TRANSFER LEARNING ON MULTI-DIMENSIONAL DATA: A NOVEL APPROACH TO NEURAL NETWORK-BASED SURROGATE MODELING

The development of efficient surrogates of partial differential equations (PDEs) is a critical step toward scalable modeling of complex, multiscale systems-of-systems. Convolutional neural networks (CNNs) have gained popularity as the basis for such surrogate models due to their success in capturing high-dimensional input-output mappings and the negligible cost of a forward pass. However, the high cost of generating training data-typically via classical numerical solvers-raises the question of whether these models are worth pursuing over more straightforward alternatives with well-established theoretical foundations such as Monte Carlo (MC) methods. To reduce the cost of data generation, we propose training a CNN surrogate model on a mixture of numerical solutions to both the d-dimensional problem and its (d-1)-dimensional approximation, taking advantage of the efficiency savings guaranteed by the curse of dimensionality. We demonstrate our approach on a multiphase flow test problem, using transfer learning to train a dense, fully convolutional encoder- decoder CNN on the two classes of data. Numerical results from a sample uncertainty quantification (UQ) task demonstrate that our surrogate model outperforms MC with several times the data generation budget.