SurroFlow: A Flow-Based Surrogate Model for Parameter Space Exploration and Uncertainty Quantification

TL;DR

SurroFlow tackles the difficulty of uncertainty quantification and efficient parameter-space exploration in scientific surrogates by using a conditional normalizing flow operating in a latent space learned via a 3D autoencoder. The model enables bidirectional predictions: forward generation of simulation data conditioned on parameters and reverse inference of parameters from data, with uncertainty naturally represented in the latent distribution $p(oldsymbol{z}\mid\boldsymbol{c})$. Coupled with a genetic algorithm and an interactive visual interface, SurroFlow supports user-guided, objective-driven exploration of the parameter space, balancing similarity, diversity, and uncertainty. Quantitative and qualitative evaluations on MPAS-Ocean and Nyx demonstrate competitive surrogate accuracy, effective reverse prediction, and meaningful uncertainty quantification, enabling more reliable and efficient ensemble simulations and design exploration in practice.

Abstract

Existing deep learning-based surrogate models facilitate efficient data generation, but fall short in uncertainty quantification, efficient parameter space exploration, and reverse prediction. In our work, we introduce SurroFlow, a novel normalizing flow-based surrogate model, to learn the invertible transformation between simulation parameters and simulation outputs. The model not only allows accurate predictions of simulation outcomes for a given simulation parameter but also supports uncertainty quantification in the data generation process. Additionally, it enables efficient simulation parameter recommendation and exploration. We integrate SurroFlow and a genetic algorithm as the backend of a visual interface to support effective user-guided ensemble simulation exploration and visualization. Our framework significantly reduces the computational costs while enhancing the reliability and exploration capabilities of scientific surrogate models.

Figures (13)

• Figure 1: A normalizing flow turns a simple base distribution into a more complex one. This mapping is invertible in the opposite direction.
• Figure 2: Overview of our approach. (1) An uncertainty-aware surrogate model is built to predict simulation outcomes for simulation parameters. (2) A genetic algorithm is utilized for efficient simulation parameter optimization. (3) Integrating the surrogate model and genetic algorithm into an interactive visual system for user-guided parameter space exploration.
• Figure 3: Autoencoder for dimensionality reduction.
• Figure 4: SurroFlow is a conditional normalizing flow for surrogate modeling. It is trained on pairs of simulation parameters ($\mathbf{c}$) and simulation data latent representations ($\mathbf{z}_K$). During inference, SurroFlow takes simulation parameters $\mathbf{c}$ as the input to sample $\mathbf{z}_0$ and outputs the reconstructed latent representation $\mathbf{z}_K$ (indicated by the blue dotted arrow). In the reverse direction, SurroFlow takes latent representations $\mathbf{z}_K$ as input and predicts the corresponding simulation parameters (black solid arrow).
• Figure 5: An overview of our visual system for efficient user-guided parameter recommendation and exploration.