用少量高精度数据修正低精度动力系统模型，提升预测准确性。
Deep learning for model correction of dynamical systems with data scarcity
- 用深度神经网络拟合低精度模型，再通过迁移学习修正
- 仅需少量高精度数据即可实现高精度预测，误差显著降低
- 无需预设修正形式，适合数据稀缺的动力系统建模
我们提出一种深度学习框架，用于在仅有少量高精度数据的情况下，对现有动力系统模型进行修正。在许多实际场景中，低精度模型虽能合理捕捉动态特性，但缺乏高分辨率，受限于模型本身和底层物理的复杂性。当高分辨率数据出现时，自然需要对模型进行修正以提升预测分辨率。本文聚焦于高精度数据极度稀缺、多数数据驱动方法难以应用的情形。提出的方法仅需少量高精度数据，首先训练深度神经网络（DNN）近似原低精度模型，再利用该数据通过迁移学习（TL）修正DNN模型。经迁移学习后，获得对底层动力学具有高预测精度的改进型DNN模型。本方法一大特点是不假设特定的修正项形式，而是通过迁移学习实现内在修正。多个数值实验验证了该方法的有效性。
原文摘要 · Abstract (English)
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.
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