Learning Spatiotemporal Dynamical Systems from Point Process Observations

• URL: http://arxiv.org/abs/2406.00368v2
• Date: Sat, 08 Feb 2025 10:48:45 GMT
• Title: Learning Spatiotemporal Dynamical Systems from Point Process Observations
• Authors: Valerii Iakovlev, Harri Lähdesmäki,
• Abstract summary: Current neural network-based model approaches fall short when faced with data that is collected randomly over time and space. In response, we developed a new method that can effectively learn from such process observations. Our model integrates techniques from neural differential equations, neural point processes, implicit neural representations and amortized variational inference.
• Score: 7.381752536547389
• License:
• Abstract: Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when faced with data that is collected randomly over time and space, as is often the case with sensor networks in real-world applications like crowdsourced earthquake detection or pollution monitoring. In response, we developed a new method that can effectively learn spatiotemporal dynamics from such point process observations. Our model integrates techniques from neural differential equations, neural point processes, implicit neural representations and amortized variational inference to model both the dynamics of the system and the probabilistic locations and timings of observations. It outperforms existing methods on challenging spatiotemporal datasets by offering substantial improvements in predictive accuracy and computational efficiency, making it a useful tool for modeling and understanding complex dynamical systems observed under realistic, unconstrained conditions.

Related papers

• Conservation-informed Graph Learning for Spatiotemporal Dynamics Prediction [84.26340606752763]
  In this paper, we introduce the conservation-informed GNN (CiGNN), an end-to-end explainable learning framework. The network is designed to conform to the general symmetry conservation law via symmetry where conservative and non-conservative information passes over a multiscale space by a latent temporal marching strategy. Results demonstrate that CiGNN exhibits remarkable baseline accuracy and generalizability, and is readily applicable to learning for prediction of varioustemporal dynamics.
  arXiv  Detail & Related papers  (2024-12-30T13:55:59Z)
• Equivariant Graph Neural Operator for Modeling 3D Dynamics [148.98826858078556]
  We propose Equivariant Graph Neural Operator (EGNO) to directly models dynamics as trajectories instead of just next-step prediction. EGNO explicitly learns the temporal evolution of 3D dynamics where we formulate the dynamics as a function over time and learn neural operators to approximate it. Comprehensive experiments in multiple domains, including particle simulations, human motion capture, and molecular dynamics, demonstrate the significantly superior performance of EGNO against existing methods.
  arXiv  Detail & Related papers  (2024-01-19T21:50:32Z)
• Spatio-Temporal Branching for Motion Prediction using Motion Increments [55.68088298632865]
  Human motion prediction (HMP) has emerged as a popular research topic due to its diverse applications. Traditional methods rely on hand-crafted features and machine learning techniques. We propose a noveltemporal-temporal branching network using incremental information for HMP.
  arXiv  Detail & Related papers  (2023-08-02T12:04:28Z)
• 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)
• Discovering Dynamic Patterns from Spatiotemporal Data with Time-Varying Low-Rank Autoregression [12.923271427789267]
  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.
  arXiv  Detail & Related papers  (2022-11-28T15:59:52Z)
• Decomposed Linear Dynamical Systems (dLDS) for learning the latent components of neural dynamics [6.829711787905569]
  We propose a new decomposed dynamical system model that represents complex non-stationary and nonlinear dynamics of time series data. Our model is trained through a dictionary learning procedure, where we leverage recent results in tracking sparse vectors over time. In both continuous-time and discrete-time instructional examples we demonstrate that our model can well approximate the original system.
  arXiv  Detail & Related papers  (2022-06-07T02:25:38Z)
• Leveraging the structure of dynamical systems for data-driven modeling [111.45324708884813]
  We consider the impact of the training set and its structure on the quality of the long-term prediction. We show how an informed design of the training set, based on invariants of the system and the structure of the underlying attractor, significantly improves the resulting models.
  arXiv  Detail & Related papers  (2021-12-15T20:09:20Z)
• Constructing Neural Network-Based Models for Simulating Dynamical Systems [59.0861954179401]
  Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. This paper provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome.
  arXiv  Detail & Related papers  (2021-11-02T10:51:42Z)
• Physics-Coupled Spatio-Temporal Active Learning for Dynamical Systems [15.923190628643681]
  One of the major challenges is to infer the underlying causes, which generate the perceived data stream. Success of machine learning based predictive models requires massive annotated data for model training. Our experiments on both synthetic and real-world datasets exhibit that the proposed ST-PCNN with active learning converges to optimal accuracy with substantially fewer instances.
  arXiv  Detail & Related papers  (2021-08-11T18:05:55Z)
• Neural Spatio-Temporal Point Processes [31.474420819149724]
  We propose a new class of parameterizations for point-trivial processes which leverage Neural ODEs as a computational method. We validate our models on data sets from a wide variety of contexts such as seismology, epidemiology, urban mobility, and neuroscience.
  arXiv  Detail & Related papers  (2020-11-09T17:28:23Z)
• Learning Continuous System Dynamics from Irregularly-Sampled Partial Observations [33.63818978256567]
  We present LG-ODE, a latent ordinary differential equation generative model for modeling multi-agent dynamic system with known graph structure. It can simultaneously learn the embedding of high dimensional trajectories and infer continuous latent system dynamics. Our model employs a novel encoder parameterized by a graph neural network that can infer initial states in an unsupervised way.
  arXiv  Detail & Related papers  (2020-11-08T01:02:22Z)

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.