Refined Grid Sampling for Efficient Implicit Neural Representations of Large-Scale Scientific Data
Authors: Guang Zhao, Xihaier Luo, Sean McCue, Luke P. Van Roekel, Seungjun Lee, Yihui Ren, Shinjae Yoo, Wei Xu
Organizations: Brookhaven National Laboratory Upton, NY 11973, USA · University of California San Diego La Jolla, CA 92093, USA · Los Alamos National Laboratory Los Alamos, NM 87545, USA
Implicit neural representations (INRs) offer a powerful framework for modeling high-dimensional physical fields, but their training remains inefficient because evaluating dense coordinate grids is computationally expensive. Existing coordinate-pruning strategies rely on local error functions that can oversample correlated points and incur substantial overhead from full-grid error evaluation. We introduce Refined Grid Sampling (RGS), which combines stratified grid sampling, error-based refinement, and dynamic grid-resolution adjustment. This design reduces spatial redundancy without evaluating errors over the full grid. On high-resolution Navier--Stokes fields, RGS achieves higher reconstruction accuracy within a fixed wall-clock budget and reaches the accuracy of full-grid training up to 6× faster than the evaluated baselines.
Figures & tables
Figure 1: Evolution of gradient cosine correlation during INR training. Left: Heatmaps of the correlation between a reference coordinate and its neighbors within a 60×60 region at training epochs t=10 , 200, and 1,600. The high-correlation area contracts during training, indicating reduced spatial redundancy. Right: Center-row correlation profiles, showing sharper decay at later epochs.
Figure 2: Refined Grid Sampling (RGS) framework. RGS combines stratified grid sampling with error-ranked selection to balance spatial coverage and informative points, reducing redundancy and forward-pass cost. Sampling starts with coarse grids and progressively refines as gradient correlations decay, improving reconstruction accuracy.
Figure 3: PSNR and error-map comparison of sampling strategies on Navier–Stokes fields.
Sampling strategy
PSNR
SSIM
Rel. RMSE
Time/epoch (s)
Full Training
37.19 ± 2.29
0.978 ± 0.024
0.092 ± 0.031
0.190
Random
43.72 ± 1.20
0.982 ± 0.004
0.042 ± 0.006
0.003
EVOS
37.41 ± 1.70
0.930 ± 0.017
0.087 ± 0.017
0.006
INT
18.38 ± 0.85
0.212 ± 0.094
0.773 ± 0.109
0.036
RGS (ours)
56.24 ± 2.73
0.998 ± 0.001
0.010 ± 0.003
0.005
Table 1: Performance after a 20-second wall-clock budget, reported as mean ± standard deviation over six independently reconstructed time frames. Best values are shown in bold.
Appendix figures & tables2 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 4: PSNR versus training epochs for different sampling strategies. RGS converges faster and attains higher final accuracy than the error-driven baselines, while random sampling converges more slowly.
Figure 5: Training time versus epochs for different sampling strategies. RGS substantially reduces training time relative to full training and INT, while remaining competitive with random sampling and EVOS.
Implicit Neural Representations (INRs) have emerged as promising surrogates for large 3D scientific simulations due to their ability to continuously model spatial and conditional fields, yet they face a critical fidelity-speed dilemma: deep MLPs suffer from high inference cost, while efficient embedding-based models lack sufficient expressiveness. To resolve this, we propose the Decoupled Representation Refinement (DRR) architectural paradigm. DRR leverages a deep refiner network, alongside non-parametric transformations, in a one-time offline process to encode rich representations into a compact and efficient embedding structure. This approach decouples slow neural networks with high representational capacity from the fast inference path. We introduce DRR-Net, a simple network that validates this paradigm, and a novel data augmentation strategy, Variational Pairs (VP) for improving INRs under complex tasks like high-dimensional surrogate modeling. Experiments on several ensemble simulation datasets demonstrate that our approach achieves state-of-the-art fidelity, while being up to 27× faster at inference than high-fidelity baselines and remaining competitive with the fastest models. The DRR paradigm offers an effective strategy for building powerful and practical neural field surrogates and INRs in broader applications, with a minimal compromise between speed and quality.
Tianyu Xiong, Skylar Wurster, Han-Wei Shen
Department of Computer Science and Engineering Ohio State University Columbus, OH 43210, USA · Adobe San Francisco, CA, USA
Implicit neural representations (INRs) provide a flexible framework for modeling high-dimensional continuous fields, but their training is often inefficient due to uniform subsampling that ignores spatial heterogeneity. Existing adaptive sampling methods partially address this issue by prioritizing high-error samples, but typically operate at the point level, often leading to redundant sampling in localized regions and insufficient coverage of the domain. We propose ACES (Adaptive Coverage-aware Efficient Sampling), a structured sampling framework that improves training efficiency by decoupling coverage and importance. ACES constructs adaptive spatial partitions to ensure domain coverage and reduce redundancy, and applies region-level importance weighting to prioritize informative regions during training. We provide a theoretical analysis showing that adaptive partitioning reduces gradient variance by increasing within-region homogeneity, and that controlled bias in region-level weighting may improve optimization efficiency relative to standard unbiased estimators. Experiments on scientific field learning tasks demonstrate that ACES achieves faster convergence and lower error than uniform and pointwise adaptive sampling baselines, with the largest gains in fields with highly localized complexity.
Guang Zhao, Xihaier Luo, Huan-Hsin Tseng +4
Computing and Data Sciences, Brookhaven National Laboratory Upton, NY 11973, USA
Implicit neural representations (INRs) for time-varying volumetric data are typically trained using dense sampling over spatiotemporal coordinates, where each observation corresponds to a single point in space and time. This coordinate-wise formulation requires extensive sampling during optimization, leading to high computational cost and inefficient use of temporal structure. In this work, we revisit this design choice and show that dense spatiotemporal sampling is not necessary for learning time-varying fields. Instead, we represent the data as a collection of spatially indexed time series and train INRs using sequence-level supervision over each spatial location, rather than coordinate-wise scalar samples. This reformulation eliminates the need for dense spatiotemporal sampling and instead learns each spatial location from its full temporal evolution in a structured manner. We demonstrate that this representation is compatible with a range of existing INR architectures and consistently improves reconstruction quality, while significantly reducing training cost. Furthermore, we show that this formulation can be combined with mixture-of-experts architectures, and that our MoE instantiation further improves reconstruction quality compared to both the base reformulation and existing MoE-based INR methods, providing a stronger capacity allocation under heterogeneous temporal dynamics.
Weihan Zhang, Xuan Zhao, Yenwen Peng +2
School of Computer Science and Engineering, Sun Yat-sen University · Department of Computer Science, Hong Kong Baptist University · School of Computer Science and Engineering, Sun Yat-sen University, Guangdong Province Key Laboratory of Computational Science, and National Supercomputer Center in Guangzhou