Supplementation of deep neural networks with simplified physics-based features to increase model prediction accuracy

TL;DR

This study investigates whether adding simplified physics-based features to deep neural networks improves prediction accuracy and generalizability in modeling natural frequencies of plates, especially with limited training data.

Contribution

It demonstrates that integrating simplified physics features into DNNs enhances model generalization to unseen materials and dimensions, particularly with small datasets.

Findings

Physics-enhanced models improve accuracy on out-of-sample data.

Adding physics features yields small gains with large training sets.

Significant accuracy improvements observed with small datasets and novel test cases.

Abstract

To improve predictive models for STEM applications, supplemental physics-based features computed from input parameters are introduced into single and multiple layers of a deep neural network (DNN). While many studies focus on informing DNNs with physics through differential equations or numerical simulation, much may be gained through integration of simplified relationships. To evaluate this hypothesis, a number of thin rectangular plates simply-supported on all edges are simulated for five materials. With plate dimensions and material properties as input features and fundamental natural frequency as the sole output, predictive performance of a purely data-driven DNN-based model is compared with models using additional inputs computed from simplified physical relationships among baseline parameters, namely plate weight, modulus of rigidity, and shear modulus. To better understand the benefit to model accuracy, these additional features are injected into various single and multiple DNN layers, and trained with four different dataset sizes. When these physics-enhanced models are evaluated against independent data of the same materials and similar dimensions to the training sets, supplementation with simplified physics-based parameters provides little reduction in prediction error over the baseline for models trained with dataset sizes of 60 and greater, although small improvement from 19.3% to 16.1% occurs when trained with a sparse size of 30. Conversely, notable accuracy gains occur when the independent test data is of material and dimensions not conforming to the training set. Specifically, when physics-enhanced data is injected into multiple DNN layers, reductions in 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 training dataset sizes of 261, 117, 60, and 30, respectively, demonstrating attainment of a degree of generalizability.