# gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification

arXiv: https://arxiv.org/abs/2204.12005 · HTML: https://mlsanity.com/paper/2204.12005/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 103 references that are in the map.
- First posted on arXiv 26 Apr 2022.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)
- [Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems](https://mlsanity.com/paper/1912.08177/) (2019)
- [A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder](https://mlsanity.com/paper/2009.11990/) (2020)
- [CaloGAN: Simulating 3D High Energy Particle Showers in Multi-Layer Electromagnetic Calorimeters with Generative Adversarial Networks](https://mlsanity.com/paper/1712.10321/) (2017)
- [Deep Dynamical Modeling and Control of Unsteady Fluid Flows](https://mlsanity.com/paper/1805.07472/) (2018)
- [Deep Learning in Bioinformatics](https://mlsanity.com/paper/1603.06430/) (2016)
- [Data-driven reduced-order models via regularized operator inference for a single-injector combustion process](https://mlsanity.com/paper/2008.02862/) (2020)
- [Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms](https://mlsanity.com/paper/2002.09726/) (2020)
- [A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks](https://mlsanity.com/paper/2105.13136/) (2021)
- [Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniques](https://mlsanity.com/paper/2107.11460/) (2021)
- [Non-intrusive reduced-order models for parametric partial differential equations via data-driven operator inference](https://mlsanity.com/paper/2110.07653/) (2021)
- [Learning physics-based reduced-order models for a single-injector combustion process](https://mlsanity.com/paper/1908.03620/) (2019)
- [Sampling low-dimensional Markovian dynamics for pre-asymptotically recovering reduced models from data with operator inference](https://mlsanity.com/paper/1908.11233/) (2019)
- [Bayesian operator inference for data-driven reduced-order modeling](https://mlsanity.com/paper/2204.10829/) (2022)
- [A Physics-Constrained Data-Driven Approach Based on Locally Convex Reconstruction for Noisy Database](https://mlsanity.com/paper/1907.12651/) (2019)
- [Efficient nonlinear manifold reduced order model](https://mlsanity.com/paper/2011.07727/) (2020)
- [Component-wise reduced order model lattice-type structure design](https://mlsanity.com/paper/2010.10770/) (2020)
- [Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learning](https://mlsanity.com/paper/2202.05460/) (2022)
- [Continuous conditional generative adversarial networks for data-driven solutions of poroelasticity with heterogeneous material properties](https://mlsanity.com/paper/2111.14984/) (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)
- [An algorithmic comparison of the Hyper-Reduction and the Discrete Empirical Interpolation Method for a nonlinear thermal problem](https://mlsanity.com/paper/1610.05029/) (2016)

## Built on by (most cited first, 30 of 30)

- [GPLaSDI: Gaussian Process-based Interpretable Latent Space Dynamics Identification through Deep Autoencoder](https://mlsanity.com/paper/2308.05882/) (2023)
- [Self-Supervised Learning with Lie Symmetries for Partial Differential Equations](https://mlsanity.com/paper/2307.05432/) (2023)
- [tLaSDI: Thermodynamics-informed latent space dynamics identification](https://mlsanity.com/paper/2403.05848/) (2024)
- [A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling](https://mlsanity.com/paper/2403.10748/) (2024)
- [Weak-Form Latent Space Dynamics Identification](https://mlsanity.com/paper/2311.12880/) (2023)
- [Thermodynamically Consistent Machine-Learned Internal State Variable Approach for Data-Driven Modeling of Path-Dependent Materials](https://mlsanity.com/paper/2205.00578/) (2022)
- [Physics-informed active learning with simultaneous weak-form latent space dynamics identification](https://mlsanity.com/paper/2407.00337/) (2024)
- [The Weak Form Is Stronger Than You Think](https://mlsanity.com/paper/2409.06751/) (2024)
- [Reduced-order modeling for parameterized PDEs via implicit neural representations](https://mlsanity.com/paper/2311.16410/) (2023)
- [Thermodynamically Consistent Latent Dynamics Identification for Parametric Systems](https://mlsanity.com/paper/2506.08475/) (2025)
- [A Multi-Resolution Physics-Informed Recurrent Neural Network: Formulation and Application to Musculoskeletal Systems](https://mlsanity.com/paper/2305.16593/) (2023)
- [Adaptive learning of effective dynamics: Adaptive real-time, online modeling for complex systems](https://mlsanity.com/paper/2304.01732/) (2023)
- [Using Conservation Laws to Infer Deep Learning Model Accuracy of Richtmyer-meshkov Instabilities](https://mlsanity.com/paper/2208.11477/) (2022)
- [Data-Driven Autoencoder Numerical Solver with Uncertainty Quantification for Fast Physical Simulations](https://mlsanity.com/paper/2312.01021/) (2023)
- [Smooth and Sparse Latent Dynamics in Operator Learning with Jerk Regularization](https://mlsanity.com/paper/2402.15636/) (2024)
- [A Deep Learning approach for parametrized and time dependent Partial Differential Equations using Dimensionality Reduction and Neural ODEs](https://mlsanity.com/paper/2502.08683/) (2025)
- [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)
- [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)
- [Enhancing Dynamic Mode Decomposition Workflow with In-Situ Visualization and Data Compression](https://mlsanity.com/paper/2208.07767/) (2022)
- [Parametric Taylor series based latent dynamics identification neural networks](https://mlsanity.com/paper/2410.04193/) (2024)
- [Understanding the role of autoencoders for stiff dynamical systems using information theory](https://mlsanity.com/paper/2503.06325/) (2025)
- [Spatially-Enhanced Temporal Fusion Transformer: Interpretable Multi-Output Prediction for Parametric Dynamical Systems with Time-Varying Inputs](https://mlsanity.com/paper/2505.00473/) (2025)
- [Data-Driven Modeling of an Unsaturated Bentonite Buffer Model Test Under High Temperatures Using an Enhanced Axisymmetric Reproducing Kernel Particle Method](https://mlsanity.com/paper/2309.13519/) (2023)
- [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)
- [Physics-conforming Latent Twins](https://mlsanity.com/paper/2606.15053/) (2026)
- [Learning Macroscopic Dynamics without Reconstructing Microscopic States](https://mlsanity.com/paper/2609.37392/) (2026)

## Abstract (arXiv)

A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic nonlinear latent representations of high-dimensional data, while dynamics identification (DI) models capture local latent-space dynamics. An interactive training algorithm is adopted for the autoencoder and local DI models, which enables identification of simple latent-space dynamics and enhances accuracy and efficiency of data-driven reduced-order modeling. To maximize and accelerate the exploration of the parameter space for the optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residual-based error indicator and random-subset evaluation is introduced to search for the optimal training samples on the fly. Further, to exploit local latent-space dynamics captured by the local DI models for an improved modeling accuracy with a minimum number of local DI models in the parameter space, a k-nearest neighbor convex interpolation scheme is employed. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including Burgers equations, nonlinear heat conduction, and radial advection. The proposed adaptive greedy sampling outperforms the conventional predefined uniform sampling in terms of accuracy. Compared with the high-fidelity models, gLaSDI achieves 17 to 2,658x speed-up with 1 to 5% relative errors.