mlsanityData to 14 Oct 2026

Higher-Order LaSDI: Reduced Order Modeling with Multiple Time Derivatives

arXiv 2512.15997 ↗First posted 17 Dec 2025cs.LGcited by 2

Not on the map. Why?

Abstract (arXiv)

Solving complex partial differential equations is vital in the physical sciences, but often requires computationally expensive numerical methods. Reduced-order models (ROMs) address this by exploiting dimensionality reduction to create fast approximations. While modern ROMs can solve parameterized families of PDEs, their predictive power degrades over long time horizons. We address this by (1) introducing a flexible, high-order, yet inexpensive finite-difference scheme and (2) proposing a Rollout loss that trains ROMs to make accurate predictions over arbitrary time horizons. We demonstrate our approach on the 2D Burgers equation.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 24 of its 62 references that are in the map. First posted on arXiv 17 Dec 2025.

Builds on

24 of 62 references.

References · 24

  1. 2017Attention Is All You Needcited by 60,361
  2. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  3. 2020Language Models are Few-Shot Learnerscited by 32,419
  4. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  5. 2018Neural Ordinary Differential Equationscited by 3,779
  6. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 494
  7. 2020Universal Differential Equations for Scientific Machine Learningcited by 353
  8. 2017Sparse identification of nonlinear dynamics for model predictive control in the low-data limitcited by 140
  9. 2021Multi-Objective Loss Balancing for Physics-Informed Deep Learningcited by 87
  10. 2018Blessing of dimensionality: mathematical foundations of the statistical physics of datacited by 55
  11. 2020Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problemscited by 45
  12. 2022gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identificationcited by 30
12 more
  1. 2023GPLaSDI: Gaussian Process-based Interpretable Latent Space Dynamics Identification through Deep Autoencodercited by 30
  2. 2021PDE-READ: Human-readable Partial Differential Equation Discovery using Deep Learningcited by 24
  3. 2024tLaSDI: Thermodynamics-informed latent space dynamics identificationcited by 23
  4. 2024A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modelingcited by 22
  5. 2022PDE-LEARN: Using Deep Learning to Discover Partial Differential Equations from Noisy, Limited Datacited by 20
  6. 2023Weak-Form Latent Space Dynamics Identificationcited by 20
  7. 2020Component-wise reduced order model lattice-type structure designcited by 16
  8. 2024Physics-informed active learning with simultaneous weak-form latent space dynamics identificationcited by 13
  9. 2023Data-Driven Autoencoder Numerical Solver with Uncertainty Quantification for Fast Physical Simulationscited by 3
  10. 2025mLaSDI: Multi-stage latent space dynamics identificationcited by 2
  11. 2025Rollout-LaSDI: Enhancing the long-term accuracy of Latent Space Dynamicscited by 2
  12. 2024DDE-Find: Learning Delay Differential Equations from Noisy, Limited Datacited by 1

Built on by

Cited by year (2026 to 14 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