Discovering Dynamic Patterns from Spatiotemporal Data with Time-Varying Low-Rank Autoregression

• URL: http://arxiv.org/abs/2211.15482v1
• Date: Mon, 28 Nov 2022 15:59:52 GMT
• Title: Discovering Dynamic Patterns from Spatiotemporal Data with Time-Varying Low-Rank Autoregression
• Authors: Xinyu Chen and Chengyuan Zhang and Xiaoxu Chen and Nicolas Saunier and Lijun Sun
• Abstract summary: We develop a time-reduced-rank vector autoregression model whose coefficient are parameterized by low-rank tensor factorization. In the temporal context, the complex time-varying system behaviors can be revealed by the temporal modes in the proposed model.
• Score: 12.923271427789267
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The problem of broad practical interest in spatiotemporal data analysis, i.e., discovering interpretable dynamic patterns from spatiotemporal data, is studied in this paper. Towards this end, we develop a time-varying reduced-rank vector autoregression (VAR) model whose coefficient matrices are parameterized by low-rank tensor factorization. Benefiting from the tensor factorization structure, the proposed model can simultaneously achieve model compression and pattern discovery. In particular, the proposed model allows one to characterize nonstationarity and time-varying system behaviors underlying spatiotemporal data. To evaluate the proposed model, extensive experiments are conducted on various spatiotemporal data representing different nonlinear dynamical systems, including fluid dynamics, sea surface temperature, USA surface temperature, and NYC taxi trips. Experimental results demonstrate the effectiveness of modeling spatiotemporal data and characterizing spatial/temporal patterns with the proposed model. In the spatial context, the spatial patterns can be automatically extracted and intuitively characterized by the spatial modes. In the temporal context, the complex time-varying system behaviors can be revealed by the temporal modes in the proposed model. Thus, our model lays an insightful foundation for understanding complex spatiotemporal data in real-world dynamical systems. The adapted datasets and Python implementation are publicly available at https://github.com/xinychen/vars.

Related papers

• Modeling Randomly Observed Spatiotemporal Dynamical Systems [7.381752536547389]
  Currently available neural network-based modeling approaches fall short when faced with data collected randomly over time and space. In response, we developed a new method that effectively handles such randomly sampled data. Our model integrates techniques from amortized variational inference, neural differential equations, neural point processes, and implicit neural representations to predict both the dynamics of the system and the timings and locations of future observations.
  arXiv  Detail & Related papers  (2024-06-01T09:03:32Z)
• OpenSTL: A Comprehensive Benchmark of Spatio-Temporal Predictive Learning [67.07363529640784]
  We propose OpenSTL to categorize prevalent approaches into recurrent-based and recurrent-free models. We conduct standard evaluations on datasets across various domains, including synthetic moving object trajectory, human motion, driving scenes, traffic flow and forecasting weather. We find that recurrent-free models achieve a good balance between efficiency and performance than recurrent models.
  arXiv  Detail & Related papers  (2023-06-20T03:02:14Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Neural Superstatistics for Bayesian Estimation of Dynamic Cognitive Models [2.7391842773173334]
  We develop a simulation-based deep learning method for Bayesian inference, which can recover both time-varying and time-invariant parameters. Our results show that the deep learning approach is very efficient in capturing the temporal dynamics of the model.
  arXiv  Detail & Related papers  (2022-11-23T17:42:53Z)
• Data-driven low-dimensional dynamic model of Kolmogorov flow [0.0]
  Reduced order models (ROMs) that capture flow dynamics are of interest for decreasing computational costs for simulation. This work presents a data-driven framework for minimal-dimensional models that effectively capture the dynamics and properties of the flow. We apply this to Kolmogorov flow in a regime consisting of chaotic and intermittent behavior.
  arXiv  Detail & Related papers  (2022-10-29T23:05:39Z)
• Capturing Actionable Dynamics with Structured Latent Ordinary Differential Equations [68.62843292346813]
  We propose a structured latent ODE model that captures system input variations within its latent representation. Building on a static variable specification, our model learns factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space.
  arXiv  Detail & Related papers  (2022-02-25T20:00:56Z)
• Closed-form Continuous-Depth Models [99.40335716948101]
  Continuous-depth neural models rely on advanced numerical differential equation solvers. We present a new family of models, termed Closed-form Continuous-depth (CfC) networks, that are simple to describe and at least one order of magnitude faster.
  arXiv  Detail & Related papers  (2021-06-25T22:08:51Z)
• Deep Convolution for Irregularly Sampled Temporal Point Clouds [39.51507835155255]
  We consider the problem of modeling the dynamics of continuous spatial-temporal processes represented by irregular samples through both space and time. We propose a new deep model that is able to directly learn and predict over this irregularly sampled data, without voxelization. We present experiments on real-world weather station data and battles between large armies in StarCraft II.
  arXiv  Detail & Related papers  (2021-05-01T00:54:32Z)
• Dynamic Mode Decomposition in Adaptive Mesh Refinement and Coarsening Simulations [58.720142291102135]
  Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract coherent schemes. This paper proposes a strategy to enable DMD to extract from observations with different mesh topologies and dimensions.
  arXiv  Detail & Related papers  (2021-04-28T22:14:25Z)
• Anomaly Detection of Time Series with Smoothness-Inducing Sequential Variational Auto-Encoder [59.69303945834122]
  We present a Smoothness-Inducing Sequential Variational Auto-Encoder (SISVAE) model for robust estimation and anomaly detection of time series. Our model parameterizes mean and variance for each time-stamp with flexible neural networks. We show the effectiveness of our model on both synthetic datasets and public real-world benchmarks.
  arXiv  Detail & Related papers  (2021-02-02T06:15:15Z)
• Spatio-Temporal Functional Neural Networks [11.73856529960872]
  We propose two novel extensions of the Neural Functional Network (FNN), a temporal regression model whose effectiveness has been proven by many researchers. The proposed models are then deployed to solve a practical and challenging precipitation prediction problem in the meteorology field.
  arXiv  Detail & Related papers  (2020-09-11T21:32:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.