High-Fidelity Compression of Seismic Velocity Models via SIREN Auto-Decoders

Caiyun Liu; Xiaoxue Luo; Jie Xiong

cs.LGMar 15, 2026

High-Fidelity Compression of Seismic Velocity Models via SIREN Auto-Decoders

Authors: Caiyun Liu, Xiaoxue Luo, Jie Xiong

Organizations: School of Information and Mathematics, Yangtze University, Jingzhou, Hubei 434023, P.R. China · School of Electronic Information and Electrical Engineering, Yangtze University, Jingzhou, Hubei 434023, P.R. China

Abstract

Implicit Neural Representations (INRs) have emerged as a powerful paradigm for representing continuous signals independently of grid resolution. In this paper, we propose a high-fidelity neural compression framework based on a SIREN (Sinusoidal Representation Networks) auto-decoder to represent multi-structural seismic velocity models from the OpenFWI benchmark. Our method compresses each 70x70 velocity map (4,900 points) into a compact 256-dimensional latent vector, achieving a compression ratio of 19:1. We evaluate the framework on 1,000 samples across five diverse geological families: FlatVel, CurveVel, FlatFault, CurveFault, and Style. Experimental results demonstrate an average PSNR of 32.47 dB and SSIM of 0.956, indicating high-quality reconstruction. Furthermore, we showcase two key advantages of our implicit representation: (1) smooth latent space interpolation that generates plausible intermediate velocity structures, and (2) zero-shot super-resolution capability that reconstructs velocity fields at arbitrary resolutions up to 280x280 without additional training. The results highlight the potential of INR-based auto-decoders for efficient storage, multi-scale analysis, and downstream geophysical applications such as full waveform inversion.

Figures & tables

Figure 1: Comparison of grid-based and implicit neural representations for seismic velocity fields. (a) Ground truth velocity model at $70\times 70$ resolution (velocity range: 1500-4000 m/s). (b) Traditional grid-based representation with $15\times 15$ sampling, showing discretization artifacts at sharp interfaces (highlighted in red). The yellow dashed rectangle indicates a single grid cell with constant velocity value. (c) SIREN implicit representation reconstructing the full $70\times 70$ field from a 256-dimensional latent code, demonstrating continuous, artifact-free modeling with PSNR of 37.93 dB. The white contour lines illustrate the continuous nature of the implicit representation.

Figure 2: Spectral bias comparison between standard ReLU MLP and SIREN. (a) Standard ReLU MLP exhibits strong low-frequency bias, with amplitude dropping rapidly above 25 Hz, failing to capture high-frequency components. (b) SIREN with periodic activation functions maintains near-uniform response across a wide frequency range, enabling accurate representation of sharp features and discontinuities.

Figure 3: Comparison of auto-encoder and auto-decoder architectures. (a) Traditional auto-encoder: input $x$ is encoded into a latent code $z$ by $E_{\phi}$ , then decoded to $\hat{x}$ by $D_{\theta}$ . (b) Auto-decoder (ours): learnable latent codes $\{z_{i}\}$ are directly optimized with a shared decoder $f_{\theta}$ , eliminating the encoder and using $L_{2}$ regularization.

Figure 4: SIREN auto-decoder framework overview. Input spatial coordinates $(x,z)$ and a learnable latent code $\mathbf{z}_{i}$ are concatenated and fed into the SIREN decoder $f_{\theta}$ , which consists of multiple layers with periodic activation functions $\sin(\omega_{0}\cdot)$ . The decoder outputs the reconstructed velocity field $\hat{\mathbf{V}}_{i}(x,z)$ . During training, the decoder parameters and latent codes are jointly optimized using reconstruction loss and $L_{2}$ regularization.

Layer	Type	Input Dim	Output Dim
Input Layer	SIREN ( $\sin$ )	$2+256=258$	512
Hidden Layer 1	SIREN ( $\sin$ )	512	512
Hidden Layer 2	SIREN ( $\sin$ )	512	512
Hidden Layer 3	SIREN ( $\sin$ )	512	512
Hidden Layer 4	SIREN ( $\sin$ )	512	512
Output Layer	Linear	512	1

Table 1: SIREN Decoder Architecture Details

Figure 5: Comparison of training and inference phases in the auto-decoder framework. (a) Training phase: learnable latent codes $\{\mathbf{z}_{i}\}$ and shared decoder $f_{\theta}$ are jointly optimized. Reconstruction loss (MSE) compares output $\hat{\mathbf{V}}_{i}$ with ground truth $\mathbf{V}_{i}$ . (b) Inference phase: fixed latent codes $\mathbf{z}_{i}^{*}$ and trained decoder $f_{\theta}^{*}$ are used for efficient reconstruction without further optimization.

Parameter	Value
Latent dimension $d$	256
Hidden features	512
Hidden layers $L$	4
Batch size	32
Learning rate	$2\times 10^{-4}$
Epochs	3000

Table 2: Training Hyperparameters

Geological Family	Description	Samples
FlatVel	Simple flat layer structures with constant velocities	200
CurveVel	Curved layer structures simulating folded geology	200
FlatFault	Flat layers with fault discontinuities	200
CurveFault	Curved layers with fault discontinuities	200
Style	Complex velocity patterns from natural images	200
Total		1000

Table 3: OpenFWI Dataset Composition

Property	Value
Total samples	1000
Grid size	$70\times 70$
Total points per sample	4,900
Value range (raw)	[1500, 4000] (approx.)
Value range (normalized)	$[-1,1]$
Compression ratio	19:1 (4,900 $\rightarrow$ 256)

Table 4: Dataset Statistics

Hardware
GPU	NVIDIA RTX 3080 (10GB)
CPU	Intel i9-10900K
RAM	32GB
Software
PyTorch version	1.12.0
CUDA version	11.6

Table 5: Experimental Configuration

Metric	Mean	Std	Max	Min
PSNR (dB)	32.47	2.31	38.92	26.14
SSIM	0.956	0.018	0.991	0.892
MSE	4.23e-4	1.89e-4	1.56e-3	8.92e-5

Table 6: Overall Reconstruction Metrics

Figure 6: Best reconstruction results for each geological family. Columns (left to right): FlatVel, CurveVel, FlatFault, CurveFault, Style. Rows (top to bottom): Ground truth, Reconstruction (PSNR in corner), Error map (max error in corner). The error maps show that reconstruction errors concentrate near sharp interfaces (faults), while smooth regions are well recovered.

Family	PSNR (dB)	SSIM	MSE
FlatVel	35.82 $\pm$ 1.24	0.978 $\pm$ 0.008	2.12e-4 $\pm$ 0.89e-4
CurveVel	33.45 $\pm$ 1.87	0.962 $\pm$ 0.012	3.45e-4 $\pm$ 1.23e-4
FlatFault	31.28 $\pm$ 2.15	0.948 $\pm$ 0.016	5.67e-4 $\pm$ 1.98e-4
CurveFault	30.56 $\pm$ 2.42	0.941 $\pm$ 0.019	6.89e-4 $\pm$ 2.34e-4
Style	31.24 $\pm$ 2.08	0.951 $\pm$ 0.015	5.02e-4 $\pm$ 1.76e-4

Table 7: Reconstruction Metrics per Geological Family

Figure 7: Reconstruction quality metrics (PSNR and SSIM) for each geological family. (a) PSNR values: FlatVel achieves highest PSNR (35.82 dB), followed by CurveVel (33.45 dB). Faulted structures show lower PSNR: FlatFault (31.28 dB), CurveFault (30.56 dB). Style achieves intermediate performance (31.24 dB). (b) SSIM values follow similar trend: FlatVel (0.978), CurveVel (0.962), FlatFault (0.948), CurveFault (0.941), Style (0.951). Error bars indicate standard deviation across 200 samples per family. Simple flat structures show highest quality and lowest variance, while faulted structures exhibit greater variance due to fault complexity.

Figure 8: Latent space interpolation between two velocity models from different geological families. Left: Sample A (FlatFault family, #A). Right: Sample B (CurveFault family, #B). Intermediate columns show linear interpolation at $\alpha=0.17,0.33,0.50,0.67,0.83$ . The smooth transition in geological features demonstrates that the learned latent space captures meaningful semantic variations and enables continuous morphing between different structures.

$\alpha$	MSE to A	MSE to B
0.00	0.00e+0	8.45e-3
0.17	2.34e-4	5.67e-3
0.33	8.92e-4	3.21e-3
0.50	1.56e-3	1.56e-3
0.67	3.21e-3	8.92e-4
0.83	5.67e-3	2.34e-4

Table 8: Interpolation Error Analysis

Figure 9: Zero-shot super-resolution results for sample #425 (Style family). Top row: full velocity fields at different resolutions (70×70, 140×140, 280×280). Bottom row: zoomed-in views of the region marked by yellow rectangle in GT. The 4× reconstruction (280×280) preserves sharp fault boundaries without additional training, demonstrating the resolution-agnostic nature of implicit neural representations.

Resolution	PSNR (dB)	SSIM	MSE
70 $\times$ 70 (1×)	32.47	0.956	4.23e-4
140 $\times$ 140 (2×)	31.82	0.948	5.12e-4
280 $\times$ 280 (4×)	30.95	0.937	6.78e-4

Table 9: Super-Resolution Quality Metrics

Method	Representation	Storage per Sample	PSNR (dB)
Raw grid	$70\times 70$ grid	4,900 floats	-
JPEG2000	Wavelet-based	500 bytes	28-31
InversionNet [ 35 ]	CNN features	1,024 features	29-33
COIN [ 31 ]	Separate MLP	50K params	30-35
Ours (SIREN auto-decoder)	256-dim latent	256 floats	32.47

Table 10: Comparison of Compression Methods

Dataset Size	Raw Grid	Ours (latents only)	Ours (total)
1,000 samples	4.9M floats	256K floats	1.30M floats

Table 11: Memory Requirements for Dataset Storage (Based on 1,000 Samples)

Direction	Priority
Latent space FWI integration	High
Scaling to large datasets (e.g., 40,000 samples)	High
3D extension	High
Hierarchical representations	Medium
Conditional generation	Medium
Uncertainty quantification	Low

Table 12: Future Research Directions

Metric	Value
Average PSNR	32.47 dB
Average SSIM	0.956
Compression ratio	19:1
Best PSNR (FlatVel)	38.92 dB
4× Super-resolution PSNR	30.95 dB
Training time	1.0 hours

Table 13: Key Quantitative Results Summary

Sinusoidal Representation Networks

See all 10 papers

Rethinking Amortized Neural Representations for High-Resolution Terrain Elevation Data
May 29, 2026Haoan Feng, Xin Xu, Leila De FlorianiImplicit Neural Representations Geospatial Representation Learning
University of Maryland, College Park MD, USA
PatchINR: Patch-Based Implicit Neural Representations for Efficient and Scalable Inference
Jun 24, 2026Jiachen Ren, Wenyong Zhou, Taiqiang Wu +4Efficient Neural Network Inference Implicit Neural Representations
The Department of Electrical and Computer Engineering, The University of Hong Kong, Hong Kong.
ImplicitTerrainV2: Wavelet-Guided Spatially Adaptive Neural Terrain Representation
May 21, 2026Haoan Feng, Xin Xu, Leila De FlorianiImplicit Neural Representations
University of Maryland, College Park MD, USA

May 29, 2026J/K move · Enter open · S save

Rethinking Amortized Neural Representations for High-Resolution Terrain Elevation Data

Haoan Feng, Xin Xu, Leila De Floriani

University of Maryland, College Park MD, USA

Implicit Neural Representations Geospatial Representation Learning Hypernetworks Sinusoidal Representation Networks

Open paper AskPDF arXiv

Implicit neural representations (INRs) model a signal as a continuous coordinate-to-value function. For terrain elevation data, this supports analytic derivatives, arbitrary-resolution decoding, and a smooth surface model of the underlying heightfield. However, fitting and storing a separate INR for every tile does not scale to large terrain datasets. Amortized neural representations reduce this cost with a shared network: a new tile is mapped to a compact per-tile payload, and a shared decoder reconstructs the heightfield from it. Most such methods are hypernetworks that predict the payload in a single forward pass, while others recover it through a short per-tile optimization. These methods were developed primarily for natural images, and their suitability for terrain heightfields remains unclear. We introduce a controlled benchmark on a 1 m/pixel terrain dataset and evaluate three representative methods under a unified protocol. Observing a clear cross-domain gap, we propose HUVR+SIREN, a hypernetwork that adapts the strongest benchmarked method (HUVR) by replacing its coordinate decoder with a smooth, analytically differentiable one. It attains the best height and derivative fidelity on the benchmark with no additional per-tile storage and lower decode cost, and tolerates aggressive post-training quantization with negligible quality loss, giving a compact terrain neural format. Ablations and diagnostics further identify which design choices transfer to terrain and show that the per-tile bottleneck is already near its useful limit, leaving the remaining gap in the shared hypernetwork's architectural design.

Abstract

Sinusoidal Representation Networks

Explore similar work

Rethinking Amortized Neural Representations for High-Resolution Terrain Elevation Data

PatchINR: Patch-Based Implicit Neural Representations for Efficient and Scalable Inference

ImplicitTerrainV2: Wavelet-Guided Spatially Adaptive Neural Terrain Representation