基于阻尼激活函数的多维度隐式神经时变体数据压缩

doi:10.11996/JG.j.2095-302X.2025040826

摘要/Abstract

摘要：

大规模数值仿真的时变体数据在科学研究中具有重要价值，但其巨大的规模对I/O带宽和磁盘存储带来了严峻挑战，影响了数据可视化和分析的效率。传统的有损压缩技术在高压缩比条件下易丢失重要特征，深度学习模型在压缩体数据上虽表现良好，但通常要求在压缩前能访问整个数据集，其存在一定的局限性。隐式神经表示(INRs)凭借其通用性成为压缩大规模体数据的有力工具，针对现有方法采用单个大型多层感知机(MLP)对全局数据进行编码，导致训练和推理过程较为缓慢，且难以准确拟合高频信息。提出了一种基于阻尼函数的均匀分区隐式神经表示方法，用于大规模时变体数据的高效压缩。首先，采用均匀分区方法，以多个MLP分别对局部数据进行拟合。通过均匀化分区大小，实现MLP之间的平衡并行化，从而显著提高了训练和推理的效率。其次，引入阻尼函数作为激活函数，克服频谱偏差问题，无需额外的位置编码即可捕捉高频信息。最后，通过复制相邻单元格信息解决了数据分割带来的边界伪影问题。实验结果表明，该方法在多个时变体数据上实现了更高的压缩效率和更精细的细节还原，展现了优越的压缩性能。

关键词: 隐式神经表示, 体数据压缩, 阻尼函数, 科学可视化, 频谱偏差

Abstract:

Time-varying volume data from large-scale numerical simulations holds significant value in scientific research, but its vast size poses severe challenges to I/O bandwidth and disk storage, hindering the efficiency of data visualization and analysis. Traditional lossy compression techniques tend to lose important features at high compression ratios. While deep learning models have shown good performance in compressing volumetric data, they typically require access to the entire dataset before compression, which presents certain limitations. Implicit neural representations (INRs) have emerged as a powerful tool for compressing large-scale volumetric data due to their versatility. However, existing methods primarily rely on a single large multi layer perceptron (MLP) to encode global data, resulting in slow training and inference, and difficulty in accurately capturing high-frequency information. To address these issues, a uniform partitioning implicit neural representation method based on a damping function was proposed for efficient compression of large-scale time-varying volume data. First, a uniform partitioning strategy was applied, where multiple MLPs were used to fit local data separately. By equalizing partition sizes, balanced parallelization among the MLPs was achieved, significantly improving the efficiency of both training and inference. Second, a damping function was introduced as the activation function to overcome spectral bias, enabling the capture of high-frequency information without the need for extra positional encoding. Finally, adjacent cell information replication was used to solve boundary artifacts from partitioning. Experimental results showed that this method achieved higher compression efficiency and finer detail preservation across several time-varying volume datasets, demonstrating superior compression performance.

Key words: implicit neural representation, volumetric data compression, damping function, scientific visualization, spectral bias

中图分类号:

郭荣, 焦辰玥, 高鑫, 邓佳康, 田校先, 毕重科. 基于阻尼激活函数的多维度隐式神经时变体数据压缩[J]. 图学学报, 2025, 46(4): 826-836.

GUO Rong, JIAO Chenyue, GAO Xin, DENG Jiakang, TIAN Xiaoxian, BI Chongke. Multi-dimensional implicit neural compression of time-varying volume data based on damping activation functions[J]. Journal of Graphics, 2025, 46(4): 826-836.

图/表 8

图1 网络结构图((a) 时间步分割；(b) 空间均匀分区；(c) MLP模型；(d) 体数据还原；(e) 空间合并结果)

Fig. 1 Network structure diagram ((a) Time step segmentation; (b) Uniform spatial partitioning; (c) MLP model; (d) Volume data restoration; (e) Space merging result)

表1 各方法在不同数据集上的PSNR、SSIM、编码时间(ET)和压缩率(CR)

Table 1 PSNR, SSIM, encoding time (ET), and compression rate (CR) of each method on different datasets

数据集	方法	PSNR/dB	SSIM	ET	CR
科考船	TTHRESH	34.56	0.970 8	266.52 s	1629
	SZ3	37.12	0.977 2	51.72 s	1647
	Neurcomp	38.45	0.975 8	11.84 h	1634
	Ours	39.85	0.980 5	3.02 h	1649
半圆柱扰流	TTHRESH	36.74	0.986 1	346.60 s	1176
	SZ3	35.45	0.982 3	12.17 s	1180
	Neurcomp	36.92	0.987 4	43.85 h	1182
	Ours	37.67	0.991 5	4.41 h	1183
激波相互作用涡	TTHRESH	26.12	0.933 1	102.72 s	765
	SZ3	28.94	0.967 0	82.55 s	775
	Neurcomp	31.49	0.962 5	4.89 h	704
	Ours	32.81	0.968 2	36.95 m	770

图2 各种方法压缩结果体渲染对比图((a) TTHRESH；(b) SZ3；(c) Neurcomp；(d) 本文方法；(e) 真值)

Fig. 2 Comparison of volumetric rendering results for different compression methods ((a) TTHRESH; (b) SZ3; (c) Neurcomp; (d) Ours; (e) Ground truth)

图3 各种方法压缩结果等值面对比图((a) TTHRESH；(b) SZ3；(c) Neurcomp；(d) 本文方法；(e) 真值)

Fig. 3 Comparison of isosurface results for different compression methods ((a) TTHRESH; (b) SZ3; (c) Neurcomp; (d) Ours; (e) Ground truth)

图4 不同激活函数损失下降速率对比

Fig. 4 Comparison of loss reduction rates of different activation functions

图5 边界伪影处理对比图((a) 真实值；(b) 无边界；(c) 边界为5；(d) 边界为10)

Fig. 5 Boundary artifact processing comparison chart ((a) Ground truth; (b) Borderless; (c) The boundary equals 5; (d) The boundary equals 10)

表2 单个MLP和多个小型MLP在“激波相互作用涡”数据集上的PSNR、SSIM、编码时间(ET)和压缩率(CR)

Table 2 PSNR, SSIM, encoding time (ET), and compression rate (CR) of a single MLP and multiple small MLPs on the ‘Shock wave’ dataset

方法	PSNR/dB	SSIM	ET	CR
Single MLP	35.44	0.957 2	6.26 h	684
Ours	36.78	0.975 6	35.11 m	693

图6 “激波相互作用涡”数据相邻时间步均方误差对比图

Fig. 6 The comparison of mean squared error for adjacent time steps of the ‘Shock wave’ data

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