A generalised novel loss function for computational fluid dynamics

Computational fluid dynamics (CFD) simulations are crucial in automotive, aerospace, maritime and medical applications, but are limited by the complexity, cost and computational requirements of directly calculating the flow, often taking days of compute time. Machine-learning architectures, such as controlled generative adversarial networks (cGANs) hold significant potential in enhancing or replacing CFD investigations, due to cGANs ability to approximate the underlying data distribution of a dataset. Unlike traditional cGAN applications, where the entire image carries information, CFD data contains small regions of highly variant data, immersed in a large context of low variance that is of minimal importance. This renders most existing deep learning techniques that give equal importance to every portion of the data during training, inefficient. To mitigate this, a novel loss function is proposed called Gradient Mean Squared Error (GMSE) which automatically and dynamically identifies the regions of importance on a field-by-field basis, assigning appropriate weights according to the local variance. To assess the effectiveness of the proposed solution, three identical networks were trained; optimised with Mean Squared Error (MSE) loss, proposed GMSE loss and a dynamic variant of GMSE (DGMSE). The novel loss function resulted in faster loss convergence, correlating to reduced training time, whilst also displaying an 83.6% reduction in structural similarity error between the generated field and ground truth simulations, a 76.6% higher maximum rate of loss and an increased ability to fool a discriminator network. It is hoped that this loss function will enable accelerated machine learning within computational fluid dynamics.