Learning Continuous-Time Dynamics by Stochastic Differential Networks

• URL: http://arxiv.org/abs/2006.06145v3
• Date: Thu, 29 Apr 2021 14:32:21 GMT
• Title: Learning Continuous-Time Dynamics by Stochastic Differential Networks
• Authors: Yingru Liu, Yucheng Xing, Xuewen Yang, Xin Wang, Jing Shi, Di Jin, Zhaoyue Chen
• Abstract summary: We propose a flexible continuous-time recurrent neural network named Variational Differential Networks (VSDN) VSDN embeds the complicated dynamics of the sporadic time series by neural Differential Equations (SDE) We show that VSDNs outperform state-of-the-art continuous-time deep learning models and achieve remarkable performance on prediction and tasks for sporadic time series.
• Score: 32.63114111531396
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Learning continuous-time stochastic dynamics is a fundamental and essential problem in modeling sporadic time series, whose observations are irregular and sparse in both time and dimension. For a given system whose latent states and observed data are high-dimensional, it is generally impossible to derive a precise continuous-time stochastic process to describe the system behaviors. To solve the above problem, we apply Variational Bayesian method and propose a flexible continuous-time stochastic recurrent neural network named Variational Stochastic Differential Networks (VSDN), which embeds the complicated dynamics of the sporadic time series by neural Stochastic Differential Equations (SDE). VSDNs capture the stochastic dependency among latent states and observations by deep neural networks. We also incorporate two differential Evidence Lower Bounds to efficiently train the models. Through comprehensive experiments, we show that VSDNs outperform state-of-the-art continuous-time deep learning models and achieve remarkable performance on prediction and interpolation tasks for sporadic time series.

Related papers

• Trajectory Flow Matching with Applications to Clinical Time Series Modeling [77.58277281319253]
  Trajectory Flow Matching (TFM) trains a Neural SDE in a simulation-free manner, bypassing backpropagation through the dynamics. We demonstrate improved performance on three clinical time series datasets in terms of absolute performance and uncertainty prediction.
  arXiv  Detail & Related papers  (2024-10-28T15:54:50Z)
• PDETime: Rethinking Long-Term Multivariate Time Series Forecasting from the perspective of partial differential equations [49.80959046861793]
  We present PDETime, a novel LMTF model inspired by the principles of Neural PDE solvers. Our experimentation across seven diversetemporal real-world LMTF datasets reveals that PDETime adapts effectively to the intrinsic nature of the data.
  arXiv  Detail & Related papers  (2024-02-25T17:39:44Z)
• Neural Continuous-Discrete State Space Models for Irregularly-Sampled Time Series [18.885471782270375]
  NCDSSM employs auxiliary variables to disentangle recognition from dynamics, thus requiring amortized inference only for the auxiliary variables. We propose three flexible parameterizations of the latent dynamics and an efficient training objective that marginalizes the dynamic states during inference. Empirical results on multiple benchmark datasets show improved imputation and forecasting performance of NCDSSM over existing models.
  arXiv  Detail & Related papers  (2023-01-26T18:45:04Z)
• Learning effective dynamics from data-driven stochastic systems [2.4578723416255754]
  This work is devoted to investigating the effective dynamics for slow-fast dynamical systems. We propose a novel algorithm including a neural network called Auto-SDE to learn in slow manifold.
  arXiv  Detail & Related papers  (2022-05-09T09:56:58Z)
• Time Series Forecasting with Ensembled Stochastic Differential Equations Driven by L\'evy Noise [2.3076895420652965]
  We use a collection of SDEs equipped with neural networks to predict long-term trend of noisy time series. Our contributions are, first, we use the phase space reconstruction method to extract intrinsic dimension of the time series data. Second, we explore SDEs driven by $alpha$-stable L'evy motion to model the time series data and solve the problem through neural network approximation.
  arXiv  Detail & Related papers  (2021-11-25T16:49:01Z)
• Consistency of mechanistic causal discovery in continuous-time using Neural ODEs [85.7910042199734]
  We consider causal discovery in continuous-time for the study of dynamical systems. We propose a causal discovery algorithm based on penalized Neural ODEs.
  arXiv  Detail & Related papers  (2021-05-06T08:48:02Z)
• Neural ODE Processes [64.10282200111983]
  We introduce Neural ODE Processes (NDPs), a new class of processes determined by a distribution over Neural ODEs. We show that our model can successfully capture the dynamics of low-dimensional systems from just a few data-points.
  arXiv  Detail & Related papers  (2021-03-23T09:32:06Z)
• Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems [65.44033635330604]
  We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system. We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony. Results are presented for a test case using load data from an electrical grid.
  arXiv  Detail & Related papers  (2020-10-08T20:25:52Z)
• Learning continuous-time PDEs from sparse data with graph neural networks [10.259254824702555]
  We propose a continuous-time differential model for dynamical systems whose governing equations are parameterized by message passing graph neural networks. We demonstrate the model's ability to work with unstructured grids, arbitrary time steps, and noisy observations. We compare our method with existing approaches on several well-known physical systems that involve first and higher-order PDEs with state-of-the-art predictive performance.
  arXiv  Detail & Related papers  (2020-06-16T07:15:40Z)
• Liquid Time-constant Networks [117.57116214802504]
  We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations.
  arXiv  Detail & Related papers  (2020-06-08T09:53:35Z)

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.