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

2025-08-18

AI Summary

Existing surrogate models primarily focus on identifying a single optimal parameter set, neglecting the broader distribution of parameters that satisfy a given target output. Method: We propose a joint input-output space density estimation framework that integrates neural surrogate modeling, feature likelihood estimation, and Bayesian inference to construct a confidence-aware parameter prior. This enables efficient sampling and visualization of plausible parameter sets in high-dimensional spaces. Contribution/Results: Our key innovation lies in unifying density estimation with inverse inference to support interactive exploration of multi-solution parameter distributions. Evaluated on three scientific simulation datasets, the method demonstrates effectiveness in goal-directed parameter analysis, significantly enhancing users’ understanding of and ability to control the parameter-feature mapping relationship.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

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

Problem

• Modeling input parameter distributions for given output features
• Addressing surrogate model approximation error and interactive distribution formation
• Visualizing plausible parameters in high-dimensional spaces efficiently

Innovation

• Density estimation for surrogate model error
• Interactive parameter distribution visualization
• Feature-driven parameter sampling method