Transfer learning for neural network surrogates of flow and transport

This thesis introduces a multi-fidelity approach to train deep neural network surrogates for efficient and accurate modeling of high-dimensional fluid dynamic systems. Due to their nonlinear, dynamic, and multi-scale nature, these complex physical phenomena require substantial computational resources. While various surrogate modeling techniques exist to help alleviate this computational burden, constructing data-driven surrogates requires several thousand high-fidelity simulations to generate adequate training samples. To tackle this challenge, we present a framework that leverages multi-fidelity simulations to reduce data generation costs and employs transfer learning to train deep Convolutional Neural Networks (CNNs). We first explore the possibility of using multi-model data sources to train a CNN to replicate blood flow dynamics within an aorta geometry while capturing the variability of the governing parameters across individual patient-specific cases. Then, we investigate the use of transfer learning on two levels of data to train an inverse CNN to solve high-dimensional inverse problems in subsurface hydrology, i.e., heterogeneity field reconstruction and contaminant source identification. Our approach optimally balances computational speed-up and predictive accuracy where traditional high-fidelity models are computationally prohibitive. To mitigate the effects of the curse of dimensionality, which can impact other model reduction techniques such as Polynomial Chaos Expansion (PCE), we propose a multi-fidelity framework combined with global sensitivity analysis as a dimensionality reduction method. This approach aims to extend the applicability of the PCE technique as an alternative to neural networks in applications with a reasonable number of parameters.