mlsanityData to 7 Oct 2026

Sequential decoder training for improved latent space dynamics identification

arXiv 2510.03535 ↗First posted 3 Oct 2025cs.LG cs.NA math.NAcited by 2

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Abstract (arXiv)

Accurate numerical solutions of partial differential equations are essential in many scientific fields but often require computationally expensive solvers, motivating reduced-order models (ROMs). Latent Space Dynamics Identification (LaSDI) is a data-driven ROM framework that combines autoencoders with equation discovery to learn interpretable latent dynamics. However, enforcing latent dynamics during training can compromise reconstruction accuracy of the model for simulation data. We introduce multi-stage LaSDI (mLaSDI), a framework that improves reconstruction and prediction accuracy by sequentially learning additional decoders to correct residual errors from previous stages. Applied to the 1D-1V Vlasov equation, mLaSDI consistently outperforms standard LaSDI, achieving lower prediction errors and reduced training time across a wide range of architectures.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 16 of its 45 references that are in the map. First posted on arXiv 3 Oct 2025.

Builds on

16 of 45 references.

References · 16

  1. 2020Discovering Symbolic Models from Deep Learning with Inductive Biasescited by 335
  2. 2019Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systemscited by 96
  3. 2020A fast and accurate physics-informed neural network reduced order model with shallow masked autoencodercited by 80
  4. 2023Multi-stage Neural Networks: Function Approximator of Machine Precisioncited by 48
  5. 2020Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear termscited by 32
  6. 2022gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identificationcited by 30
  7. 2023GPLaSDI: Gaussian Process-based Interpretable Latent Space Dynamics Identification through Deep Autoencodercited by 29
  8. 2024tLaSDI: Thermodynamics-informed latent space dynamics identificationcited by 23
  9. 2024A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modelingcited by 22
  10. 2023Stacked networks improve physics-informed training: applications to neural networks and deep operator networkscited by 21
  11. 2023Weak-Form Latent Space Dynamics Identificationcited by 20
  12. 2020Component-wise reduced order model lattice-type structure designcited by 16
4 more
  1. 2024Physics-informed active learning with simultaneous weak-form latent space dynamics identificationcited by 13
  2. 2025Thermodynamically Consistent Latent Dynamics Identification for Parametric Systemscited by 8
  3. 2023Train Small, Model Big: Scalable Physics Simulators via Reduced Order Modeling and Domain Decompositioncited by 7
  4. 2022Certified data-driven physics-informed greedy auto-encoder simulatorcited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Latent Space Element Methodcited by 1
  2. 2026Time-Dependent PDE-Constrained Optimization via Weak-Form Latent Dynamicscited by 0