Tiffany Fan

Tiffany Fan, Murray Cutforth, Marta D'Elia et al.

Computational Fluid Dynamics (CFD) plays a pivotal role in fluid mechanics, enabling precise simulations of fluid behavior through partial differential equations (PDEs). However, traditional CFD methods are resource-intensive, particularly for high-fidelity simulations of complex flows, which are further complicated by high dimensionality, inherent stochasticity, and limited data availability. This paper addresses these challenges by proposing a data-driven approach that leverages a Gaussian Mixture Variational Autoencoder (GMVAE) to encode high-dimensional scientific data into low-dimensional, physically meaningful representations. The GMVAE learns a structured latent space where data can be categorized based on physical properties such as the Reynolds number while maintaining global physical consistency. To assess the interpretability of the learned representations, we introduce a novel metric based on graph spectral theory, quantifying the smoothness of physical quantities along the latent manifold. We validate our approach using 2D Navier-Stokes simulations of flow past a cylinder over a range of Reynolds numbers. Our results demonstrate that the GMVAE provides improved clustering, meaningful latent structure, and robust generative capabilities compared to baseline dimensionality reduction methods. This framework offers a promising direction for data-driven turbulence modeling and broader applications in computational fluid dynamics and engineering systems.

Murray Cutforth, Yiming Yang, Tiffany Fan et al.

Many science and engineering problems rely on expensive computational simulations, where a multi-fidelity approach can accelerate the exploration of a parameter space. We study efficient allocation of a simulation budget using a Gaussian Process (GP) model in the binary simulation output case. This paper introduces Bernoulli Parameter Mutual Information (BPMI), a batch active learning algorithm for multi-fidelity GP classifiers. BPMI circumvents the intractability of calculating mutual information in the probability space by employing a first-order Taylor expansion of the link function. We evaluate BPMI against several baselines on two synthetic test cases and a complex, real-world application involving the simulation of a laser-ignited rocket combustor. In all experiments, BPMI demonstrates superior performance, achieving higher predictive accuracy for a fixed computational budget.