Implicit Neural Spatial Representation (INSR) has emerged as an effective representation of spatially-dependent vector fields. This work explores solving time-dependent PDEs with INSR. Classical PDE solvers introduce both temporal and spatial discretizations. Common spatial discretizations include meshes and meshless point clouds, where each degree-of-freedom corresponds to a location in space. While these explicit spatial correspondences are intuitive to model and understand, these representations are not necessarily optimal for accuracy, memory usage, or adaptivity. Keeping the classical temporal discretization unchanged (e.g., explicit/implicit Euler), we explore INSR as an alternative spatial discretization, where spatial information is implicitly stored in the neural network weights. The network weights then evolve over time via time integration. Our approach does not require any training data generated by existing solvers because our approach is the solver itself. We validate our approach on various PDEs with examples involving large elastic deformations, turbulent fluids, and multi-scale phenomena. While slower to compute than traditional representations, our approach exhibits higher accuracy and lower memory consumption. Whereas classical solvers can dynamically adapt their spatial representation only by resorting to complex remeshing algorithms, our INSR approach is intrinsically adaptive. By tapping into the rich literature of classic time integrators, e.g., operator-splitting schemes, our method enables challenging simulations in contact mechanics and turbulent flows where previous neural-physics approaches struggle. Videos and codes are available on the project page: http://www.cs.columbia.edu/cg/INSR-PDE/

Wind power is attracting increasing attention around the world due to its renewable, pollution-free, and other advantages. However, safely and stably integrating the high permeability intermittent power energy into electric power systems remains challenging. Accurate wind power forecasting (WPF) can effectively reduce power fluctuations in power system operations. Existing methods are mainly designed for short-term predictions and lack effective spatial-temporal feature augmentation. In this work, we propose a novel end-to-end wind power forecasting model named Hierarchical Spatial-Temporal Transformer Network (HSTTN) to address the long-term WPF problems. Specifically, we construct an hourglass-shaped encoder-decoder framework with skip-connections to jointly model representations aggregated in hierarchical temporal scales, which benefits long-term forecasting. Based on this framework, we capture the inter-scale long-range temporal dependencies and global spatial correlations with two parallel Transformer skeletons and strengthen the intra-scale connections with downsampling and upsampling operations. Moreover, the complementary information from spatial and temporal features is fused and propagated in each other via Contextual Fusion Blocks (CFBs) to promote the prediction further. Extensive experimental results on two large-scale real-world datasets demonstrate the superior performance of our HSTTN over existing solutions.

Effective use of camera-based vision systems is essential for robust performance in autonomous off-road driving, particularly in the high-speed regime. Despite success in structured, on-road settings, current end-to-end approaches for scene prediction have yet to be successfully adapted for complex outdoor terrain. To this end, we present TerrainNet, a vision-based terrain perception system for semantic and geometric terrain prediction for aggressive, off-road navigation. The approach relies on several key insights and practical considerations for achieving reliable terrain modeling. The network includes a multi-headed output representation to capture fine- and coarse-grained terrain features necessary for estimating traversability. Accurate depth estimation is achieved using self-supervised depth completion with multi-view RGB and stereo inputs. Requirements for real-time performance and fast inference speeds are met using efficient, learned image feature projections. Furthermore, the model is trained on a large-scale, real-world off-road dataset collected across a variety of diverse outdoor environments. We show how TerrainNet can also be used for costmap prediction and provide a detailed framework for integration into a planning module. We demonstrate the performance of TerrainNet through extensive comparison to current state-of-the-art baselines for camera-only scene prediction. Finally, we showcase the effectiveness of integrating TerrainNet within a complete autonomous-driving stack by conducting a real-world vehicle test in a challenging off-road scenario.

In the era of big data, there has been a surge in the availability of data containing rich spatial and temporal information, offering valuable insights into dynamic systems and processes for applications such as weather forecasting, natural disaster management, intelligent transport systems, and precision agriculture. Graph neural networks (GNNs) have emerged as a powerful tool for modeling and understanding data with dependencies to each other such as spatial and temporal dependencies. There is a large amount of existing work that focuses on addressing the complex spatial and temporal dependencies in spatiotemporal data using GNNs. However, the strong interdisciplinary nature of spatiotemporal data has created numerous GNNs variants specifically designed for distinct application domains. Although the techniques are generally applicable across various domains, cross-referencing these methods remains essential yet challenging due to the absence of a comprehensive literature review on GNNs for spatiotemporal data. This article aims to provide a systematic and comprehensive overview of the technologies and applications of GNNs in the spatiotemporal domain. First, the ways of constructing graphs from spatiotemporal data are summarized to help domain experts understand how to generate graphs from various types of spatiotemporal data. Then, a systematic categorization and summary of existing spatiotemporal GNNs are presented to enable domain experts to identify suitable techniques and to support model developers in advancing their research. Moreover, a comprehensive overview of significant applications in the spatiotemporal domain is offered to introduce a broader range of applications to model developers and domain experts, assisting them in exploring potential research topics and enhancing the impact of their work. Finally, open challenges and future directions are discussed.

Navigating to destinations using human speech instructions is essential for autonomous mobile robots operating in the real world. Although robots can take different paths toward the same goal, the shortest path is not always optimal. A desired approach is to flexibly accommodate waypoint specifications, planning a better alternative path, even with detours. Furthermore, robots require real-time inference capabilities. Spatial representations include semantic, topological, and metric levels, each capturing different aspects of the environment. This study aims to realize a hierarchical spatial representation by a topometric semantic map and path planning with speech instructions, including waypoints. We propose SpCoTMHP, a hierarchical path-planning method that utilizes multimodal spatial concepts, incorporating place connectivity. This approach provides a novel integrated probabilistic generative model and fast approximate inference, with interaction among the hierarchy levels. A formulation based on control as probabilistic inference theoretically supports the proposed path planning. Navigation experiments using speech instruction with a waypoint demonstrated the performance improvement of path planning, WN-SPL by 0.589, and reduced computation time by 7.14 sec compared to conventional methods. Hierarchical spatial representations offer a mutually understandable form for humans and robots, enabling language-based navigation tasks.

Multivariate time-series (MTS) forecasting is a paramount and fundamental problem in many real-world applications. The core issue in MTS forecasting is how to effectively model complex spatial-temporal patterns. In this paper, we develop a modular and interpretable forecasting framework, which seeks to individually model each component of the spatial-temporal patterns. We name this framework SCNN, short for Structured Component-based Neural Network. SCNN works with a pre-defined generative process of MTS, which arithmetically characterizes the latent structure of the spatial-temporal patterns. In line with its reverse process, SCNN decouples MTS data into structured and heterogeneous components and then respectively extrapolates the evolution of these components, the dynamics of which is more traceable and predictable than the original MTS. Extensive experiments are conducted to demonstrate that SCNN can achieve superior performance over state-of-the-art models on three real-world datasets. Additionally, we examine SCNN with different configurations and perform in-depth analyses of the properties of SCNN.

FLAIR: French Land cover from Aerospace ImageRy. Soils play a vital role in providing a range of ecosystem services. Building upon this datset, the FLAIR #2 dataset According to a report by the Food and Agriculture extends the capabilities by incorporating a new input modality, Organization of the United Nations (FAO) in 2015 [1], namely Sentinel-2 satellite image time series, and introduces a a significant portion of the world's soil resources are in a new test dataset Both FLAIR #1 and #2 datasets are part of the condition that can be classified as fair, poor, or very poor. This currently explored or exploited resources by IGN to produce degradation of soils, coupled with the loss of biodiversity, has the French national land cover map reference Occupation du far-reaching implications for the state of ecosystems and their sol à grande échelle (OCS-GE). Remote sensing data have several main characteristics that are of crucial importance depending on the intended purpose. Spatial, temporal and spectral resolutions will influence the choice of data and their importance in a process.

Federated weather forecasting is a promising collaborative learning framework for analyzing meteorological data across participants from different countries and regions, thus embodying a global-scale real-time weather data predictive analytics platform to tackle climate change. This paper is to model the meteorological data in a federated setting where many distributed low-resourced sensors are deployed in different locations. Specifically, we model the spatial-temporal weather data into a federated prompt learning framework that leverages lightweight prompts to share meaningful representation and structural knowledge among participants. Prompts-based communication allows the server to establish the structural topology relationships among participants and further explore the complex spatial-temporal correlations without transmitting private data while mitigating communication overhead. Moreover, in addition to a globally shared large model at the server, our proposed method enables each participant to acquire a personalized model that is highly customized to tackle climate changes in a specific geographic area. We have demonstrated the effectiveness of our method on classical weather forecasting tasks by utilizing three spatial-temporal multivariate time-series weather data.

Although large-scale video-language pre-training models, which usually build a global alignment between the video and the text, have achieved remarkable progress on various downstream tasks, the idea of adopting fine-grained information during the pre-training stage is not well explored. In this work, we propose STOA-VLP, a pre-training framework that jointly models object and action information across spatial and temporal dimensions. More specifically, the model regards object trajectories across frames and multiple action features from the video as fine-grained features. Besides, We design two auxiliary tasks to better incorporate both kinds of information into the pre-training process of the video-language model. The first is the dynamic object-text alignment task, which builds a better connection between object trajectories and the relevant noun tokens. The second is the spatial-temporal action set prediction, which guides the model to generate consistent action features by predicting actions found in the text. Extensive experiments on three downstream tasks (video captioning, text-video retrieval, and video question answering) demonstrate the effectiveness of our proposed STOA-VLP (e.g. 3.7 Rouge-L improvements on MSR-VTT video captioning benchmark, 2.9% accuracy improvements on MSVD video question answering benchmark, compared to previous approaches).

As the field of deep learning steadily transitions from the realm of academic research to practical application, the significance of self-supervised pretraining methods has become increasingly prominent. These methods, particularly in the image domain, offer a compelling strategy to effectively utilize the abundance of unlabeled image data, thereby enhancing downstream tasks' performance. In this paper, we propose a novel auxiliary pretraining method that is based on spatial reasoning. Our proposed method takes advantage of a more flexible formulation of contrastive learning by introducing spatial reasoning as an auxiliary task for discriminative self-supervised methods. Spatial Reasoning works by having the network predict the relative distances between sampled non-overlapping patches. We argue that this forces the network to learn more detailed and intricate internal representations of the objects and the relationships between their constituting parts. Our experiments demonstrate substantial improvement in downstream performance in linear evaluation compared to similar work and provide directions for further research into spatial reasoning.