# A parametric framework for kernel-based dynamic mode decomposition using deep learning

arXiv: https://arxiv.org/abs/2409.16817 · HTML: https://mlsanity.com/paper/2409.16817/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 44 references that are in the map.
- First posted on arXiv 25 Sep 2024.

## Builds on (most cited first, 10 of 10)

- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Machine Learning of Linear Differential Equations using Gaussian Processes](https://mlsanity.com/paper/1701.02440/) (2017)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [Neural Networks Fail to Learn Periodic Functions and How to Fix It](https://mlsanity.com/paper/2006.08195/) (2020)
- [Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition](https://mlsanity.com/paper/1409.5496/) (2014)
- [Kernel Learning for Robust Dynamic Mode Decomposition: Linear and Nonlinear Disambiguation Optimization (LANDO)](https://mlsanity.com/paper/2106.01510/) (2021)
- [Operator inference with roll outs for learning reduced models from scarce and low-quality data](https://mlsanity.com/paper/2212.01418/) (2022)
- [Gaussian process learning of nonlinear dynamics](https://mlsanity.com/paper/2312.12193/) (2023)

## Built on by (most cited first, 1 of 1)

- [Unified Spatiotemporal Physics-Informed Learning (USPIL): A Framework for Modeling Complex Predator-Prey Dynamics](https://mlsanity.com/paper/2509.13425/) (2025)

## Abstract (arXiv)

Surrogate modelling is widely applied in computational science and engineering to mitigate computational efficiency issues for the real-time simulations of complex and large-scale computational models or for many-query scenarios, such as uncertainty quantification and design optimisation. In this work, we propose a parametric framework for kernel-based dynamic mode decomposition method based on the linear and nonlinear disambiguation optimization (LANDO) algorithm. The proposed parametric framework consists of two stages, offline and online. The offline stage prepares the essential component for prediction, namely a series of LANDO models that emulate the dynamics of the system with particular parameters from a training dataset. The online stage leverages those LANDO models to generate new data at a desired time instant, and approximate the mapping between parameters and the state with the data using deep learning techniques. Moreover, dimensionality reduction technique is applied to high-dimensional dynamical systems to reduce the computational cost of training. Three numerical examples including Lotka-Volterra model, heat equation and reaction-diffusion equation are presented to demonstrate the efficiency and effectiveness of the proposed framework.