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

arXiv: https://arxiv.org/abs/2508.13088 · HTML: https://mlsanity.com/paper/2508.13088/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 47 references that are in the map.
- First posted on arXiv 18 Aug 2025.

## Builds on (most cited first, 22 of 22)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [From data to functa: Your data point is a function and you can treat it like one](https://mlsanity.com/paper/2201.12204/) (2022)
- [Uncertainty Estimates and Multi-Hypotheses Networks for Optical Flow](https://mlsanity.com/paper/1802.07095/) (2018)
- [Bayes' Rays: Uncertainty Quantification for Neural Radiance Fields](https://mlsanity.com/paper/2309.03185/) (2023)
- [Compressive Neural Representations of Volumetric Scalar Fields](https://mlsanity.com/paper/2104.04523/) (2021)
- [FisherRF: Active View Selection and Uncertainty Quantification for Radiance Fields using Fisher Information](https://mlsanity.com/paper/2311.17874/) (2023)
- [Spatial Functa: Scaling Functa to ImageNet Classification and Generation](https://mlsanity.com/paper/2302.03130/) (2023)
- [InSituNet: Deep Image Synthesis for Parameter Space Exploration of Ensemble Simulations](https://mlsanity.com/paper/1908.00407/) (2019)
- [GNN-Surrogate: A Hierarchical and Adaptive Graph Neural Network for Parameter Space Exploration of Unstructured-Mesh Ocean Simulations](https://mlsanity.com/paper/2202.08956/) (2022)
- [A Generative Model for Volume Rendering](https://mlsanity.com/paper/1710.09545/) (2017)
- [VDL-Surrogate: A View-Dependent Latent-based Model for Parameter Space Exploration of Ensemble Simulations](https://mlsanity.com/paper/2207.13091/) (2022)
- [Compositional Generative Inverse Design](https://mlsanity.com/paper/2401.13171/) (2024)
- [NNVA: Neural Network Assisted Visual Analysis of Yeast Cell Polarization Simulation](https://mlsanity.com/paper/1904.09044/) (2019)
- [Explorable INR: An Implicit Neural Representation for Ensemble Simulation Enabling Efficient Spatial and Parameter Exploration](https://mlsanity.com/paper/2504.00904/) (2025)
- [Regularized Multi-Decoder Ensemble for an Error-Aware Scene Representation Network](https://mlsanity.com/paper/2407.19082/) (2024)
- [SurroFlow: A Flow-Based Surrogate Model for Parameter Space Exploration and Uncertainty Quantification](https://mlsanity.com/paper/2407.12884/) (2024)
- [Neural Fields for Interactive Visualization of Statistical Dependencies in 3D Simulation Ensembles](https://mlsanity.com/paper/2307.02203/) (2023)
- [Uncertainty-Informed Volume Visualization using Implicit Neural Representation](https://mlsanity.com/paper/2408.06018/) (2024)

## Abstract (arXiv)

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