Large-scale latent variable models require expressive continuous distributions that support efficient sampling and low-variance differentiation, achievable through the reparameterization trick. The Kumaraswamy (KS) distribution is both expressive and supports the reparameterization trick with a simple closed-form inverse CDF. Yet, its adoption remains limited. We identify and resolve numerical instabilities in the inverse CDF and log-pdf, exposing issues in libraries like PyTorch and TensorFlow. We then introduce simple and scalable latent variable models based on the KS, improving exploration-exploitation trade-offs in contextual multi-armed bandits and enhancing uncertainty quantification for link prediction with graph neural networks. Our results support the stabilized KS distribution as a core component in scalable variational models for bounded latent variables.

The optimization of expensive black-box simulators arises in a myriad of modern scientific and engineering applications. Bayesian optimization provides an appealing solution, by leveraging a fitted surrogate model to guide the selection of subsequent simulator evaluations. In practice, however, the objective is often not to obtain a single good solution, but rather a ''basket'' of good solutions from which users can choose for downstream decision-making. This need arises in our motivating application for real-time control of internal combustion engines for flight propulsion, where a diverse set of control strategies is essential for stable flight control. There has been little work on this front for Bayesian optimization. We thus propose a new Diverse Expected Improvement (DEI) method that searches for diverse ''$\epsilon$-optimal'' solutions: locally-optimal solutions within a tolerance level $\epsilon > 0$ from a global optimum. We show that DEI yields a closed-form acquisition function under a Gaussian process surrogate model, which facilitates efficient sequential queries via automatic differentiation. This closed form further reveals a novel exploration-exploitation-diversity trade-off, which incorporates the desired diversity property within the well-known exploration-exploitation trade-off. We demonstrate the improvement of DEI over existing methods in a suite of numerical experiments, then explore the DEI in two applications on rover trajectory optimization and engine control for flight propulsion.

This paper investigates the enhancement of spatial resolution in Sentinel-2 bands that contain spectral information using advanced super-resolution techniques by a factor of 2. State-of-the-art CNN models are compared with enhanced GAN approaches in terms of quality and feasibility. Therefore, a representative dataset comprising Sentinel-2 low-resolution images and corresponding high-resolution aerial orthophotos is required. Literature study reveals no feasible dataset for the land type of interest (forests), for which reason an adequate dataset had to be generated in addition, accounting for accurate alignment and image source optimization. The results reveal that while CNN-based approaches produce satisfactory outcomes, they tend to yield blurry images. In contrast, GAN-based models not only provide clear and detailed images, but also demonstrate superior performance in terms of quantitative assessment, underlying the potential of the framework beyond the specific land type investigated.

Learning the evolutionary dynamics of Partial Differential Equations (PDEs) is critical in understanding dynamic systems, yet current methods insufficiently learn their representations. This is largely due to the multi-scale nature of the solution, where certain regions exhibit rapid oscillations while others evolve more slowly. This paper introduces a framework of multi-scale and multi-expert (M$^2$M) neural operators designed to simulate and learn PDEs efficiently. We employ a divide-and-conquer strategy to train a multi-expert gated network for the dynamic router policy. Our method incorporates a controllable prior gating mechanism that determines the selection rights of experts, enhancing the model's efficiency. To optimize the learning process, we have implemented a PI (Proportional, Integral) control strategy to adjust the allocation rules precisely. This universal controllable approach allows the model to achieve greater accuracy. We test our approach on benchmark 2D Navier-Stokes equations and provide a custom multi-scale dataset. M$^2$M can achieve higher simulation accuracy and offer improved interpretability compared to baseline methods.

Embodied AI is a rapidly advancing field that bridges the gap between cyberspace and physical space, enabling a wide range of applications. This evolution has led to the development of the Vehicular Embodied AI NETwork (VEANET), where advanced AI capabilities are integrated into vehicular systems to enhance autonomous operations and decision-making. Embodied agents, such as Autonomous Vehicles (AVs), are autonomous entities that can perceive their environment and take actions to achieve specific goals, actively interacting with the physical world. Embodied twins are digital models of these embodied agents, with various embodied AI twins for intelligent applications in cyberspace. In VEANET, embodied AI twins act as in-vehicle AI assistants to perform diverse tasks supporting autonomous driving using generative AI models. Due to limited computational resources of AVs, these AVs often offload computationally intensive tasks, such as constructing and updating embodied AI twins, to nearby RSUs. However, since the rapid mobility of AVs and the limited provision coverage of a single RSU, embodied AI twins require dynamic migrations from current RSU to other RSUs in real-time, resulting in the challenge of selecting suitable RSUs for efficient embodied AI twins migrations. Given information asymmetry, AVs cannot know the detailed information of RSUs. To this end, in this paper, we construct a multi-dimensional contract theoretical model between AVs and alternative RSUs. Considering that AVs may exhibit irrational behavior, we utilize prospect theory instead of expected utility theory to model the actual utilities of AVs. Finally, we employ a generative diffusion model-based algorithm to identify the optimal contract designs. Compared with traditional deep reinforcement learning algorithms, numerical results demonstrate the effectiveness of the proposed scheme.

Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each presents its unique limitations and generally balances training cost, numerical accuracy, and ease of applicability to different problem setups. To address these limitations, we introduce several methods to apply latent diffusion models to physics simulation. Firstly, we introduce a mesh autoencoder to compress arbitrarily discretized PDE data, allowing for efficient diffusion training across various physics. Furthermore, we investigate full spatio-temporal solution generation to mitigate autoregressive error accumulation. Lastly, we investigate conditioning on initial physical quantities, as well as conditioning solely on a text prompt to introduce text2PDE generation. We show that language can be a compact, interpretable, and accurate modality for generating physics simulations, paving the way for more usable and accessible PDE solvers. Through experiments on both uniform and structured grids, we show that the proposed approach is competitive with current neural PDE solvers in both accuracy and efficiency, with promising scaling behavior up to 3 billion parameters. By introducing a scalable, accurate, and usable physics simulator, we hope to bring neural PDE solvers closer to practical use. Neural PDE solvers are an exciting new class of physics solvers that have the potential to improve many aspects of conventional numerical solvers. Initial works have proposed various architectures to accomplish this, such as graph-based (Li & Farimani, 2022; Battaglia et al., 2016), physicsinformed (Raissi et al., 2019), or convolutional approaches (Thuerey et al., 2020). Subsequent work on developing neural operators (Li et al., 2021; Lu et al., 2021; Kovachki et al., 2023) established them as powerful physics approximators that can quickly and accurately predict PDEs, and recent work has focused on improving many of their different aspects. Despite these advances, there are still many factors that limit the practical adoption of neural PDE surrogates. Figure 1: We introduce latent diffusion models for physics simulation, with the remarkable ability of generating an entire PDE rollout from a text prompt. Two generated solutions are displayed with their model inputs.

This paper investigates the transformative potential of generative AI technologies, particularly large language models (LLMs), within the building industry. By leveraging these advanced AI tools, the study explores their application across key areas such as energy code compliance, building design optimization, and workforce training. The research highlights how LLMs can automate labor-intensive processes, significantly improving efficiency, accuracy, and safety in building practices. The paper also addresses the challenges associated with interpreting complex visual and textual data in architectural plans and regulatory codes, proposing innovative solutions to enhance AI-driven compliance checking and design processes. Additionally, the study considers the broader implications of AI integration, including the development of AI-powered tools for comprehensive code compliance across various regulatory domains and the potential for AI to revolutionize workforce training through realistic simulations. This paper provides a comprehensive analysis of the current capabilities of generative AI in the building industry while outlining future directions for research and development, aiming to pave the way for smarter, more sustainable, and responsive construction practices.

This paper proposes a robust nonlinear observer synthesis method for a population of systems modelled using the Koopman operator. The Koopman operator allows nonlinear systems to be rewritten as infinite-dimensional linear systems. A finite-dimensional approximation of the Koopman operator can be identified directly from data, yielding an approximately linear model of a nonlinear system. The proposed observer synthesis method is made possible by this linearity that in turn allows uncertainty within a population of Koopman models to be quantified in the frequency domain. Using this uncertainty model, linear robust control techniques are used to synthesize robust nonlinear Koopman observers. A population of several dozen motor drives is used to experimentally demonstrate the proposed method. Manufacturing variation is characterized in the frequency domain, and a robust Koopman observer is synthesized using mixed $\mathcal{H}_2$-$\mathcal{H}_\infty$ optimal control.

Power system operators must ensure that dispatch decisions remain feasible in case of grid outages or contingencies to prevent cascading failures and ensure reliable operation. However, checking the feasibility of all $N - k$ contingencies -- every possible simultaneous failure of $k$ grid components -- is computationally intractable for even small $k$, requiring system operators to resort to heuristic screening methods. Because of the increase in uncertainty and changes in system behaviors, heuristic lists might not include all relevant contingencies, generating false negatives in which unsafe scenarios are misclassified as safe. In this work, we propose to use input-convex neural networks (ICNNs) for contingency screening. We show that ICNN reliability can be determined by solving a convex optimization problem, and by scaling model weights using this problem as a differentiable optimization layer during training, we can learn an ICNN classifier that is both data-driven and has provably guaranteed reliability. Namely, our method can ensure a zero false negative rate. We empirically validate this methodology in a case study on the IEEE 39-bus test network, observing that it yields substantial (10-20x) speedups while having excellent classification accuracy.

Evidential Deep Learning (EDL) is an emerging method for uncertainty estimation that provides reliable predictive uncertainty in a single forward pass, attracting significant attention. Grounded in subjective logic, EDL derives Dirichlet concentration parameters from neural networks to construct a Dirichlet probability density function (PDF), modeling the distribution of class probabilities. Despite its success, EDL incorporates several nonessential settings: In model construction, (1) a commonly ignored prior weight parameter is fixed to the number of classes, while its value actually impacts the balance between the proportion of evidence and its magnitude in deriving predictive scores. In model optimization, (2) the empirical risk features a variance-minimizing optimization term that biases the PDF towards a Dirac delta function, potentially exacerbating overconfidence. (3) Additionally, the structural risk typically includes a KL-divergence-minimizing regularization, whose optimization direction extends beyond the intended purpose and contradicts common sense, diminishing the information carried by the evidence magnitude. Therefore, we propose Re-EDL, a simplified yet more effective variant of EDL, by relaxing the nonessential settings and retaining the essential one, namely, the adoption of projected probability from subjective logic. Specifically, Re-EDL treats the prior weight as an adjustable hyperparameter rather than a fixed scalar, and directly optimizes the expectation of the Dirichlet PDF provided by deprecating both the variance-minimizing optimization term and the divergence regularization term. Extensive experiments and state-of-the-art performance validate the effectiveness of our method. The source code is available at https://github.com/MengyuanChen21/Re-EDL.