Simulating the long-term dynamics of multi-scale and multi-physics systems poses a significant challenge in understanding complex phenomena across science and engineering. The complexity arises from the intricate interactions between scales and the interplay of diverse physical processes. Neural operators have emerged as promising models for predicting such dynamics due to their flexibility and computational efficiency. However, they often fail to effectively capture multi-scale interactions or quantify the uncertainties inherent in the predictions. These limitations lead to rapid error accumulation, particularly in long-term forecasting of systems characterized by complex and coupled dynamics. To address these challenges, we propose a spatio-temporal Fourier transformer (StFT), in which each transformer block is designed to learn dynamics at a specific scale. By leveraging a structured hierarchy of StFT blocks, the model explicitly captures dynamics across both macro- and micro- spatial scales. Furthermore, a generative residual correction mechanism is integrated to estimate and mitigate predictive uncertainties, enhancing both the accuracy and reliability of long-term forecasts. Evaluations conducted on three benchmark datasets (plasma, fluid, and atmospheric dynamics) demonstrate the advantages of our approach over state-of-the-art ML methods.

FastMap was first introduced in the Data Mining community for generating Euclidean embeddings of complex objects. In this dissertation, we first present FastMap to generate Euclidean embeddings of graphs in near-linear time: The pairwise Euclidean distances approximate a desired graph-based distance function on the vertices. We then apply the graph version of FastMap to efficiently solve various graph-theoretic problems of significant interest in AI: including facility location, top-K centrality computations, community detection and block modeling, and graph convex hull computations. We also present a novel learning framework, called FastMapSVM, by combining FastMap and Support Vector Machines. We then apply FastMapSVM to predict the satisfiability of Constraint Satisfaction Problems and to classify seismograms in Earthquake Science.

A timely and effective response is crucial to minimize damage and save lives during natural disasters like earthquakes. Microblogging platforms, particularly Twitter, have emerged as valuable real-time information sources for such events. This work explores the potential of leveraging Twitter data for earthquake response analysis. We develop a machine learning (ML) framework by incorporating natural language processing (NLP) techniques to extract and analyze relevant information from tweets posted during earthquake events. The approach primarily focuses on extracting location data from tweets to identify affected areas, generating severity maps, and utilizing WebGIS to display valuable information. The insights gained from this analysis can aid emergency responders, government agencies, humanitarian organizations, and NGOs in enhancing their disaster response strategies and facilitating more efficient resource allocation during earthquake events.

Solving partial differential equations (PDEs) with discontinuous solutions , such as shock waves in multiphase viscous flow in porous media , is critical for a wide range of scientific and engineering applications, as they represent sudden changes in physical quantities. Physics-Informed Neural Networks (PINNs), an approach proposed for solving PDEs, encounter significant challenges when applied to such systems. Accurately solving PDEs with discontinuities using PINNs requires specialized techniques to ensure effective solution accuracy and numerical stability. A benchmarking study was conducted on two multiphase flow problems in porous media: the classic Buckley-Leverett (BL) problem and a fully coupled system of equations involving shock waves but with varying levels of solution complexity. The findings show that PM and LM approaches can provide accurate solutions for the BL problem by effectively addressing the infinite gradients associated with shock occurrences. In contrast, AM methods failed to effectively resolve the shock waves. When applied to fully coupled PDEs (with more complex loss landscape), the generalization error in the solutions quickly increased, highlighting the need for ongoing innovation. This study provides a comprehensive review of existing techniques for managing PDE discontinuities using PINNs, offering information on their strengths and limitations. The results underscore the necessity for further research to improve PINNs ability to handle complex discontinuities, particularly in more challenging problems with complex loss landscapes. This includes problems involving higher dimensions or multiphysics systems, where current methods often struggle to maintain accuracy and efficiency.

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.