Neural-Network-Augmented Empirical Interpolation Method for Field Reconstruction with Noise and Vibration Tolerance

Field reconstruction methods based on machine learning often face challenges when handling unstructured data and designing complex model structures. On the other hand, Reduced Order Models (ROM) struggle with robustness in the presence of observation noise and sensor vibrations. Striking a balance between lightweight design, the ability to handle unstructured data, and robustness presents a significant challenge. In this paper, we introduce the EIM-NN algorithm, which leverages neural networks to determine the coefficients of the subspace found by the EIM algorithm. Furthermore, we present the EIM-TNN algorithm, which enhances robustness by designing a loss function incorporating Tikhonov regularization. Our neural network consists of only two fully connected layers, allowing it to handle unstructured data while maintaining a lightweight profile. Experimental results demonstrate the algorithm’s ability to significantly enhance robustness against noise and sensor vibrations without compromising its accuracy in fitting the original data. Additionally, the algorithm’s lightweight nature ensures that the added training time and memory requirements over EIM remain acceptable, making it adaptable to a range of industrial applications.