Performance Assessment on Neural Operator Surrogate Models For Porous Media Flows

Resumo

Despite being resource demanding for real world applications, numerical simulations are a powerful tool for investigating physical phenomena. For many applications - especially those involving many-query procedures such as optimization and uncertainty quantification -, the extensive use of numerical simulations can be prohibitive due to computational effort. The growing interest in Scientific Machine Learning (SciML) techniques have been enabling the construction of data-driven surrogate models able to predict unseen scenarios and reduce the dependency on the said expensive numerical simulations. Amidst the wide variety of SciML models, Fourier Neural Operators (FNOs) arise as a powerful tool to learn the mapping between functions using spectral convolutions over the problem dimensions as their kernel operations, leading to a more generalizable model for parameter exploitation or time prediction. It is known, however, that high-dimensional tensors are used for data ingestion on FNOs, leading to an undesired spatial complexity and memory footprint when considering these algorithms. In this study, we investigate the computational complexity of using FNOs on different flow applications by identifying bottlenecks and limitations of the existing architectures for porous media flow. PyTorch's Memory Viz profiler is selected as our tool to measure the GPU memory usage while Weights & Biases is set to instrument the code efficiency. Our surrogate model results are assessed via SciML metrics for the model performance.