mlsanityData to 7 Oct 2026

Modeling unknown dynamical systems with hidden parameters

arXiv 2202.01858 ↗First posted 3 Feb 2022stat.ML cs.LGcited by 4

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Abstract (arXiv)

We present a data-driven numerical approach for modeling unknown dynamical systems with missing/hidden parameters. The method is based on training a deep neural network (DNN) model for the unknown system using its trajectory data. A key feature is that the unknown dynamical system contains system parameters that are completely hidden, in the sense that no information about the parameters is available through either the measurement trajectory data or our prior knowledge of the system. We demonstrate that by training a DNN using the trajectory data with sufficient time history, the resulting DNN model can accurately model the unknown dynamical system. For new initial conditions associated with new, and unknown, system parameters, the DNN model can produce accurate system predictions over longer time.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 16 of its 26 references that are in the map. First posted on arXiv 3 Feb 2022.

Builds on

16 of 26 references.

References · 16

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4 more
  1. 2020Learning reduced systems via deep neural networks with memorycited by 20
  2. 2019Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Datacited by 18
  3. 2020On generalized residue network for deep learning of unknown dynamical systemscited by 16
  4. 2020Data-driven learning of non-autonomous systemscited by 7

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Cited by year

Citing papers per year: 2023: 2; 2024: 0; 2025: 2.

4 papers.

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  2. 2025DUE: A Deep Learning Framework and Library for Modeling Unknown Equationscited by 8
  3. 2023InVAErt networks: a data-driven framework for model synthesis and identifiability analysiscited by 6
  4. 2025Targeted Digital Twin via Flow Map Learning and Its Application to Fluid Dynamicscited by 5