用域分解提升微分方程模型发现，FBPINN在弱动态数据下更优
Towards Model Discovery Using Domain Decomposition and PINNs
- 采用域分解结合物理信息神经网络，分段学习复杂系统动态
- FBPINN在低动态、高噪声条件下仍优于传统PINN
- 适合数据稀疏或仅含稳态信息的系统建模任务
我们通过域分解方法增强机器学习算法在常微分方程（ODE）表示的复杂系统中学习模型参数的能力。研究评估了两种方法——标准物理信息神经网络（PINNs）与有限基物理信息神经网络（FBPINNs）——在具有准稳态长期行为的测试模型上的表现。实验在不同动力学区域的数据集上进行，并设置了多种噪声水平。结果显示，即使在仅包含准稳态时间域且动态极少的数据条件下，FBPINN的表现也优于标准PINN。
原文摘要 · Abstract (English)
We enhance machine learning algorithms for learning model parameters in complex systems represented by ordinary differential equations (ODEs) with domain decomposition methods. The study evaluates the performance of two approaches, namely (vanilla) Physics-Informed Neural Networks (PINNs) and Finite Basis Physics-Informed Neural Networks (FBPINNs), in learning the dynamics of test models with a quasi-stationary longtime behavior. We test the approaches for data sets in different dynamical regions and with varying noise level. As results, we find a better performance for the FBPINN approach compared to the vanilla PINN approach, even in cases with data from only a quasi-stationary time domain with few dynamics.
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