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Register a new userEffects of boundary conditions in fully convolutional networks for learning spatio-temporal dynamics
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Accurate modeling of boundary conditions is crucial in computational physics. The ever increasing use of neural networks as surrogates for physics-related problems calls for an improved understanding of boundary condition treatment, and its influence on the network accuracy. In this paper, several strategies to impose boundary conditions (namely padding, improved spatial context, and explicit encoding of physical boundaries) are investigated in the context of fully convolutional networks applied to recurrent tasks. These strategies are evaluated on two spatio-temporal evolving problems modeled by partial differential equations: the 2D propagation of acoustic waves (hyperbolic PDE) and the heat equation (parabolic PDE). Results reveal a high sensitivity of both accuracy and stability on the boundary implementation in such recurrent tasks. It is then demonstrated that the choice of the optimal padding strategy is directly linked to the data semantics. Furthermore, the inclusion of additional input spatial context or explicit physics-based rules allows a better handling of boundaries in particular for large number of recurrences, resulting in more robust and stable neural networks, while facilitating the design and versatility of such networks.
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Telecommunication networks play a critical role in modern society. With the arrival of 5G networks, these systems are becoming even more diversified, integrated, and intelligent. Traffic forecasting is one of the key components in such a system, however, it is particularly challenging due to the complex spatial-temporal dependency. In this work, we consider this problem from the aspect of a cellular network and the interactions among its base stations. We thoroughly investigate the characteristics of cellular network traffic and shed light on the dependency complexities based on data collected from a densely populated metropolis area. Specifically, we observe that the traffic shows both dynamic and static spatial dependencies as well as diverse cyclic temporal patterns. To address these complexities, we propose an effective deep-learning-based approach, namely, Spatio-Temporal Hybrid Graph Convolutional Network (STHGCN). It employs GRUs to model the temporal dependency, while capturing the complex spatial dependency through a hybrid-GCN from three perspectives: spatial proximity, functional similarity, and recent trend similarity. We conduct extensive experiments on real-world traffic datasets collected from telecommunication networks. Our experimental results demonstrate the superiority of the proposed model in that it consistently outperforms both classical methods and state-of-the-art deep learning models, while being more robust and stable.
We present a new nonlinear mode decomposition method to visualize the decomposed flow fields, named the mode decomposing convolutional neural network autoencoder (MD-CNN-AE). The proposed method is applied to a flow around a circular cylinder at $Re_D=100$ as a test case. The flow attributes are mapped into two modes in the latent space and then these two modes are visualized in the physical space. Because the MD-CNN-AEs with nonlinear activation functions show lower reconstruction errors than the proper orthogonal decomposition (POD), the nonlinearity contained in the activation function is considered the key to improve the capability of the model. It is found by applying POD to each field decomposed using the MD-CNN-AE with hyperbolic tangent activation that a single nonlinear MD-CNN-AE mode contains multiple orthogonal bases, in contrast to the linear methods, i.e., POD and the MD-CNN-AE with linear activation. We further assess the proposed MD-CNN-AE by applying it to a transient process of a circular cylinder wake in order to examine its capability for flows containing high-order spatial modes. The present results suggest a great potential for the nonlinear MD-CNN-AE to be used for feature extraction of flow fields in lower dimension than POD, while retaining interpretable relationships with the conventional POD modes.
Ocean current, fluid mechanics, and many other spatio-temporal physical dynamical systems are essential components of the universe. One key characteristic of such systems is that certain physics laws -- represented as ordinary/partial differential equations (ODEs/PDEs) -- largely dominate the whole process, irrespective of time or location. Physics-informed learning has recently emerged to learn physics for accurate prediction, but they often lack a mechanism to leverage localized spatial and temporal correlation or rely on hard-coded physics parameters. In this paper, we advocate a physics-coupled neural network model to learn parameters governing the physics of the system, and further couple the learned physics to assist the learning of recurring dynamics. A spatio-temporal physics-coupled neural network (ST-PCNN) model is proposed to achieve three goals: (1) learning the underlying physics parameters, (2) transition of local information between spatio-temporal regions, and (3) forecasting future values for the dynamical system. The physics-coupled learning ensures that the proposed model can be tremendously improved by using learned physics parameters, and can achieve good long-range forecasting (e.g., more than 30-steps). Experiments, using simulated and field-collected ocean current data, validate that ST-PCNN outperforms existing physics-informed models.
The objective of this study is to predict the near-future flooding status of road segments based on their own and adjacent road segments current status through the use of deep learning framework on fine-grained traffic data. Predictive flood monitoring for situational awareness of road network status plays a critical role to support crisis response activities such as evaluation of the loss of access to hospitals and shelters. Existing studies related to near-future prediction of road network flooding status at road segment level are missing. Using fine-grained traffic speed data related to road sections, this study designed and implemented three spatio-temporal graph convolutional network (STGCN) models to predict road network status during flood events at the road segment level in the context of the 2017 Hurricane Harvey in Harris County (Texas, USA). Model 1 consists of two spatio-temporal blocks considering the adjacency and distance between road segments, while Model 2 contains an additional elevation block to account for elevation difference between road segments. Model 3 includes three blocks for considering the adjacency and the product of distance and elevation difference between road segments. The analysis tested the STGCN models and evaluated their prediction performance. Our results indicated that Model 1 and Model 2 have reliable and accurate performance for predicting road network flooding status in near future (e.g., 2-4 hours) with model precision and recall values larger than 98% and 96%, respectively. With reliable road network status predictions in floods, the proposed model can benefit affected communities to avoid flooded roads and the emergency management agencies to implement evacuation and relief resource delivery plans.
Farm parcel delineation provides cadastral data that is important in developing and managing climate change policies. Specifically, farm parcel delineation informs applications in downstream governmental policies of land allocation, irrigation, fertilization, green-house gases (GHGs), etc. This data can also be useful for the agricultural insurance sector for assessing compensations following damages associated with extreme weather events - a growing trend related to climate change. Using satellite imaging can be a scalable and cost effective manner to perform the task of farm parcel delineation to collect this valuable data. In this paper, we break down this task using satellite imaging into two approaches: 1) Segmentation of parcel boundaries, and 2) Segmentation of parcel areas. We implemented variations of UNets, one of which takes into account temporal information, which achieved the best results on our dataset on farmland parcels in France in 2017.
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