Learning problems in which multiple conflicting objectives must be considered simultaneously often arise in various fields, including engineering, drug design, and environmental management. Traditional methods for dealing with multiple black-box objective functions, such as scalarization and identification of the Pareto set under the componentwise order, have limitations in incorporating objective preferences and exploring the solution space accordingly. While vector optimization offers improved flexibility and adaptability via specifying partial orders based on ordering cones, current techniques designed for sequential experiments either suffer from high sample complexity or lack theoretical guarantees. To address these issues, we propose Vector Optimization with Gaussian Process (VOGP), a probably approximately correct adaptive elimination algorithm that performs black-box vector optimization using Gaussian process bandits. VOGP allows users to convey objective preferences through ordering cones while performing efficient sampling by exploiting the smoothness of the objective function, resulting in a more effective optimization process that requires fewer evaluations. We establish theoretical guarantees for VOGP and derive information gain-based and kernel-specific sample complexity bounds. We also conduct experiments on both real-world and synthetic datasets to compare VOGP with the state-of-the-art methods.

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Global carbon emissions would be 6% lower than today if not for the "inaccurate narrative" against nuclear power since the Chornobyl disaster that has created "unfounded public concern", according to Tony Blair's thinktank. A report from the Tony Blair Institute (TBI) has found that if the nuclear power industry had continued to grow at the same pace as before the 1986 nuclear disaster, the carbon savings would be the equivalent of removing the emissions of Canada, South Korea, Australia and Mexico combined. The world's emissions are higher than they might have been because of a sharp slowdown in the number of nuclear reactors opened since the 1980s, said the report, released on Monday. It found that more than 400 reactors started up in the 30 years before the Chornobyl disaster, but fewer than 200 had been commissioned in the almost 30 years since. "The result is that nuclear energy has never become the ubiquitous power source many had projected, with countries instead turning towards alternatives such as coal and gas," the report said. The thinktank has predicted a "new nuclear age" in the years ahead, driven by a surge in demand for low-carbon electricity from the power-thirsty datacentres needed to power artificial intelligence.

Multi-modal large language models (MLLMs) have demonstrated promising capabilities across various tasks by integrating textual and visual information to achieve visual understanding in complex scenarios. Despite the availability of several benchmarks aims to evaluating MLLMs in tasks from visual question answering to complex problem-solving, most focus predominantly on mathematics or general visual understanding tasks. This reveals a critical gap in current benchmarks, which often overlook the inclusion of other key scientific disciplines such as physics and chemistry. To address this gap, we meticulously construct a comprehensive benchmark, named VisScience, which is utilized to assess the multi-modal scientific reasoning across the three disciplines of mathematics, physics, and chemistry. This benchmark comprises 3,000 questions drawn from K12 education - spanning elementary school through high school - equally distributed across three disciplines, with 1,000 questions per discipline. The questions within VisScience span 21 distinct subjects and are categorized into five difficulty levels, offering a broad spectrum of topics within each discipline. With VisScience, we present a detailed evaluation of the performance of 25 representative MLLMs in scientific reasoning. Experimental results demonstrate that closed-source MLLMs generally outperform open-source models. The best performance observed include a 53.4\% accuracy in mathematics by Claude3.5-Sonnet, 38.2\% in physics by GPT-4o, and 47.0\% in chemistry by Gemini-1.5-Pro. These results underscore the strengths and limitations of MLLMs, suggesting areas for future improvement and highlighting the importance of developing models that can effectively handle the diverse demands of multi-modal scientific reasoning.

Scientific computing has benefited from using operator networks to enhance or replace numerical computation for the purpose of simulation and forecasting on a wide array of applications to include computational fluid dynamics and weather forecasting [3]. The two primary neural operators that demonstrated immediate success are the deep operator network (DeepONet) [4] based on the universal approximation theorem in [5], and the Fourier neural operator (FNO) [6]. The basic DeepONet approximates the operator by applying a weighted sum to the product of each of the transformed outputs from two FNN sub-networks. The upper sub-network, or branch net, is applied to the input functions while the lower trunk net is applied to the querying locations of the output function. In contrast, the FNO is a particular type of Neural Operator network [7], which accepts only input functions (not querying locations for the output) and applies a global transformation on the function input via a more intricate architecture. Motivated by fundamental solutions to partial differential equations (PDEs), the FNO network sums the output of an integral kernel transformation to the input function with the output of a linear transformation. The sum is then passed through a non-linear activation function. To accelerate the integral kernel transformation, the FNO applies a Fourier transform (FT) to the input data, with the FT of the integral kernel assumed as trainable parameters.

Mangroves play a crucial role in maintaining coastal ecosystem health and protecting biodiversity. Therefore, continuous mapping of mangroves is essential for understanding their dynamics. Earth observation imagery typically provides a cost-effective way to monitor mangrove dynamics. However, there is a lack of regional studies on mangrove areas in the UAE. This study utilizes the UNet++ deep learning model combined with Sentinel-2 multispectral data and manually annotated labels to monitor the spatiotemporal dynamics of densely distributed mangroves (coverage greater than 70%) in the UAE from 2017 to 2024, achieving an mIoU of 87.8% on the validation set. Results show that the total mangrove area in the UAE in 2024 was approximately 9,142.21 hectares, an increase of 2,061.33 hectares compared to 2017, with carbon sequestration increasing by approximately 194,383.42 tons, equivalent to fixing about 713,367.36 tons of carbon dioxide. Abu Dhabi has the largest mangrove area and plays a dominant role in the UAE's mangrove growth, increasing by 1,855.6 hectares between 2017-2024, while other emirates have also contributed to mangrove expansion through stable and sustainable growth in mangrove areas. This comprehensive growth pattern reflects the collective efforts of all emirates in mangrove restoration.

Text-to-image diffusion models have demonstrated remarkable capability in generating realistic images from arbitrary text prompts. However, they often produce inconsistent results for compositional prompts such as "two dogs" or "a penguin on the right of a bowl". Understanding these inconsistencies is crucial for reliable image generation. In this paper, we highlight the significant role of initial noise in these inconsistencies, where certain noise patterns are more reliable for compositional prompts than others. Our analyses reveal that different initial random seeds tend to guide the model to place objects in distinct image areas, potentially adhering to specific patterns of camera angles and image composition associated with the seed. To improve the model's compositional ability, we propose a method for mining these reliable cases, resulting in a curated training set of generated images without requiring any manual annotation. By fine-tuning text-to-image models on these generated images, we significantly enhance their compositional capabilities. For numerical composition, we observe relative increases of 29.3% and 19.5% for Stable Diffusion and PixArt-{\alpha}, respectively. Spatial composition sees even larger gains, with 60.7% for Stable Diffusion and 21.1% for PixArt-{\alpha}.

Many partial differential equations (PDEs) such as Navier--Stokes equations in fluid mechanics, inelastic deformation in solids, and transient parabolic and hyperbolic equations do not have an exact, primal variational structure. Recently, a variational principle based on the dual (Lagrange multiplier) field was proposed. The essential idea in this approach is to treat the given PDE as constraints, and to invoke an arbitrarily chosen auxiliary potential with strong convexity properties to be optimized. This leads to requiring a convex dual functional to be minimized subject to Dirichlet boundary conditions on dual variables, with the guarantee that even PDEs that do not possess a variational structure in primal form can be solved via a variational principle. The vanishing of the first variation of the dual functional is, up to Dirichlet boundary conditions on dual fields, the weak form of the primal PDE problem with the dual-to-primal change of variables incorporated. We derive the dual weak form for the linear, one-dimensional, transient convection-diffusion equation. A Galerkin discretization is used to obtain the discrete equations, with the trial and test functions chosen as linear combination of either RePU activation functions (shallow neural network) or B-spline basis functions; the corresponding stiffness matrix is symmetric. For transient problems, a space-time Galerkin implementation is used with tensor-product B-splines as approximating functions. Numerical results are presented for the steady-state and transient convection-diffusion equation, and transient heat conduction. The proposed method delivers sound accuracy for ODEs and PDEs and rates of convergence are established in the $L^2$ norm and $H^1$ seminorm for the steady-state convection-diffusion problem.

We address the decision-making capability within an end-to-end planning framework that focuses on motion prediction, decision-making, and trajectory planning. Specifically, we formulate decision-making and trajectory planning as a differentiable nonlinear optimization problem, which ensures compatibility with learning-based modules to establish an end-to-end trainable architecture. This optimization introduces explicit objectives related to safety, traveling efficiency, and riding comfort, guiding the learning process in our proposed pipeline. Intrinsic constraints resulting from the decision-making task are integrated into the optimization formulation and preserved throughout the learning process. By integrating the differentiable optimizer with a neural network predictor, the proposed framework is end-to-end trainable, aligning various driving tasks with ultimate performance goals defined by the optimization objectives. The proposed framework is trained and validated using the Waymo Open Motion dataset. The open-loop testing reveals that while the planning outcomes using our method do not always resemble the expert trajectory, they consistently outperform baseline approaches with improved safety, traveling efficiency, and riding comfort. The closed-loop testing further demonstrates the effectiveness of optimizing decisions and improving driving performance. Ablation studies demonstrate that the initialization provided by the learning-based prediction module is essential for the convergence of the optimizer as well as the overall driving performance.

Generative models, particularly diffusion models, have achieved remarkable success in density estimation for multimodal data, drawing significant interest from the reinforcement learning (RL) community, especially in policy modeling in continuous action spaces. However, existing works exhibit significant variations in training schemes and RL optimization objectives, and some methods are only applicable to diffusion models. In this study, we compare and analyze various generative policy training and deployment techniques, identifying and validating effective designs for generative policy algorithms. Specifically, we revisit existing training objectives and classify them into two categories, each linked to a simpler approach. The first approach, Generative Model Policy Optimization (GMPO), employs a native advantage-weighted regression formulation as the training objective, which is significantly simpler than previous methods. The second approach, Generative Model Policy Gradient (GMPG), offers a numerically stable implementation of the native policy gradient method. We introduce a standardized experimental framework named GenerativeRL. Our experiments demonstrate that the proposed methods achieve state-of-the-art performance on various offline-RL datasets, offering a unified and practical guideline for training and deploying generative policies.