mlsanityData to 14 Oct 2026

A Model-Constrained Tangent Slope Learning Approach for Dynamical Systems

arXiv 2208.04995 ↗First posted 9 Aug 2022cs.LG math.DS physics.flu-dyncited by 3

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Abstract (arXiv)

Real-time accurate solutions of large-scale complex dynamical systems are in critical need for control, optimization, uncertainty quantification, and decision-making in practical engineering and science applications, especially digital twin applications. This paper contributes in this direction a model-constrained tangent slope learning (mcTangent) approach. At the heart of mcTangent is the synergy of several desirable strategies: i) a tangent slope learning to take advantage of the neural network speed and the time-accurate nature of the method of lines; ii) a model-constrained approach to encode the neural network tangent slope with the underlying governing equations; iii) sequential learning strategies to promote long-time stability and accuracy; and iv) data randomization approach to implicitly enforce the smoothness of the neural network tangent slope and its likeliness to the truth tangent slope up second order derivatives in order to further enhance the stability and accuracy of mcTangent solutions. Rigorous results are provided to analyze and justify the proposed approach. Several numerical results for the transport equation, viscous Burgers equation, and Navier-Stokes equation are presented to study and demonstrate the robustness and long-time accuracy of the proposed mcTangent learning approach.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 29 of its 59 references that are in the map. First posted on arXiv 9 Aug 2022.

Builds on

29 of 59 references.

References · 29

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 1; 2026: 1.

3 papers.

  1. 2024TAEN: A Model-Constrained Tikhonov Autoencoder Network for Forward and Inverse Problemscited by 3
  2. 2025LiLaN: A Linear Latent Network as the Solution Operator for Real-Time Solutions to Stiff Nonlinear Ordinary Differential Equationscited by 0
  3. 2026Second-order consistency for learning chaotic dynamics via randomized Jacobian matchingcited by 0