The Clebsch-Gordan Transform (CG transform) effectively encodes many-body interactions. Many studies have proven its accuracy in depicting atomic environments, although this comes with high computational needs. The computational burden of this challenge is hard to reduce due to the need for permutation equivariance, which limits the design space of the CG transform layer. We show that, implementing the CG transform layer on permutation-invariant inputs allows complete freedom in the design of this layer without affecting symmetry. Developing further on this premise, our idea is to create a CG transform layer that operates on permutation-invariant abstract edges generated from real edge information. We bring in group CG transform with sparse path, abstract edges shuffling, and attention enhancer to form a powerful and efficient CG transform layer. Our method, known as FreeCG, achieves State-of-The-Art (SoTA) results in force prediction for MD17, rMD17, MD22, and property prediction in QM9 datasets with notable enhancement. It introduces a novel paradigm for carrying out efficient and expressive CG transform in future geometric neural network designs.

Long Document Classification (LDC) has gained significant attention recently. However, multi-modal data in long documents such as texts and images are not being effectively utilized. Prior studies in this area have attempted to integrate texts and images in document-related tasks, but they have only focused on short text sequences and images of pages. How to classify long documents with hierarchical structure texts and embedding images is a new problem and faces multi-modal representation difficulties. In this paper, we propose a novel approach called Hierarchical Multi-modal Transformer (HMT) for cross-modal long document classification. The HMT conducts multi-modal feature interaction and fusion between images and texts in a hierarchical manner. Our approach uses a multi-modal transformer and a dynamic multi-scale multi-modal transformer to model the complex relationships between image features, and the section and sentence features. Furthermore, we introduce a new interaction strategy called the dynamic mask transfer module to integrate these two transformers by propagating features between them. To validate our approach, we conduct cross-modal LDC experiments on two newly created and two publicly available multi-modal long document datasets, and the results show that the proposed HMT outperforms state-of-the-art single-modality and multi-modality methods.

Optimizing the fuel cycle cost through the optimization of nuclear reactor core loading patterns involves multiple objectives and constraints, leading to a vast number of candidate solutions that cannot be explicitly solved. To advance the state-of-the-art in core reload patterns, we have developed methods based on Deep Reinforcement Learning (DRL) for both single- and multi-objective optimization. Our previous research has laid the groundwork for these approaches and demonstrated their ability to discover high-quality patterns within a reasonable time frame. On the other hand, stochastic optimization (SO) approaches are commonly used in the literature, but there is no rigorous explanation that shows which approach is better in which scenario. In this paper, we demonstrate the advantage of our RL-based approach, specifically using Proximal Policy Optimization (PPO), against the most commonly used SO-based methods: Genetic Algorithm (GA), Parallel Simulated Annealing (PSA) with mixing of states, and Tabu Search (TS), as well as an ensemble-based method, Prioritized Replay Evolutionary and Swarm Algorithm (PESA). We found that the LP scenarios derived in this paper are amenable to a global search to identify promising research directions rapidly, but then need to transition into a local search to exploit these directions efficiently and prevent getting stuck in local optima. PPO adapts its search capability via a policy with learnable weights, allowing it to function as both a global and local search method. Subsequently, we compared all algorithms against PPO in long runs, which exacerbated the differences seen in the shorter cases. Overall, the work demonstrates the statistical superiority of PPO compared to the other considered algorithms.

Although Model Predictive Control (MPC) can effectively predict the future states of a system and thus is widely used in robotic manipulation tasks, it does not have the capability of environmental perception, leading to the failure in some complex scenarios. To address this issue, we introduce Vision-Language Model Predictive Control (VLMPC), a robotic manipulation framework which takes advantage of the powerful perception capability of vision language model (VLM) and integrates it with MPC. Specifically, we propose a conditional action sampling module which takes as input a goal image or a language instruction and leverages VLM to sample a set of candidate action sequences. Then, a lightweight action-conditioned video prediction model is designed to generate a set of future frames conditioned on the candidate action sequences. VLMPC produces the optimal action sequence with the assistance of VLM through a hierarchical cost function that formulates both pixel-level and knowledge-level consistence between the current observation and the goal image. We demonstrate that VLMPC outperforms the state-of-the-art methods on public benchmarks. More importantly, our method showcases excellent performance in various real-world tasks of robotic manipulation. Code is available at~\url{https://github.com/PPjmchen/VLMPC}.

High-performance computing (HPC) has revolutionized our ability to perform detailed simulations of complex real-world processes. A prominent contemporary example is from aerospace propulsion, where HPC is used for rotating detonation rocket engine (RDRE) simulations in support of the design of next-generation rocket engines; however, these simulations take millions of core hours even on powerful supercomputers, which makes them impractical for engineering tasks like design exploration and risk assessment. Reduced-order models (ROMs) address this limitation by constructing computationally cheap yet sufficiently accurate approximations that serve as surrogates for the high-fidelity model. This paper contributes a new distributed algorithm that achieves fast and scalable construction of predictive physics-based ROMs trained from sparse datasets of extremely large state dimension. The algorithm learns structured physics-based ROMs that approximate the dynamical systems underlying those datasets. This enables model reduction for problems at a scale and complexity that exceeds the capabilities of existing approaches. We demonstrate our algorithm's scalability using up to $2,048$ cores on the Frontera supercomputer at the Texas Advanced Computing Center. We focus on a real-world three-dimensional RDRE for which one millisecond of simulated physical time requires one million core hours on a supercomputer. Using a training dataset of $2,536$ snapshots each of state dimension $76$ million, our distributed algorithm enables the construction of a predictive data-driven reduced model in just $13$ seconds on $2,048$ cores on Frontera.

Through this comprehensive survey of Kolmogorov-Arnold Networks(KAN), we have gained a thorough understanding of its theoretical foundation, architectural design, application scenarios, and current research progress. KAN, with its unique architecture and flexible activation functions, excels in handling complex data patterns and nonlinear relationships, demonstrating wide-ranging application potential. While challenges remain, KAN is poised to pave the way for innovative solutions in various fields, potentially revolutionizing how we approach complex computational problems.

This paper introduces a control architecture for real-time and onboard control of Unmanned Aerial Vehicles (UAVs) in environments with obstacles using the Model Predictive Path Integral (MPPI) methodology. MPPI allows the use of the full nonlinear model of UAV dynamics and a more general cost function at the cost of a high computational demand. To run the controller in real-time, the sampling-based optimization is performed in parallel on a graphics processing unit onboard the UAV. We propose an approach to the simulation of the nonlinear system which respects low-level constraints, while also able to dynamically handle obstacle avoidance, and prove that our methods are able to run in real-time without the need for external computers. The MPPI controller is compared to MPC and SE(3) controllers on the reference tracking task, showing a comparable performance. We demonstrate the viability of the proposed method in multiple simulation and real-world experiments, tracking a reference at up to 44 km/h and acceleration close to 20 m/s^2, while still being able to avoid obstacles. To the best of our knowledge, this is the first method to demonstrate an MPPI-based approach in real flight.

Scaling model capacity enhances its capabilities but significantly increases computation. Mixture-of-Experts models (MoEs) address this by allowing model capacity to scale without substantially increasing training or inference costs. Despite their promising results, MoE models encounter several challenges. Primarily, the dispersion of training tokens across multiple experts can lead to underfitting, particularly for infrequent tokens. Additionally, while fixed routing mechanisms can mitigate this issue, they compromise on the diversity of representations. In this paper, we propose MaskMoE, a method designed to enhance token-level learning by employing a routing masking technique within the Mixture-of-Experts model. MaskMoE is capable of maintaining representation diversity while achieving more comprehensive training. Experimental results demonstrate that our method outperforms previous dominant Mixture-of-Experts models in both perplexity (PPL) and downstream tasks.

The paper reflects on the future role of AI in scientific research, with a special focus on turbulence studies, and examines the evolution of AI, particularly through Diffusion Models rooted in non-equilibrium statistical mechanics. It underscores the significant impact of AI on advancing reduced, Lagrangian models of turbulence through innovative use of deep neural networks. Additionally, the paper reviews various other AI applications in turbulence research and outlines potential challenges and opportunities in the concurrent advancement of AI and statistical hydrodynamics. This discussion sets the stage for a future where AI and turbulence research are intricately intertwined, leading to more profound insights and advancements in both fields.

Bridging the gap between classical scientific computing and machine learning, the emerging field called scientific machine learning has introduced a completely different framework to compute the solutions of partial differential equations (PDEs). The forefront of this evolution lies within the area of physicsinformed neural networks (PINNs) [18, 10]. Based on the universal approximation property of deep neural networks, the PINNs approximate the solutions of PDEs by incorporating underlying physics into deep neural networks. Due to their simplicity and flexibility in handling a wide range of physical problems involving PDEs, PINNs have recently gained great attention and have been applied to various fields in computational science: bio-medical science [22, 11], fluids mechanics [20, 19, 9, 4, 21], uncertainty quantification [30, 32, 29] and meta-material design [12, 3]. Moreover, since the PINNs utilize randomlyselected collocation points as training samples in the spatio-temporal domain, the PINNs are available for high-dimensional PDEs [24, 6], on the domains with complex geometries [13, 23, 26, 14]. However, despite the significant empirical success of PINNs, we only have limited knowledge about the behavior of these constrained neural networks during their training process, and the training of PINNs often fails. In particular, since neural networks typically assume a smooth prior, it is often challenging to train PINNs to learn a solution with a sharp transition which poses significant obstacles for the model prediction. For example, some recent studies have illustrated that training PINNs with fully-connected neural networks usually suffers from so-called spectral bias or F-principle meaning that it is difficult for PINNs to learn functions with high frequencies [17, 2, 25].