# Deep learning for model correction of dynamical systems with data scarcity

arXiv: https://arxiv.org/abs/2410.17913 · HTML: https://mlsanity.com/paper/2410.17913/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 35 references that are in the map.
- First posted on arXiv 23 Oct 2024.

## Builds on (most cited first, 12 of 12)

- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [What is being transferred in transfer learning?](https://mlsanity.com/paper/2008.11687/) (2020)
- [Data Driven Governing Equations Approximation Using Deep Neural Networks](https://mlsanity.com/paper/1811.05537/) (2018)
- [Deep transfer operator learning for partial differential equations under conditional shift](https://mlsanity.com/paper/2204.09810/) (2022)
- [Correcting model misspecification in physics-informed neural networks (PINNs)](https://mlsanity.com/paper/2310.10776/) (2023)
- [Discovering a reaction-diffusion model for Alzheimer's disease by combining PINNs with symbolic regression](https://mlsanity.com/paper/2307.08107/) (2023)
- [On generalized residue network for deep learning of unknown dynamical systems](https://mlsanity.com/paper/2002.02528/) (2020)
- [Discrepancy Modeling Framework: Learning missing physics, modeling systematic residuals, and disambiguating between deterministic and random effects](https://mlsanity.com/paper/2203.05164/) (2022)
- [Learning About Structural Errors in Models of Complex Dynamical Systems](https://mlsanity.com/paper/2401.00035/) (2023)
- [Embedded Model Error Representation for Bayesian Model Calibration](https://mlsanity.com/paper/1801.06768/) (2018)
- [A PINN Approach to Symbolic Differential Operator Discovery with Sparse Data](https://mlsanity.com/paper/2212.04630/) (2022)
- [Learning Fine Scale Dynamics from Coarse Observations via Inner Recurrence](https://mlsanity.com/paper/2206.01807/) (2022)

## Built on by (most cited first, 2 of 2)

- [Residual Correction Models for AC Optimal Power Flow Using DC Optimal Power Flow Solutions](https://mlsanity.com/paper/2510.16064/) (2025)
- [Data-Driven Modeling and Correction of Vehicle Dynamics](https://mlsanity.com/paper/2512.00289/) (2025)

## Abstract (arXiv)

We present a deep learning framework for correcting existing dynamical system models utilizing only a scarce high-fidelity data set. In many practical situations, one has a low-fidelity model that can capture the dynamics reasonably well but lacks high resolution, due to the inherent limitation of the model and the complexity of the underlying physics. When high resolution data become available, it is natural to seek model correction to improve the resolution of the model predictions. We focus on the case when the amount of high-fidelity data is so small that most of the existing data driven modeling methods cannot be applied. In this paper, we address these challenges with a model-correction method which only requires a scarce high-fidelity data set. Our method first seeks a deep neural network (DNN) model to approximate the existing low-fidelity model. By using the scarce high-fidelity data, the method then corrects the DNN model via transfer learning (TL). After TL, an improved DNN model with high prediction accuracy to the underlying dynamics is obtained. One distinct feature of the propose method is that it does not assume a specific form of the model correction terms. Instead, it offers an inherent correction to the low-fidelity model via TL. A set of numerical examples are presented to demonstrate the effectiveness of the proposed method.