Supplementation of deep neural networks with simplified physics-based features to increase accuracy of plate fundamental frequency predictions

Abstract

To improve predictive machine learning-based models limited by sparse data, supplemental physics-related features are introduced into a deep neural network (DNN). While some approaches inject physics through differential equations or numerical simulation, improvements are possible using simplified relationships from engineering references. To evaluate this hypothesis, thin rectangular plates were simulated to generate training datasets. With plate dimensions and material properties as input features and fundamental natural frequency as the output, predictive performance of a data-driven DNN-based model is compared with models using supplemental inputs, such as modulus of rigidity. To evaluate model accuracy improvements, these additional features are injected into various DNN layers, and the network is trained with four different dataset sizes. When evaluated against independent data of similar features to the training sets, supplementation provides no statistically-significant prediction error reduction. However, notable accuracy gains occur when independent test data is of material and dimensions different from the original training set. Furthermore, when physics-enhanced data is injected into multiple DNN layers, reductions in mean error from 33.2% to 19.6%, 34.9% to 19.9%, 35.8% to 22.4%, and 43.0% to 28.4% are achieved for dataset sizes of 261, 117, 60, and 30, respectively, demonstrating potential for generalizability using a data supplementation approach. Additionally, when compared with other methods—such as linear regression and support vector machine (SVM) approaches—the physics-enhanced DNN demonstrates an order of magnitude reduction in percentage error for dataset sizes of 261, 117, and 60 and a 30% reduction for a size of 30 when compared with a cubic SVM model independently tested with data divergent from the training and validation set.