# Explorable INR: An Implicit Neural Representation for Ensemble Simulation Enabling Efficient Spatial and Parameter Exploration

arXiv: https://arxiv.org/abs/2504.00904 · HTML: https://mlsanity.com/paper/2504.00904/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 53 references that are in the map.
- First posted on arXiv 1 Apr 2025.

## Builds on (most cited first, 28 of 28)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [Compressive Neural Representations of Volumetric Scalar Fields](https://mlsanity.com/paper/2104.04523/) (2021)
- [Reconstructing continuous distributions of 3D protein structure from cryo-EM images](https://mlsanity.com/paper/1909.05215/) (2019)
- [EikoNet: Solving the Eikonal equation with Deep Neural Networks](https://mlsanity.com/paper/2004.00361/) (2020)
- [NTopo: Mesh-free Topology Optimization using Implicit Neural Representations](https://mlsanity.com/paper/2102.10782/) (2021)
- [ContactNets: Learning Discontinuous Contact Dynamics with Smooth, Implicit Representations](https://mlsanity.com/paper/2009.11193/) (2020)
- [InSituNet: Deep Image Synthesis for Parameter Space Exploration of Ensemble Simulations](https://mlsanity.com/paper/1908.00407/) (2019)
- [Fast Neural Representations for Direct Volume Rendering](https://mlsanity.com/paper/2112.01579/) (2021)
- [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)
- [VDL-Surrogate: A View-Dependent Latent-based Model for Parameter Space Exploration of Ensemble Simulations](https://mlsanity.com/paper/2207.13091/) (2022)
- [Continuous Field Reconstruction from Sparse Observations with Implicit Neural Networks](https://mlsanity.com/paper/2401.11611/) (2024)
- [Interactive Volume Visualization via Multi-Resolution Hash Encoding based Neural Representation](https://mlsanity.com/paper/2207.11620/) (2022)
- [Adaptively Placed Multi-Grid Scene Representation Networks for Large-Scale Data Visualization](https://mlsanity.com/paper/2308.02494/) (2023)
- [NNVA: Neural Network Assisted Visual Analysis of Yeast Cell Polarization Simulation](https://mlsanity.com/paper/1904.09044/) (2019)
- [Hierarchical Neural Operator Transformer with Learnable Frequency-aware Loss Prior for Arbitrary-scale Super-resolution](https://mlsanity.com/paper/2405.12202/) (2024)
- [Regularized Multi-Decoder Ensemble for an Error-Aware Scene Representation Network](https://mlsanity.com/paper/2407.19082/) (2024)
- [Neural Fields for Interactive Visualization of Statistical Dependencies in 3D Simulation Ensembles](https://mlsanity.com/paper/2307.02203/) (2023)
- [Improving Efficiency of Iso-Surface Extraction on Implicit Neural Representations Using Uncertainty Propagation](https://mlsanity.com/paper/2402.13861/) (2024)

## Built on by (most cited first, 8 of 8)

- [ECoNGS: Efficient Compressive Neural Gaussian Splats for Volume Visualization](https://mlsanity.com/paper/2607.18466/) (2026)
- [FA-INR: Adaptive Implicit Neural Representations for Interpretable Exploration of Simulation Ensembles](https://mlsanity.com/paper/2506.06858/) (2025)
- [Seeing the Many: Exploring Parameter Distributions Conditioned on Features in Surrogates](https://mlsanity.com/paper/2508.13088/) (2025)
- [Refine Now, Query Fast: A Decoupled Refinement Paradigm for Implicit Neural Fields](https://mlsanity.com/paper/2602.15155/) (2026)
- [DiffUNet^2: Bidirectional Conditional Diffusion for Probabilistic Scientific Spatiotemporal Modeling](https://mlsanity.com/paper/2606.03926/) (2026)
- [Lossless-INR: Lossless Volumetric Implicit Neural Representations](https://mlsanity.com/paper/2607.18150/) (2026)
- [Direct Topology Tracking in Continuous Implicit Models](https://mlsanity.com/paper/2609.12157/) (2026)
- [DiffusionShadow: Diffusion-based Shadow Caching for Neural Volume Rendering](https://mlsanity.com/paper/2609.30658/) (2026)

## Abstract (arXiv)

With the growing computational power available for high-resolution ensemble simulations in scientific fields such as cosmology and oceanology, storage and computational demands present significant challenges. Current surrogate models fall short in the flexibility of point- or region-based predictions as the entire field reconstruction is required for each parameter setting, hence hindering the efficiency of parameter space exploration. Limitations exist in capturing physical attribute distributions and pinpointing optimal parameter configurations. In this work, we propose Explorable INR, a novel implicit neural representation-based surrogate model, designed to facilitate exploration and allow point-based spatial queries without computing full-scale field data. In addition, to further address computational bottlenecks of spatial exploration, we utilize probabilistic affine forms (PAFs) for uncertainty propagation through Explorable INR to obtain statistical summaries, facilitating various ensemble analysis and visualization tasks that are expensive with existing models. Furthermore, we reformulate the parameter exploration problem as optimization tasks using gradient descent and KL divergence minimization that ensures scalability. We demonstrate that the Explorable INR with the proposed approach for spatial and parameter exploration can significantly reduce computation and memory costs while providing effective ensemble analysis.