Improving this capability requires high-quality vision-language data, which is costly and labor-intensive to acquire.

Improving this capability requires high-quality vision-language data, which is costly and labor-intensive to acquire.

Traffic state estimation (TSE) fundamentally involves solving high-dimensional spatiotemporal partial differential equations (PDEs) governing traffic flow dynamics from limited, noisy measurements. While Physics-Informed Neural Networks (PINNs) enforce PDE constraints point-wise, this paper adopts a physics-informed deep operator network (PI-DeepONet) framework that reformulates TSE as an operator learning problem. Our approach trains a parameterized neural operator that maps sparse input data to the full spatiotemporal traffic state field, governed by the traffic flow conservation law. Crucially, unlike PINNs that enforce PDE constraints point-wise, PI-DeepONet integrates traffic flow conservation model and the fundamental diagram directly into the operator learning process, ensuring physical consistency while capturing congestion propagation, spatial correlations, and temporal evolution. Experiments on the NGSIM dataset demonstrate superior performance over state-of-the-art baselines. Further analysis reveals insights into optimal function generation strategies and branch network complexity. Additionally, the impact of input function generation methods and the number of functions on model performance is explored, highlighting the robustness and efficacy of proposed framework.

Neural networks have emerged as a powerful tool for modeling physical systems, offering the ability to learn complex representations from limited data while integrating foundational scientific knowledge. In particular, neuro-symbolic approaches that combine data-driven learning, the neuro, with symbolic equations and rules, the symbolic, address the tension between methods that are purely empirical, which risk straying from established physical principles, and traditional numerical solvers that demand complete geometric knowledge and can be prohibitively expensive for high-fidelity simulations. In this work, we present a novel neuro-symbolic framework for reconstructing and simulating elastic objects directly from sparse multi-view image sequences, without requiring explicit geometric information. Specifically, we integrate a neural radiance field (NeRF) for object reconstruction with physics-informed neural networks (PINN) that incorporate the governing partial differential equations of elasticity. In doing so, our method learns a spatiotemporal representation of deforming objects that leverages both image supervision and symbolic physical constraints. To handle complex boundary and initial conditions, which are traditionally confronted using finite element methods, boundary element methods, or sensor-based measurements, we employ an energy-constrained Physics-Informed Neural Network architecture. This design enhances both simulation accuracy and the explainability of results.

Global Fréchet functional regression has been recently addressed from time correlated bivariate curve data evaluated in a manifold (see Torres et al. 2025). For this type of curve data sets, the present paper solves the problem of local linear approximation of the Fréchet conditional mean in an extrinsic and intrinsic way. The extrinsic local linear Fréchet functional regression predictor is obtained in the time varying tangent space by projection into an orthornormal basis of the ambient Hilbert space. The conditions assumed ensure the existence and uniqueness of this predictor, and its computation via exponential and logarithmic maps. A weighted Fréchet mean approach is adopted in the computation of an intrinsic local linear Fréchet functional regression predictor. The asymptotic optimality of this intrinsic local approximation is also proved. The performance of the empirical version of both, extrinsic and intrinsic functional predictors, and of a Nadaraya-Watson type Fréchet curve predictor is illustrated in the simulation study undertaken. The finite-sample size properties are also tested in a real-data application via cross-validation. Specifically, functional prediction of the magnetic vector field from the time-varying geocentric latitude and longitude of the satellite NASA's MAGSAT spacecraft is addressed.

Existing model reduction techniques for high-dimensional models of conservative partial differential equations (PDEs) encounter computational bottlenecks when dealing with systems featuring non-polynomial nonlinearities. This work presents a nonlinear model reduction method that employs lifting variable transformations to derive structure-preserving quadratic reduced-order models for conservative PDEs with general nonlinearities. We present an energy-quadratization strategy that defines the auxiliary variable in terms of the nonlinear term in the energy expression to derive an equivalent quadratic lifted system with quadratic system energy. The proposed strategy combined with proper orthogonal decomposition model reduction yields quadratic reduced-order models that conserve the quadratized lifted energy exactly in high dimensions. We demonstrate the proposed model reduction approach on four nonlinear conservative PDEs: the one-dimensional wave equation with exponential nonlinearity, the two-dimensional sine-Gordon equation, the two-dimensional Klein-Gordon equation with parametric dependence, and the two-dimensional Klein-Gordon-Zakharov equations. The numerical results show that the proposed lifting approach is competitive with the state-of-the-art structure-preserving hyper-reduction method in terms of both accuracy and computational efficiency in the online stage while providing significant computational gains in the offline stage.

Camouflaged Object Detection (COD) aims to identify objects that blend seamlessly into their surroundings. The inherent visual complexity of camouflaged objects, including their low contrast with the background, diverse textures, and subtle appearance variations, often obscures semantic cues, making accurate segmentation highly challenging. Existing methods primarily rely on visual features, which are insufficient to handle the variability and intricacy of camouflaged objects, leading to unstable object perception and ambiguous segmentation results. To tackle these limitations, we introduce a novel task, class-guided camouflaged object detection (CGCOD), which extends traditional COD task by incorporating object-specific class knowledge to enhance detection robustness and accuracy. To facilitate this task, we present a new dataset, CamoClass, comprising real-world camouflaged objects with class annotations. Furthermore, we propose a multi-stage framework, CGNet, which incorporates a plug-and-play class prompt generator and a simple yet effective class-guided detector. This establishes a new paradigm for COD, bridging the gap between contextual understanding and class-guided detection. Extensive experimental results demonstrate the effectiveness of our flexible framework in improving the performance of proposed and existing detectors by leveraging class-level textual information.

Camouflaged Object Detection (COD) refers to the task of identifying and segmenting objects that blend seamlessly into their surroundings, posing a significant challenge for computer vision systems. In recent years, COD has garnered widespread attention due to its potential applications in surveillance, wildlife conservation, autonomous systems, and more. While several surveys on COD exist, they often have limitations in terms of the number and scope of papers covered, particularly regarding the rapid advancements made in the field since mid-2023. To address this void, we present the most comprehensive review of COD to date, encompassing both theoretical frameworks and practical contributions to the field. This paper explores various COD methods across four domains, including both image-level and video-level solutions, from the perspectives of traditional and deep learning approaches. We thoroughly investigate the correlations between COD and other camouflaged scenario methods, thereby laying the theoretical foundation for subsequent analyses. Beyond object-level detection, we also summarize extended methods for instance-level tasks, including camouflaged instance segmentation, counting, and ranking. Additionally, we provide an overview of commonly used benchmarks and evaluation metrics in COD tasks, conducting a comprehensive evaluation of deep learning-based techniques in both image and video domains, considering both qualitative and quantitative performance. Finally, we discuss the limitations of current COD models and propose 9 promising directions for future research, focusing on addressing inherent challenges and exploring novel, meaningful technologies. For those interested, a curated list of COD-related techniques, datasets, and additional resources can be found at https://github.com/ChunmingHe/awesome-concealed-object-segmentation

We introduce GreenCOD, a green method for detecting camouflaged objects, distinct in its avoidance of backpropagation techniques. GreenCOD leverages gradient boosting and deep features extracted from pre-trained Deep Neural Networks (DNNs). Traditional camouflaged object detection (COD) approaches often rely on complex deep neural network architectures, seeking performance improvements through backpropagation-based fine-tuning. However, such methods are typically computationally demanding and exhibit only marginal performance variations across different models. This raises the question of whether effective training can be achieved without backpropagation. Addressing this, our work proposes a new paradigm that utilizes gradient boosting for COD. This approach significantly simplifies the model design, resulting in a system that requires fewer parameters and operations and maintains high performance compared to state-of-the-art deep learning models. Remarkably, our models are trained without backpropagation and achieve the best performance with fewer than 20G Multiply-Accumulate Operations (MACs). This new, more efficient paradigm opens avenues for further exploration in green, backpropagation-free model training.

Seismic imaging is the numerical process of creating a volumetric representation of the subsurface geological structures from elastic waves recorded at the surface of the Earth. As such, it is widely utilized in the energy and construction sectors for applications ranging from oil and gas prospection, to geothermal production and carbon capture and storage monitoring, to geotechnical assessment of infrastructures. Extracting quantitative information from seismic recordings, such as an acoustic impedance model, is however a highly ill-posed inverse problem, due to the band-limited and noisy nature of the data. This paper introduces IntraSeismic, a novel hybrid seismic inversion method that seamlessly combines coordinate-based learning with the physics of the post-stack modeling operator. Key features of IntraSeismic are i) unparalleled performance in 2D and 3D post-stack seismic inversion, ii) rapid convergence rates, iii) ability to seamlessly include hard constraints (i.e., well data) and perform uncertainty quantification, and iv) potential data compression and fast randomized access to portions of the inverted model. Synthetic and field data applications of IntraSeismic are presented to validate the effectiveness of the proposed method.