Double projection for reconstructing dynamical systems: between stochastic and deterministic regimes
Not on the map. Why?
Abstract (arXiv)
Learning stochastic models of dynamical systems from observed data is of interest in many scientific fields. Here, we propose a new method for this task within the family of dynamical variational autoencoders. The proposed double projection method estimates both the system state trajectories and the noise time series from data. This approach naturally allows us to perform multi-step system evolution and to learn models with a comparatively low-dimensional state space. We evaluate the performance of the method on six benchmark problems, including both simulated and experimental data. We further illustrate the effects of the teacher forcing interval of the multi-step scheme on the nature of the internal dynamics and compare the resulting behavior to that of deterministic models of equivalent architecture.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 28 of its 57 references that are in the map. First posted on arXiv 1 Oct 2025.
Builds on
28 of 57 references.
References · 28
- 2018Neural Ordinary Differential Equationscited by 3,733
- 2016WaveNet: A Generative Model for Raw Audiocited by 1,710
- 2014On the Properties of Neural Machine Translation: Encoder-Decoder Approachescited by 1,303
- 2018Learning Latent Dynamics for Planning from Pixelscited by 1,221
- 2015Scheduled Sampling for Sequence Prediction with Recurrent Neural Networkscited by 779
- 2013Generating Sequences With Recurrent Neural Networkscited by 549
- 2015A Recurrent Latent Variable Model for Sequential Datacited by 362
- 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecastingcited by 332
- 2016Structured Inference Networks for Nonlinear State Space Modelscited by 182
- 2015Deep Kalman Filterscited by 163
- 2020Dynamical Variational Autoencoders: A Comprehensive Reviewcited by 127
- 2017Variational Sequential Monte Carlocited by 93
16 more
- 2021Chaos as an interpretable benchmark for forecasting and data-driven modellingcited by 87
- 2018Probabilistic Recurrent State-Space Modelscited by 64
- 2021On the difficulty of learning chaotic dynamics with RNNscited by 64
- 2014Learning Stochastic Recurrent Networkscited by 60
- 2023Generalized Teacher Forcing for Learning Chaotic Dynamicscited by 55
- 2019Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRIcited by 39
- 2020Hierarchical Deep Learning of Multiscale Differential Equation Time-Stepperscited by 37
- 2021Constructing Neural Network-Based Models for Simulating Dynamical Systemscited by 29
- 2021Reconstructing Nonlinear Dynamical Systems from Multi-Modal Time Seriescited by 16
- 2024Inferring stochastic low-rank recurrent neural networks from neural datacited by 15
- 2018Learning Awareness Modelscited by 13
- 2021Reservoir Computing with Diverse Timescales for Prediction of Multiscale Dynamicscited by 13
- 2022Integrating Multimodal Data for Joint Generative Modeling of Complex Dynamicscited by 13
- 2020Sparse Identification of Slow Timescale Dynamicscited by 10
- 2020Stochastic embeddings of dynamical phenomena through variational autoencoderscited by 3
- 2024RefreshNet: Learning Multiscale Dynamics through Hierarchical Refreshingcited by 2
Built on by
Citing papers per year: 2026: 1.
1 paper.