A methodology to assess and improve the physics consistency of an artificial neural network regression model for engineering applications

Abstract

Abstract In recent times, artificial neural networks (ANNs) have become the popular choice of model for researchers while performing regression analysis between inputs and output. However; in scientific and engineering applications, developed ANN regression model is often found to be inconsistent with the physical laws. This is due to the fact that ANNs are purely based on data and do not have any understanding of underlying physical laws. Alternate ANN frameworks like PGNN (Physics guided neural network) has been proposed in literature which incorporate physics loss function in the overall loss function to partially alleviate this issue. However, these frameworks don’t evaluate the physics consistency of relationship between inputs and output mapped by the ANN model which is the source of all physics inconsistencies. Hence, the present paper presents a methodology to assess and improve the physics consistency of the input output relationship mapped by the ANN regression model. The developed methodology can therefore be used to develop physics consistent ANN regression model. The heart of the methodology is an inferencing algorithm which interprets the input output relationship mapped by the ANN regression model. The inferencing algorithm is based on Taylor series and decomposes the ANN regression model into several region-wise polynomial models. Moreover, the inferencing algorithm can also find regions of singular zones in the ANN model predictions. The region-wise polynomial from inferencing algorithm can be used to assess the physics consistency of the ANN model. In the region of physics inconsistency, additional data points can be added and the ANN model can be re-trained. In cases, where the addition of data points is not possible, a physics based loss function can be used. The developed methodology is illustrated using several datasets. The developed methodology will help engineers and researchers built physics consistent ANN regression models.

Keywords

• Neural network regression model
• Taylor series
• Radius of convergence
• Degree of Taylor polynomial
• Physics consistency
• Physics loss function