Seeing the Many: Exploring Parameter Distributions Conditioned on Features in Surrogates

TL;DR

This paper introduces a method to model and visualize the distribution of input parameters in surrogate models conditioned on output features, addressing approximation errors and enabling interactive exploration of plausible parameters.

Contribution

It presents a novel approach combining density estimation and likelihood modeling to visualize parameter distributions conditioned on features in surrogate models.

Findings

Effective visualization of parameter distributions conditioned on features.

Improved sampling of plausible parameters considering surrogate errors.

Demonstrated usability on three simulation datasets.

Abstract

Recently, neural surrogate models have emerged as a compelling alternative to traditional simulation workflows. This is accomplished by modeling the underlying function of scientific simulations, removing the need to run expensive simulations. Beyond just mapping from input parameter to output, surrogates have also been shown useful for inverse problems: output to input parameters. Inverse problems can be understood as search, where we aim to find parameters whose surrogate outputs contain a specified feature. Yet finding these parameters can be costly, especially for high-dimensional parameter spaces. Thus, existing surrogate-based solutions primarily focus on finding a small set of matching parameters, in the process overlooking the broader picture of plausible parameters. Our work aims to model and visualize the distribution of possible input parameters that produce a given output feature. To achieve this goal, we aim to address two challenges: (1) the approximation error inherent in the surrogate model and (2) forming the parameter distribution in an interactive manner. We model error via density estimation, reporting high density only if a given parameter configuration is close to training parameters, measured both over the input and output space. Our density estimate is used to form a prior belief on parameters, and when combined with a likelihood on features, gives us an efficient way to sample plausible parameter configurations that generate a target output feature. We demonstrate the usability of our solution through a visualization interface by performing feature-driven parameter analysis over the input parameter space of three simulation datasets. Source code is available at https://github.com/matthewberger/seeing-the-many