Refine Now, Query Fast: A Decoupled Refinement Paradigm for Implicit Neural Fields

Tianyu Xiong; Skylar Wurster; Han-Wei Shen

cs.LGFeb 16, 2026

Refine Now, Query Fast: A Decoupled Refinement Paradigm for Implicit Neural Fields

Authors: Tianyu Xiong, Skylar Wurster, Han-Wei Shen

Organizations: Department of Computer Science and Engineering Ohio State University Columbus, OH 43210, USA · Adobe San Francisco, CA, USA

Abstract

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 $\times$ 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.

Figures & tables

Figure 1: Our Decoupled Representation Refinement (DRR) paradigm synthesizes the strengths of slow, high-fidelity MLPs and fast, less expressive feature grid, or embedding-based models (compared at similar model sizes) as a well-rounded design pattern for fast and accurate INRs.

Figure 2: Concrete instantiation of the DRR paradigm via DRR-Net. Part (a) illustrates the overall architectural components, while part (b) and (c) detail the unification and refinement procedure applied to the base multi-resolution embedding structures.

Dataset	Structure	Variable	# Parameters	Resolution	# Training	# Testing
Nyx	3D Cartesian Grid	Dark Matter Density	3	$256^{3}$	100	30
MPAS-Ocean	Voronoi Mesh	Ocean Temperature	4	11845146 vertices	70	30
Cloverleaf3D	3D Cartesian Grid	Energy	6	$128^{3}$	500	100

Table 1: Description of ensemble simulation datasets used for evaluations.

Dataset	Model	Rel L2 $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	TFLOPs / $10^{9}$ pts $\downarrow$	Inference Time (sec)	Training Time (hr)	# Params
Nyx	K-Planes	1.96e-01	28.86	0.797	57.0	21.6s	23.8h	12.1M
	FA-INR	3.95e-02	42.79	0.975	2569.2	287.2s	64.1h	9.5M
	Explorable-INR	4.64e-02	41.39	0.972	39.6	9.6s	24.7h	14.7M
	DRR-Net (ours)	3.18e-02	44.69	0.986	57.2	10.7s	24.0h	8.9M
MPAS-Ocean	K-Planes	3.81e-01	15.45	-	60.0	16.9s	6.6h	13.5M
	FA-INR	5.58e-03	52.13	-	422.1	89.8s	21.1h	1.0M

Table 2: Results for the conditional generalization task. DRR-Net achieves a state-of-the-art fidelity and efficiency in all datasets, with more pronounced benefits for Nyx and Cloverleaf3D.

Dataset	Model	Unseen Fields ( Rel L2 $\downarrow$ / PSNR $\uparrow$ / SSIM $\uparrow$ )	Trained Fields ( Rel L2 $\downarrow$ / PSNR $\uparrow$ / SSIM $\uparrow$ )	Inference Time (sec)	# Params
Nyx	K-Planes	1.89e-01 / 29.18 / 0.709	2.91e-01 / 29.62 / 0.716	75.3s	3.9M
	FA-INR	4.55e-02 / 41.57 / 0.971	7.29e-02 / 41.65 / 0.971	1245.1s	9.5M
	Explorable-INR	6.48e-02 / 38.50 / 0.959	8.44e-02 / 40.38 / 0.963	38.6s	10.0M
	DRR-Net (ours)	4.31e-02 / 42.04 / 0.975	7.07e-02 / 41.92 / 0.975	43.7s	8.7M
Cloverleaf3D	K-Planes	4.47e-01 / 35.52 / 0.914	5.78e-01 / 36.04 / 0.919	81.5s	3.1M
	FA-INR	1.07e-01 / 47.98 / 0.992	9.15e-02 / 52.06 / 0.996	327.8s	1.0M

Table 3: Spatio-conditional generalization results. DRR-Net consistently attains the best fidelity with highly competitive inference efficiency matching the embedding-only model Explorable-INR.

Model	Augment Method	Nyx			Cloverleaf3D
	Augment Method	Rel L2 $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	Rel L2 $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$
K-Planes	None	2.07e-01	28.41	0.783	8.57e-01	29.87	0.784
	VC	1.98e-01	28.80	0.792	8.87e-01	29.57	0.775
	VP-S (ours)	2.05e-01	28.48	0.804	7.89e-01	30.59	0.801
	VP-SC (ours)	1.96e-01	28.86	0.797	8.42e-01	30.02	0.787
FA-INR	None	4.96e-02	40.81	0.961	6.40e-01	32.40	0.764

Table 4: Ablation study of data augmentation strategies, showing that proposed VP methods consistently outperform the no-augmentation and VC baselines across diverse INR architectures.

Appendix figures & tables17 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 3: Architecture of the refiner network, which consists of stacked GLU blocks with pre-normalization and a ReLU intermediate activation.

Model	Hyperparameter	Nyx	MPAS-Ocean	Cloverleaf3D
K-Planes	Spatial Plane Base Resolution	$32$	$32$	$16$
	Spatial Plane Multi-Res Multipliers	$[1,2,4,8]$	$[1,2,4,8]$	$[1,2,4,8]$
	Condition-Only Plane Resolution	$25$	$25$	$25$
	Plane Embedding Dim	32	32	32
	Decoder MLP Hidden Dim	128	128	128
	Decoder MLP Layers	3 layers	3 layers	3 layers

Appendix

Table 5: Architectural hyperparameters for INR surrogate models across the evaluated ensemble simulation datasets.

Dataset	epochs	condition batch size $N_{c}$	coordinate batch size $N_{x}$	condition- impsmp	coordinate-impsmp
Nyx	50	16	$2^{16}$	$\checkmark$	$\checkmark$
MPAS-Ocean	50	16	$2^{16}$	$\times$	$\checkmark$
Cloverleaf3D	50	32	$2^{12}$	$\times$	$\checkmark$

Appendix

Table 6: Training hyperparameters for each dataset.

Figure 4: Visual comparison on an unseen field from the Cloverleaf3D (top) and Nyx (bottom) dataset. Reconstructed $128^{3}$ points in just 0.05 seconds, our DRR-Net better captures complex high-energy and high-density structures in respective datasets than competing state-of-the-art surrogates, demonstrating a superior balance of fidelity and speed.

Figure 5: Qualitative comparison on the unstructured MPAS-Ocean dataset with one depth layer extracted. The visualization highlights the effectiveness of the DRR paradigm: while the standard embedding-based Explorable-INR suffers from severe artifacts, our DRR-Net successfully captures fine temperature variations, demonstrating the framework’s power to enhance a grid-based backbone on challenging, non-Cartesian data, while maintaining efficiency.

Dataset	Model	Unseen Fields (Rel L2 $\downarrow$ / PSNR $\uparrow$ / SSIM $\uparrow$ )	Trained Fields (Rel L2 $\downarrow$ / PSNR $\uparrow$ / SSIM $\uparrow$ )	Inference Time (sec)	# Params
Nyx	K-Planes	1.49e-01 / 29.44 / 0.667	1.46e-01 / 29.91 / 0.688	11.4s	3.9M
	FA-INR	2.78e-02 / 44.00 / 0.987	2.76e-02 / 44.38 / 0.988	156.3s	9.5M
	Explorable-INR	4.46e-02 / 39.89 / 0.979	3.29e-02 / 42.86 / 0.984	6.5s	10.0M
	DRR-Net (ours)	1.11e-02 / 51.95 / 0.998	1.15e-02 / 51.99 / 0.998	8.0s	8.7M
Cloverleaf3D	K-Planes	4.33e-01 / 35.32 / 0.903	4.15e-01 / 35.94 / 0.909	16.1s	3.1M
	FA-INR	9.92e-02 / 48.12 / 0.991	6.24e-02 / 52.39 / 0.995	53.8s	1.0M

Appendix

Table 7: Conditional generalization results for models trained on data with

\times

2 reduced spatial resolution. Consistent with findings in Sec. 4.3 , DRR-Net achieves the highest fidelity and efficiency. Notably, DRR-Net exhibits a significant expressiveness advantage in modeling the Nyx dataset in the low-resolution setup.

Dataset	DRR-Net Variants	Rel L2 $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	TFLOPs / $10^{9}$ pts $\downarrow$	# Params
Nyx	Embedding-Only	4.02e-02	42.64	0.979	40.1	8.1M
	+ Spatial Refiner	3.17e-02	44.71	0.986	57.2	8.7M
	+ Condition Refiner	3.18e-02	44.69	0.986	57.2	8.9M
MPAS-Ocean	Embedding-Only	1.24e-02	45.22	-	25.8	3.57M
	+ Spatial Refiner	8.54e-03	48.43	-	47.3	4.57M
	+ Condition Refiner	7.76e-03	49.26	-	47.3	4.64M

Appendix

Table 8: Ablation study on the DRR components, demonstrating that the embedding refinement procedure provides considerable performance gains over the embedding-only baseline.

Dataset	Refinement Regime	Rel L2 $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	TFLOPs / $10^{9}$ pts $\downarrow$	# Params
Nyx	No Refinement	4.02e-02	42.64	0.979	40.1	8.1M
	+ Refiners	4.48e-02	41.70	0.975	40.1	8.3M
	$\pi$ Refinement	4.04e-02	42.60	0.978	55.9	8.1M
	+ Refiners	3.18e-02	44.69	0.986	57.2	8.9M
MPAS-Ocean	No Refinement	1.24e-02	45.22	-	25.8	3.57M
	+ Refiners	1.38e-02	44.29	-	25.8	3.65M

Appendix

Table 9: Ablation study analyzing the impact of the refiner on low-capacity base embeddings versus

\pi

-transformed embeddings. Accuracy metrics are reported for the unseen simulation conditions. We categorize the results into two groups, using the base embedding and the

\pi

-transformed embedding as their respective baselines. The results demonstrate that the proposed

\pi

-transformation not only enhances embedding capacity on its own but also acts as a pivotal enabler, unlocking the full potential of the refiner network.

Figure 6: Ablation studies of the frequency hyperparameter of Positional Encoding for feature upsampling. A moderate frequency level around 6 is observed to consistently improve the efficacy of DRR-Net.

Figure 7: Comparisons of DRR-Net with different maximum resolution for the structural super-resolution (SSR). The baseline configuration without SSR is presented. SSR exhibits the most advantage for MPAS-Ocean and Cloverleaf3D.

Figure 8: Visual ablation on unseen Cloverleaf3D (top) and Nyx (bottom) members with volume rendering for understanding the role of refiner in the proposed DRR paradigm. Columns: (1) Ground Truth; (2) Full DRR-Net; (3) Inference with refiner disabled; (4) $\pi$ -Refinement baseline. Two key observations: (1) Disabling the refiner yields severe artifacts (Col. 3), confirming it is an integral part of the learned representation in DRR-Net. (2) Compared to the model trained only with the $\pi$ refinement (Col. 4), the Full DRR-Net (Col. 2) effectively suppresses noisy artifacts in smooth regions while sharply resolving high-frequency details in shades of red, validating its superior multi-scale feature fusion.

Figure 9: Comparison of the noise threshold for the isolated spatial-only and condition-only VP methods in the Nyx dataset. We observe that incorporating VP-S or VP-C can both improve the accuracy over a non-augmented baseline.

Figure 10: Ablation study on varying the condition noise thresholds for VP-SC with a constant spatial noise level. Results show that adding the condition noises can consistently improve DRR-Net quality marginally, compared to VP-S.

Gigapixel Image	Model	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	Inference Time (sec)	# Params
Girl with a Pearl Earring 23466 $\times$ 20000	Grid	25.80	0.9180	0.2504	0.86s	4.2M
	+ DRR	+0.12	+0.0016	-0.0040	1.16s	4.3M
	MRGrid	25.86	0.9191	0.2468	1.17s	4.2M
	+ DRR	-0.02	-0.0012	+0.0055	2.28s	4.3M
	NGP	26.45	0.9154	0.2235	0.90s	5.2M
	SIREN	24.64	0.8713	0.2827	27.82s	2.1M

Appendix

Table 10: Performance comparison of various INRs with and without DRR for two Gigapixel images. Rows marked “+ DRR” show the change (

\Delta

) relative to the base model above. Green indicates an improvement. Strong baseline models, including NGP and SIREN, are also evaluated to serve as a reference.

Figure 11: Visualization of a Gigapixel image with a highly complex object composition at a progressive level of detail. The addition of DRR significantly improves the visual fidelity for the Multi-Resolution Grid (MRGrid) model. “Tokyo” by Trevor Dobson (CC BY-NC-ND 2.0).

Gigapixel Image	Model	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	Inference Time (sec)	# Params
Girl with a Pearl Earring Train: 11733 $\times$ 10000 Test: 23466 $\times$ 20000	Grid	25.80	0.9178	0.2514	0.88s	4.2M
	+ DRR	+0.13	+0.0021	-0.0053	1.16s	4.3M
	MRGrid	25.86	0.9188	0.2489	1.19s	4.2M
	+ DRR	+0.03	+0.0003	+0.0009	3.21s	4.3M
	NGP	26.31	0.9151	0.2354	0.90s	5.2M
	SIREN	24.81	0.8776	0.2786	27.82s	2.1M

Appendix

Table 11: Zero-shot

\times

2 super-resolution evaluation for Gigapixel images. The results for DRR-enhanced models are shown as the

\Delta

compared to the baseline in the previous row. NGP and SIREN are shown as performance references. Green indicates an improvement.

Dataset	Model	PSNR $\uparrow$	LPIPS $\downarrow$	Inference Time (sec)	# Params
Lego	Grid	33.33	0.041	48s	33.6M
	+ DRR	+0.06	+0.002	51s	33.6M
	MRGrid	32.49	0.053	55s	19.0M
	+ DRR	+0.31	-0.001	51s	19.0M
	TriPlane	35.32	0.032	71s	9.4M
	+ DRR	+0.07	-0.005	67s	9.7M

Appendix

Table 12: Performance comparison of neural radiance field (NeRF) models with DRR-Enhanced embedding structures. The performance of NGP ( Müller et al., 2022 ) and the original NeRF model ( Mildenhall et al., 2020 ) is presented as a reference. Values for “+ DRR” rows show the change relative to the baseline structure above. Green indicates an improvement (higher PSNR, lower LPIPS).

Implicit Neural Representations

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Implicit Neural Representations Adaptive Sampling

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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\times

faster than the evaluated baselines.

Abstract

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