# A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling

arXiv: https://arxiv.org/abs/2403.10748 · HTML: https://mlsanity.com/paper/2403.10748/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 73 references that are in the map.
- First posted on arXiv 16 Mar 2024.

## Builds on (most cited first, 22 of 22)

- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (2020)
- [A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder](https://mlsanity.com/paper/2009.11990/) (2020)
- [Structure-preserving neural networks](https://mlsanity.com/paper/2004.04653/) (2020)
- [Machine learning structure preserving brackets for forecasting irreversible processes](https://mlsanity.com/paper/2106.12619/) (2021)
- [GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems](https://mlsanity.com/paper/2109.00092/) (2021)
- [gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification](https://mlsanity.com/paper/2204.12005/) (2022)
- [GPLaSDI: Gaussian Process-based Interpretable Latent Space Dynamics Identification through Deep Autoencoder](https://mlsanity.com/paper/2308.05882/) (2023)
- [PDE-READ: Human-readable Partial Differential Equation Discovery using Deep Learning](https://mlsanity.com/paper/2111.00998/) (2021)
- [Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants](https://mlsanity.com/paper/2211.10575/) (2022)
- [tLaSDI: Thermodynamics-informed latent space dynamics identification](https://mlsanity.com/paper/2403.05848/) (2024)
- [Direct Estimation of Parameters in ODE Models Using WENDy: Weak-form Estimation of Nonlinear Dynamics](https://mlsanity.com/paper/2302.13271/) (2023)
- [Weak-Form Latent Space Dynamics Identification](https://mlsanity.com/paper/2311.12880/) (2023)
- [WeakIdent: Weak formulation for Identifying Differential Equations using Narrow-fit and Trimming](https://mlsanity.com/paper/2211.03134/) (2022)
- [Efficient nonlinear manifold reduced order model](https://mlsanity.com/paper/2011.07727/) (2020)
- [Bayesian Deep Learning for Partial Differential Equation Parameter Discovery with Sparse and Noisy Data](https://mlsanity.com/paper/2108.04085/) (2021)
- [Non-intrusive Nonlinear Model Reduction via Machine Learning Approximations to Low-dimensional Operators](https://mlsanity.com/paper/2106.09658/) (2021)
- [S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models](https://mlsanity.com/paper/2203.16494/) (2022)
- [Certified data-driven physics-informed greedy auto-encoder simulator](https://mlsanity.com/paper/2211.13698/) (2022)
- [Sliced gradient-enhanced Kriging for high-dimensional function approximation](https://mlsanity.com/paper/2204.03562/) (2022)
- [Data-Driven Autoencoder Numerical Solver with Uncertainty Quantification for Fast Physical Simulations](https://mlsanity.com/paper/2312.01021/) (2023)

## Built on by (most cited first, 22 of 22)

- [On latent dynamics learning in nonlinear reduced order modeling](https://mlsanity.com/paper/2408.15183/) (2024)
- [Physics-informed active learning with simultaneous weak-form latent space dynamics identification](https://mlsanity.com/paper/2407.00337/) (2024)
- [Accelerating Phase Field Simulations Through a Hybrid Adaptive Fourier Neural Operator with U-Net Backbone](https://mlsanity.com/paper/2406.17119/) (2024)
- [Thermodynamically Consistent Latent Dynamics Identification for Parametric Systems](https://mlsanity.com/paper/2506.08475/) (2025)
- [Sparse L1-Autoencoders for Scientific Data Compression](https://mlsanity.com/paper/2405.14270/) (2024)
- [Data-Augmented Predictive Deep Neural Network: Enhancing the extrapolation capabilities of non-intrusive surrogate models](https://mlsanity.com/paper/2410.13376/) (2024)
- [Latent Twins](https://mlsanity.com/paper/2509.20615/) (2025)
- [mLaSDI: Multi-stage latent space dynamics identification](https://mlsanity.com/paper/2506.09207/) (2025)
- [Rollout-LaSDI: Enhancing the long-term accuracy of Latent Space Dynamics](https://mlsanity.com/paper/2509.08191/) (2025)
- [Differentiable Autoencoding Neural Operator for Interpretable and Integrable Latent Space Modeling](https://mlsanity.com/paper/2510.00233/) (2025)
- [Neural non-canonical Hamiltonian dynamics for long-time simulations](https://mlsanity.com/paper/2510.01788/) (2025)
- [Sequential decoder training for improved latent space dynamics identification](https://mlsanity.com/paper/2510.03535/) (2025)
- [Higher-Order LaSDI: Reduced Order Modeling with Multiple Time Derivatives](https://mlsanity.com/paper/2512.15997/) (2025)
- [Extrapolating Phase-Field Simulations in Space and Time with Purely Convolutional Architectures](https://mlsanity.com/paper/2509.20770/) (2025)
- [Latent Space Element Method](https://mlsanity.com/paper/2601.01741/) (2026)
- [Revealing Low-Dimensional Structure in 2D Richtmyer-Meshkov Instabilities via Parametric Reduced-Order Modeling](https://mlsanity.com/paper/2510.16197/) (2025)
- [Calibrated Principal Component Regression](https://mlsanity.com/paper/2510.19020/) (2025)
- [Towards Spatio-Temporal Extrapolation of Phase-Field Simulations with Convolution-Only Neural Networks](https://mlsanity.com/paper/2601.04510/) (2026)
- [Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs](https://mlsanity.com/paper/2601.11259/) (2026)
- [WGFINNs: Weak formulation-based GENERIC formalism informed neural networks](https://mlsanity.com/paper/2604.02601/) (2026)
- [Time-Dependent PDE-Constrained Optimization via Weak-Form Latent Dynamics](https://mlsanity.com/paper/2605.20639/) (2026)
- [Learning Prognostic Variables for AI Convective Parameterizations via Symbolic Distillation](https://mlsanity.com/paper/2609.24882/) (2026)

## Abstract (arXiv)

Numerical solvers of partial differential equations (PDEs) have been widely employed for simulating physical systems. However, the computational cost remains a major bottleneck in various scientific and engineering applications, which has motivated the development of reduced-order models (ROMs). Recently, machine-learning-based ROMs have gained significant popularity and are promising for addressing some limitations of traditional ROM methods, especially for advection dominated systems. In this chapter, we focus on a particular framework known as Latent Space Dynamics Identification (LaSDI), which transforms the high-fidelity data, governed by a PDE, to simpler and low-dimensional latent-space data, governed by ordinary differential equations (ODEs). These ODEs can be learned and subsequently interpolated to make ROM predictions. Each building block of LaSDI can be easily modulated depending on the application, which makes the LaSDI framework highly flexible. In particular, we present strategies to enforce the laws of thermodynamics into LaSDI models (tLaSDI), enhance robustness in the presence of noise through the weak form (WLaSDI), select high-fidelity training data efficiently through active learning (gLaSDI, GPLaSDI), and quantify the ROM prediction uncertainty through Gaussian processes (GPLaSDI). We demonstrate the performance of different LaSDI approaches on Burgers equation, a non-linear heat conduction problem, and a plasma physics problem, showing that LaSDI algorithms can achieve relative errors of less than a few percent and up to thousands of times speed-ups.