Solving the Fokker-Planck equation for high-dimensional complex dynamical systems remains a pivotal yet challenging task due to the intractability of analytical solutions and the limitations of traditional numerical methods. In this work, we present FlowKac, a novel approach that reformulates the Fokker-Planck equation using the Feynman-Kac formula, allowing to query the solution at a given point via the expected values of stochastic paths. A key innovation of FlowKac lies in its adaptive stochastic sampling scheme which significantly reduces the computational complexity while maintaining high accuracy. This sampling technique, coupled with a time-indexed normalizing flow, designed for capturing time-evolving probability densities, enables robust sampling of collocation points, resulting in a flexible and mesh-free solver. This formulation mitigates the curse of dimensionality and enhances computational efficiency and accuracy, which is particularly crucial for applications that inherently require dimensions beyond the conventional three. We validate the robustness and scalability of our method through various experiments on a range of stochastic differential equations, demonstrating significant improvements over existing techniques.

Recurrent Neural Networks (RNNs) have shown remarkable performances in system identification, particularly in nonlinear dynamical systems such as thermal processes. However, stability remains a critical challenge in practical applications: although the underlying process may be intrinsically stable, there may be no guarantee that the resulting RNN model captures this behavior. This paper addresses the stability issue by deriving a sufficient condition for Input-to-State Stability based on the infinity-norm (ISS$_{\infty}$) for Long Short-Term Memory (LSTM) networks. The obtained condition depends on fewer network parameters compared to prior works. A ISS$_{\infty}$-promoted training strategy is developed, incorporating a penalty term in the loss function that encourages stability and an ad hoc early stopping approach. The quality of LSTM models trained via the proposed approach is validated on a thermal system case study, where the ISS$_{\infty}$-promoted LSTM outperforms both a physics-based model and an ISS$_{\infty}$-promoted Gated Recurrent Unit (GRU) network while also surpassing non-ISS$_{\infty}$-promoted LSTM and GRU RNNs.

Prognostic and Health Management (PHM) are crucial ways to avoid unnecessary maintenance for Cyber-Physical Systems (CPS) and improve system reliability. Predicting the Remaining Useful Life (RUL) is one of the most challenging tasks for PHM. Existing methods require prior knowledge about the system, contrived assumptions, or temporal mining to model the life cycles of machine equipment/devices, resulting in diminished accuracy and limited applicability in real-world scenarios. This paper proposes a Bi-directional Adversarial network with Covariate Encoding for machine Remaining Useful Life (BACE-RUL) prediction, which only adopts sensor measurements from the current life cycle to predict RUL rather than relying on previous consecutive cycle recordings. The current sensor measurements of mechanical devices are encoded to a conditional space to better understand the implicit inner mechanical status. The predictor is trained as a conditional generative network with the encoded sensor measurements as its conditions. Various experiments on several real-world datasets, including the turbofan aircraft engine dataset and the dataset collected from degradation experiments of Li-Ion battery cells, show that the proposed model is a general framework and outperforms state-of-the-art methods.

Accurate fine-grained geospatial scene classification using remote sensing imagery is essential for a wide range of applications. However, existing approaches often rely on manually zooming remote sensing images at different scales to create typical scene samples. This approach fails to adequately support the fixed-resolution image interpretation requirements in real-world scenarios. To address this limitation, we introduce the Million-scale finE-grained geospatial scEne classification dataseT (MEET), which contains over 1.03 million zoom-free remote sensing scene samples, manually annotated into 80 fine-grained categories. In MEET, each scene sample follows a scene-inscene layout, where the central scene serves as the reference, and auxiliary scenes provide crucial spatial context for finegrained classification. Moreover, to tackle the emerging challenge of scene-in-scene classification, we present the Context-Aware Transformer (CAT), a model specifically designed for this task, which adaptively fuses spatial context to accurately classify the scene samples. CAT adaptively fuses spatial context to accurately classify the scene samples by learning attentional features that capture the relationships between the center and auxiliary scenes. Based on MEET, we establish a comprehensive benchmark for fine-grained geospatial scene classification, evaluating CAT against 11 competitive baselines. The results demonstrate that CAT significantly outperforms these baselines, achieving a 1.88% higher balanced accuracy (BA) with the Swin-Large backbone, and a notable 7.87% improvement with the Swin-Huge backbone. Further experiments validate the effectiveness of each module in CAT and show the practical applicability of CAT in the urban functional zone mapping. The source code and dataset will be publicly available at https://jerrywyn.github.io/project/MEET.html.

Abstract--Underwater environments pose significant challenges for visual Simultaneous Localization and Mapping (SLAM) systems due to limited visibility, inadequate illumination, and sporadic loss of structural features in images. Addressing these challenges, this paper introduces a novel, tightly-coupled Acoustic-Visual-Inertial SLAM approach, termed AQUA-SLAM, to fuse a Doppler Velocity Log (DVL), a stereo camera, and an Inertial Measurement Unit (IMU) within a graph optimization framework. The proposed system will be made open-source for the community. These vehicles are indispensable occasionally outside the camera's field of view leading to for tasks such as seabed mapping, pipeline and intermittent loss of visual tracking. Therefore, although visual cable inspections, biological and environmental monitoring, SLAM techniques have recently made tremendous progress and the maintenance of underwater infrastructure. A key in terrestrial settings [1], [2], [3], their performance and application area is the detailed visual inspection of subsea robustness are inevitably compromised in underwater due to structures, including offshore wind turbine foundations, where the complex and dynamic nature of aquatic environments. Considering cameras are widely equipped on underwater (IMU), known as visual-inertial SLAM (VI-SLAM) [4], [5], robots, visual Simultaneous Localization and Mapping can alleviate some of the challenges arising from transient, (SLAM) techniques emerge as natural solutions. The rapid attenuation of underwater SLAM systems, particularly against shortterm of light energy in water severely limits the visibility of visual disruptions, can be substantially enhanced [6]. However, most of the challenges for underwater vision, such Moreover, underwater vision often suffers from poor lighting as the limited visibility and the "marine snow", are longterm and blizzards of "marine snow" caused by small particles of effects that last at least from tens of seconds to a few organic matter in water, severely reducing image quality with minutes before being mitigated. VI-SLAM also encounters increased motion blur and dynamic image regions.

Sensor simulation is pivotal for scalable validation of autonomous driving systems, yet existing Neural Radiance Fields (NeRF) based methods face applicability and efficiency challenges in industrial workflows. This paper introduces a Gaussian Splatting (GS) based system to address these challenges: We first break down sensor simulator components and analyze the possible advantages of GS over NeRF. Then in practice, we refactor three crucial components through GS, to leverage its explicit scene representation and real-time rendering: (1) choosing the 2D neural Gaussian representation for physics-compliant scene and sensor modeling, (2) proposing a scene editing pipeline to leverage Gaussian primitives library for data augmentation, and (3) coupling a controllable diffusion model for scene expansion and harmonization. We implement this framework on a proprietary autonomous driving dataset supporting cameras and LiDAR sensors. We demonstrate through ablation studies that our approach reduces frame-wise simulation latency, achieves better geometric and photometric consistency, and enables interpretable explicit scene editing and expansion. Furthermore, we showcase how integrating such a GS-based sensor simulator with traffic and dynamic simulators enables full-stack testing of end-to-end autonomy algorithms. Our work provides both algorithmic insights and practical validation, establishing GS as a cornerstone for industrial-grade sensor simulation.

This work presents a three-phase ML prediction framework designed to handle a high dimensionality and multivariate time series character of the electricity market curves. In the preprocessing phase, we transform the original data to achieve a unified structure and mitigate the effect of possible outliers. Further, to address the challenge of high dimensionality, we test three dimensionality reduction techniques (PCA, kPCA, UMAP). Finally, we predict supply and demand curves, once represented in a latent space, with a variety of machine learning methods (RF, LSTM, TSMixer). As our results on the MIBEL dataset show, a high dimensional structure of the market curves can be best handled by the nonlinear reduction technique UMAP. Regardless of the ML technique used for prediction, we achieved the lowest values for all considered precision metrics with a UMAP latent space representation in only two or three dimensions, even when compared to PCA and kPCA with five or six dimensions. Further, we demonstrate that the most promising machine learning technique to handle the complex structure of the electricity market curves is a novel TSMixer architecture. Finally, we fill the gap in the field of electricity market curves prediction literature: in addition to standard analysis on the supply side, we applied the ML framework and predicted demand curves too. We discussed the differences in the achieved results for these two types of curves.

Multi-agent reinforcement learning is a challenging and active field of research due to the inherent nonstationary property and coupling between agents. A popular approach to modeling the multi-agent interactions underlying the multi-agent RL problem is the Markov Game. There is a special type of Markov Game, termed Markov Potential Game, which allows us to reduce the Markov Game to a single-objective optimal control problem where the objective function is a potential function. In this work, we prove that a multi-agent collaborative field coverage problem, which is found in many engineering applications, can be formulated as a Markov Potential Game, and we can learn a parameterized closed-loop Nash Equilibrium by solving an equivalent single-objective optimal control problem. As a result, our algorithm is 10x faster during training compared to a game-theoretic baseline and converges faster during policy execution.

The key-value (KV) cache in autoregressive transformers presents a significant bottleneck during inference, which restricts the context length capabilities of large language models (LLMs). While previous work analyzes the fundamental space complexity barriers in standard attention mechanism [Haris and Onak, 2025], our work generalizes the space complexity barriers result to tensor attention version. Our theoretical contributions rely on a novel reduction from communication complexity and deduce the memory lower bound for tensor-structured attention mechanisms when $d = \Omega(\log n)$. In the low dimensional regime where $d = o(\log n)$, we analyze the theoretical bounds of the space complexity as well. Overall, our work provides a theoretical foundation for us to understand the compression-expressivity tradeoff in tensor attention mechanisms and offers more perspectives in developing more memory-efficient transformer architectures.

The applications of Large Language Models (LLMs) in political science are rapidly expanding. This paper demonstrates how LLMs, when augmented with predefined functions and specialized tools, can serve as dynamic agents capable of streamlining tasks such as data collection, preprocessing, and analysis. Central to this approach is agentic retrieval-augmented generation (Agentic RAG), which equips LLMs with action-calling capabilities for interaction with external knowledge bases. Beyond information retrieval, LLM agents may incorporate modular tools for tasks like document summarization, transcript coding, qualitative variable classification, and statistical modeling. To demonstrate the potential of this approach, we introduce CongressRA, an LLM agent designed to support scholars studying the U.S. Congress. Through this example, we highlight how LLM agents can reduce the costs of replicating, testing, and extending empirical research using the domain-specific data that drives the study of political institutions.