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

TL;DR

Explorable INR introduces an implicit neural representation surrogate tailored for high-resolution ensemble simulations that supports point-based spatial queries and efficient region- and parameter-space exploration. By combining grid- and plane-based spatial encodings with 1D parameter lines and fusing them via Hadamard products, the model achieves fast training and compact memory footprint while allowing direct uncertainty propagation through probabilistic affine forms. Uncertainty propagation yields mean/variance and covariance insights across spatial regions without dense reconstructions, and gradient-based KL-divergence optimization enables efficient inverse problem solving in parameter space. The approach demonstrates superior data-level accuracy against baseline surrogates and other INRs, with notable gains in mean-field quality, ensemble statistics, and rapid parameter discovery, offering a practical tool for exploring large-scales and highly parameterized scientific ensembles.

Abstract

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.

Figures (9)

• Figure 1: The proposed Explorable INR works as follows: (A) Take coordinates and simulation parameters as input. (B) Query spatial coordinates in XYZ 3D feature grid ($64^{3}$), and XY, YZ, and XZ feature planes ($256^{2}$); query simulation parameters on 1D feature lines ($16^{1}$). The features are interpolated by corner features. (C) The spatial and parameter features are fused via the Hadamard product; the fused vectors are concatenated into an ensemble feature, which is then decoded by an MLP with 3 hidden layers and 128 hidden nodes to predict the physical feature.
• Figure 2: The plot of interpolated feature element value against input parameter is a piecewise linear function for a specific parameter. Different color indicates different pieces of the function.
• Figure 3: Given the input distribution, we compute a linear approximation of the nonlinear function. The red area represents the approximation error. The actual error is quantified by integrating this red area weighted by the input distribution.
• Figure 4: The comparison of images generated by the Explorable INR, VDL-Surrogate, InSituNet, Instant-NGP, and K-Planes for the Nyx dataset against the ground truth image is presented. The red box highlights the intricate details in the Nyx data. The blue/red points stand for the voxel difference between the ground truth and the reconstructed field.
• Figure 5: The figure compares the performance of uncertainty propagation (UP) and sampling (SPL) methods through statistics on Nyx results. Given the same running time, (a) and (b) are the PSNR and similarity index measures (SSIM) of mean and standard deviation (STD) for both methods. Given the same PSNR and SSIM of mean and STD, (c) and (d) are the running time for both methods to achieve the value.