Convolutional autoencoders for the reconstruction of three-dimensional interfacial multiphase flows

TL;DR

This work systematically evaluates 3D convolutional autoencoders for reconstructing interfacial geometries in multiphase flows, focusing on how interface representations (sharp, diffuse tanh, and signed-distance level-set) affect accuracy. It demonstrates a spectral-bias mechanism, where moderately diffuse interfaces balance preservation of small-scale features with overall fidelity, outperforming both sharp and signed-distance representations across synthetic and HIT datasets. The study combines a 3D ResNet-like encoder–decoder with a fixed compression ratio, analyzes performance with Dice and Hausdorff metrics, and shows that nonlinear autoencoders significantly outperform linear baselines. These insights establish practical guidance for designing ROMs of multiphase flows and point to future extensions such as conservation constraints and variational approaches.

Abstract

We present a systematic investigation of convolutional autoencoders for the reduced-order representation of three-dimensional interfacial multiphase flows. Focusing on the reconstruction of phase indicators, we examine how the choice of interface representation, including sharp, diffuse, and level-set formulations, impacts reconstruction accuracy across a range of interface complexities. Training and validation are performed using both synthetic datasets with controlled geometric complexity and high-fidelity simulations of multiphase homogeneous isotropic turbulence. We show that the interface representation plays a critical role in autoencoder performance. Excessively sharp interfaces lead to the loss of small-scale features, while overly diffuse interfaces degrade overall accuracy. Across all datasets and metrics considered, a moderately diffuse interface provides the best balance between preserving fine-scale structures and achieving accurate reconstructions. These findings elucidate key limitations and best practices for dimensionality reduction of multiphase flows using autoencoders. By clarifying how interface representations interact with the inductive biases of convolutional neural networks, this work lays the foundation for decoupling the training of autoencoders for accurate state compression from the training of surrogate models for temporal forecasting or input-output prediction in latent space.

Figures (13)

• Figure 1: Illustration of the three interface representations compared in this study: (a) signed-distance (level-set) functions, (b) a diffuse (tanh) interface profile, and (c) a sharp-interface indicator function, showing the interface in one snapshot of the simulation of a droplet in homogeneous isotropic turbulence.
• Figure 2: Visualization of the interfacial contour for 3 samples from each of the four datasets considered in this work. In (a) the HIT simulation dataset is shown, while the remaining three panels show the synthetic dataset which is parameterized by $\mu$. $\mu=1$ in (b), $\mu=2$ in (c), and $\mu=2.5$ in (d). $\mu$ parametrizes these datasets through Equation \ref{['eq:mu']}.
• Figure 3: Default residual block used in the autoencoder.
• Figure 4: Parallel coordinate plot showing hyper-parameter grid search results for three different interface representations. Each line corresponds to a single hyper-parameter set, colored by validation set performance. Line thickness is also proportional to performance in order to highlight the best hyperparameter sets.
• Figure 5: