mlsanityData to 14 Oct 2026

tLaSDI: Thermodynamics-informed latent space dynamics identification

arXiv 2403.05848 ↗First posted 9 Mar 2024cs.LG math.DScited by 23

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Abstract (arXiv)

We propose a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The latent dynamics are constructed by a neural network-based model that precisely preserves certain structures for the thermodynamic laws through the GENERIC formalism. An abstract error estimate is established, which provides a new loss formulation involving the Jacobian computation of autoencoder. The autoencoder and the latent dynamics are simultaneously trained to minimize the new loss. Computational examples demonstrate the effectiveness of tLaSDI, which exhibits robust generalization ability, even in extrapolation. In addition, an intriguing correlation is empirically observed between a quantity from tLaSDI in the latent space and the behaviors of the full-state solution.

Key facts. Cited by 23 papers in the map (data through 14 Oct 2026). Builds on 19 of its 55 references that are in the map. First posted on arXiv 9 Mar 2024.

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19 of 55 references.

References · 19

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  12. 2022gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identificationcited by 30
7 more
  1. 2023GPLaSDI: Gaussian Process-based Interpretable Latent Space Dynamics Identification through Deep Autoencodercited by 30
  2. 2022Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutionscited by 29
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 4; 2025: 11; 2026: 8.

23 papers.

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  1. 2024A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modelingcited by 22
  2. 2024Physics-informed active learning with simultaneous weak-form latent space dynamics identificationcited by 13
  3. 2025Stable Port-Hamiltonian Neural Networkscited by 13
  4. 2025Thermodynamically Consistent Latent Dynamics Identification for Parametric Systemscited by 8
  5. 2024Learning Macroscopic Dynamics from Partial Microscopic Observationscited by 3
  6. 2025A Deep Learning approach for parametrized and time dependent Partial Differential Equations using Dimensionality Reduction and Neural ODEscited by 3
  7. 2025Latent Twinscited by 3
  8. 2025Identifiable learning of dissipative dynamicscited by 3
  9. 2025mLaSDI: Multi-stage latent space dynamics identificationcited by 2
  10. 2025Rollout-LaSDI: Enhancing the long-term accuracy of Latent Space Dynamicscited by 2
  11. 2025Differentiable Autoencoding Neural Operator for Interpretable and Integrable Latent Space Modelingcited by 2
  12. 2025Sequential decoder training for improved latent space dynamics identificationcited by 2
11 more
  1. 2025Higher-Order LaSDI: Reduced Order Modeling with Multiple Time Derivativescited by 2
  2. 2025Understanding the role of autoencoders for stiff dynamical systems using information theorycited by 1
  3. 2026Latent Space Element Methodcited by 1
  4. 2026NN-OpInf: an operator inference approach using structure-preserving composable neural networkscited by 1
  5. 2026Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentialscited by 1
  6. 2024Tracking control of latent dynamic systems with application to spacecraft attitude controlcited by 0
  7. 2026Systematic Performance Assessment of Deep Material Networks for Multiscale Material Modelingcited by 0
  8. 2026WGFINNs: Weak formulation-based GENERIC formalism informed neural networkscited by 0
  9. 2026Time-Dependent PDE-Constrained Optimization via Weak-Form Latent Dynamicscited by 0
  10. 2026Physics-conforming Latent Twinscited by 0
  11. 2026Learning Macroscopic Dynamics without Reconstructing Microscopic Statescited by 0