Introducing dynamic correction terms for relative error metrics in physics computational surrogate models

Abstract

Numerical methods like Finite Element Method (FEM) are key in product development, but they demand increasing computational resources, particularly as they scale and encompass complex physical phenomena. Recent trends involve substituting these numerical calculations with deep learning to achieve faster, equivalent data processing. However, in physics computations, managing computational error is crucial, and relative error metrics are often preferred. Yet, traditional metrics like MAPE and RMSPE face issues of instability, especially with small true values. Addressing this, we’ve innovated by integrating dynamic correction terms into existing relative error metrics, enhancing their stability and adaptability across various computational scenarios. This advancement led to the development of a simplified computational model as an alternative to traditional FEM calculations. Our model, benchmarked against those using standard metrics, showcased not only stable learning across varying magnitudes of true values but also superior accuracy. This represents a significant improvement in computational techniques, promising more efficient and precise industrial product development.