Reconstruction of dynamical systems from data without time labels
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Abstract (arXiv)
In this paper, we study the method to reconstruct dynamical systems from data without time labels. Data without time labels appear in many applications, such as molecular dynamics, single-cell RNA sequencing etc. Reconstruction of dynamical system from time sequence data has been studied extensively. However, these methods do not apply if time labels are unknown. Without time labels, sequence data becomes distribution data. Based on this observation, we propose to treat the data as samples from a probability distribution and try to reconstruct the underlying dynamical system by minimizing the distribution loss, sliced Wasserstein distance more specifically. Extensive experiment results demonstrate the effectiveness of the proposed method.
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References · 11
- 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
- 2021Score-based Generative Modeling in Latent Spacecited by 634
- 2019Generalized Sliced Wasserstein Distancescited by 205
- 2020Physics-informed learning of governing equations from scarce datacited by 167
- 2020Weak SINDy For Partial Differential Equationscited by 154
- 2021Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and controlcited by 134
- 2020SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamicscited by 125
- 2022Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distancescited by 41
- 2023Energy-Based Sliced Wasserstein Distancecited by 39
- 2020Revealing hidden dynamics from time-series data by ODENetcited by 17
- 2021Learning quantum dynamics with latent neural ODEscited by 4
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