the quality of actions proposed by the AI controller. If an unsafe action is detected, MORTAR then initiates a repair process to correct it. The generation of repaired actions is achieved through an optimization process guided by the safety estimates from the prediction model. We evaluate the effectiveness of MORTAR across various CPS tasks and AI controllers. The results demonstrate that MORTAR can efficiently improve task completion rates of AI controllers under specified safety specifications. Meanwhile, it also maintains minimal computational overhead, ensuring real-time operation of the AI-CPSs.

In real case applications within the virtual prototyping process, it is not always possible to reduce the complexity of the physical models and to obtain numerical models which can be solved quickly. Usually, every single numerical simulation takes hours or even days. Although the progresses in numerical methods and high performance computing, in such cases, it is not possible to explore various model configurations, hence efficient surrogate models are required. Generally the available meta-model techniques show several advantages and disadvantages depending on the investigated problem. In this paper we present an automatic approach for the selection of the optimal suitable meta-model for the actual problem. Together with an automatic reduction of the variable space using advanced filter techniques an efficient approximation is enabled also for high dimensional problems. This filter techniques enable a reduction of the high dimensional variable space to a much smaller subspace where meta-model-based sensitivity analyses are carried out to assess the influence of important variables and to identify the optimal subspace with corresponding surrogate model which enables the most accurate probabilistic analysis. For this purpose we investigate variance-based and moment-free sensitivity measures in combination with advanced meta-models as moving least squares and kriging.

Bayesian analysis enables combining prior knowledge with measurement data to learn model parameters. Commonly, one resorts to computing the maximum a posteriori (MAP) estimate, when only a point estimate of the parameters is of interest. We apply MAP estimation in the context of structural dynamic models, where the system response can be described by the frequency response function. To alleviate high computational demands from repeated expensive model calls, we utilize a rational polynomial chaos expansion (RPCE) surrogate model that expresses the system frequency response as a rational of two polynomials with complex coefficients. We propose an extension to an existing sparse Bayesian learning approach for RPCE based on Laplace's approximation for the posterior distribution of the denominator coefficients. Furthermore, we introduce a Bayesian optimization approach, which allows to adaptively enrich the experimental design throughout the optimization process of MAP estimation. Thereby, we utilize the expected improvement acquisition function as a means to identify sample points in the input space that are possibly associated with large objective function values. The acquisition function is estimated through Monte Carlo sampling based on the posterior distribution of the expansion coefficients identified in the sparse Bayesian learning process. By combining the sparsity-inducing learning procedure with the sequential experimental design, we effectively reduce the number of model evaluations in the MAP estimation problem. We demonstrate the applicability of the presented methods on the parameter updating problem of an algebraic two-degree-of-freedom system and the finite element model of a cross-laminated timber plate.

This work presents the development of a parallel manipulator used for otological surgery from the perspective of co-design. Co-design refers to the simultaneous involvement of the end-users (surgeons), stakeholders (designers, ergonomic experts, manufacturers), and experts from the fields of optimization and mechanisms. The role of each member is discussed in detail and the interactions between the stakeholders are presented. Co-design facilitates a reduction in the parameter space considered during mechanism optimization, leading to a more efficient design process. Additionally, the co-design principles help avoid unforeseen errors and help in quicker adaptation of the proposed solution.

Humans often learn new skills by imitating the experts and gradually developing their proficiency. In this work, we introduce Stochastic Trajectory Optimization for Demonstration Imitation (STODI), a trajectory optimization framework for robots to imitate the shape of demonstration trajectories with improved dynamic performance. Consistent with the human learning process, demonstration imitation serves as an initial step, while trajectory optimization aims to enhance robot motion performance. By generating random noise and constructing proper cost functions, the STODI effectively explores and exploits generated noisy trajectories while preserving the demonstration shape characteristics. We employ three metrics to measure the similarity of trajectories in both the time and frequency domains to help with demonstration imitation. Theoretical analysis reveals relationships among these metrics, emphasizing the benefits of frequency-domain analysis for specific tasks. Experiments on a 7-DOF robotic arm in the PyBullet simulator validate the efficacy of the STODI framework, showcasing the improved optimization performance and stability compared to previous methods.

In this article, we describe an algorithm for solving Quadratic Unconstrained Binary Optimization problems on the Intel Loihi 2 neuromorphic processor. The solver is based on a hardware-aware fine-grained parallel simulated annealing algorithm developed for Intel's neuromorphic research chip Loihi 2. Preliminary results show that our approach can generate feasible solutions in as little as 1 ms and up to 37x more energy efficient compared to two baseline solvers running on a CPU. These advantages could be especially relevant for size-, weight-, and power-constrained edge computing applications.

Multi-suction-cup grippers are frequently employed to perform pick-and-place robotic tasks, especially in industrial settings where grasping a wide range of light to heavy objects in limited amounts of time is a common requirement. However, most existing works focus on using one or two suction cups to grasp only irregularly shaped but light objects. There is a lack of research on robust manipulation of heavy objects using larger arrays of suction cups, which introduces challenges in modeling and predicting grasp failure. This paper presents a general approach to modeling grasp strength in multi-suction-cup grippers, introducing new constraints usable for trajectory planning and optimization to achieve fast and reliable pick-and-place maneuvers. The primary modeling challenge is the accurate prediction of the distribution of loads at each suction cup while grasping objects. To solve for this load distribution, we find minimum spring potential energy configurations through a simple quadratic program. This results in a computationally efficient analytical solution that can be integrated to formulate grasp failure constraints in time-optimal trajectory planning. Finally, we present experimental results to validate the efficiency and accuracy of the proposed model.

Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are poorly understood from a theoretical perspective. In this work we consider a generalized version of multidimensional scaling, which is posed as an optimization problem in which a mapping from a high-dimensional feature space to a lower-dimensional embedding space seeks to preserve either inner products or norms of the distribution in feature space, and which encompasses many commonly used dimension reduction algorithms. We analytically investigate the variational properties of this problem, leading to the following insights: 1) Solutions found using standard particle descent methods may lead to non-deterministic embeddings, 2) A relaxed or probabilistic formulation of the problem admits solutions with easily interpretable necessary conditions, 3) The globally optimal solutions to the relaxed problem actually must give a deterministic embedding. This progression of results mirrors the classical development of optimal transportation, and in a case relating to the Gromov-Wasserstein distance actually gives explicit insight into the structure of the optimal embeddings, which are parametrically determined and discontinuous. Finally, we illustrate that a standard computational implementation of this task does not learn deterministic embeddings, which means that it learns sub-optimal mappings, and that the embeddings learned in that context have highly misleading clustering structure, underscoring the delicate nature of solving this problem computationally.

The independence assumption is a useful tool to increase the tractability of one's modelling framework. However, this assumption does not match reality; failing to take dependencies into account can cause models to fail dramatically. The field of multi-axis graphical modelling (also called multi-way modelling, Kronecker-separable modelling) has seen growth over the past decade, but these models require that the data have zero mean. In the multi-axis case, inference is typically done in the single sample scenario, making mean inference impossible. In this paper, we demonstrate how the zero-mean assumption can cause egregious modelling errors, as well as propose a relaxation to the zero-mean assumption that allows the avoidance of such errors. Specifically, we propose the "Kronecker-sum-structured mean" assumption, which leads to models with nonconvex-but-unimodal log-likelihoods that can be solved efficiently with coordinate descent.