Full-Waveform Inversion (FWI)

Full-Waveform Inversion (FWI)

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Standard reconstruction benchmark — forward model perfectly known, no calibration needed. Score = 0.5 × clip((PSNR−15)/30, 0, 1) + 0.5 × SSIM

# Method Score PSNR (dB) SSIM Source
🥇 VelocityGAN 0.742 32.2 0.910 ✓ Certified Zhang & Lin, JGR 2020
🥈 InversionNet 0.698 30.5 0.880 ✓ Certified Wu & Lin, JGR 2019
🥉 TV-Reg FWI 0.587 26.8 0.780 ✓ Certified Esser et al., Geophysics 2018
4 L-BFGS FWI 0.467 23.5 0.650 ✓ Certified Virieux & Operto, Geophysics 2009

Dataset: PWM Benchmark (4 algorithms)

Blind Reconstruction Challenge — forward model has unknown mismatch, must calibrate from data. Score = 0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖)

# Method Overall Score Public
PSNR / SSIM
 Dev
PSNR / SSIM
 Hidden
PSNR / SSIM
 Trust Source
🥇 VelocityGAN + gradient 0.665
0.739
29.39 dB / 0.907
0.664
26.37 dB / 0.842
0.592
23.78 dB / 0.761
✓ Certified Zhang & Lin, JGR 2020
🥈 InversionNet + gradient 0.638
0.716
28.63 dB / 0.893
0.602
23.24 dB / 0.740
0.597
23.48 dB / 0.750
✓ Certified Wu & Lin, JGR 2019
🥉 TV-Reg FWI + gradient 0.625
0.644
25.03 dB / 0.803
0.631
24.76 dB / 0.794
0.600
23.8 dB / 0.761
✓ Certified Esser et al., Geophysics 2018
4 L-BFGS FWI + gradient 0.498
0.542
20.71 dB / 0.632
0.503
19.58 dB / 0.578
0.448
18.01 dB / 0.500
✓ Certified Virieux & Operto, Geophysics 2009

Complete score requires all 3 tiers (Public + Dev + Hidden).

Join the competition →
Scoring: 0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖) PSNR 40% · SSIM 40% · Consistency 20%
Public 5 scenes

Full-access development tier with all data visible.

What you get & how to use

What you get: Measurements (y), ideal forward operator (H), spec ranges, ground truth (x_true), and true mismatch spec.

How to use: Load HDF5 → compare reconstruction vs x_true → check consistency → iterate.

What to submit: Reconstructed signals (x_hat) and corrected spec as HDF5.

Public Leaderboard
# Method Score PSNR SSIM
1 VelocityGAN + gradient 0.739 29.39 0.907
2 InversionNet + gradient 0.716 28.63 0.893
3 TV-Reg FWI + gradient 0.644 25.03 0.803
4 L-BFGS FWI + gradient 0.542 20.71 0.632
Spec Ranges (4 parameters)
Parameter Min Max Unit
starting_velocity_model_error -3.0 6.0 -
source_wavelet_error -2.0 4.0 -
anelastic_attenuation_(q) -100.0 200.0 -
source_location_error -20.0 40.0 m
View Details →
Dev 5 scenes

Blind evaluation tier — no ground truth available.

What you get & how to use

What you get: Measurements (y), ideal forward operator (H), and spec ranges only.

How to use: Apply your pipeline from the Public tier. Use consistency as self-check.

What to submit: Reconstructed signals and corrected spec. Scored server-side.

Dev Leaderboard
# Method Score PSNR SSIM
1 VelocityGAN + gradient 0.664 26.37 0.842
2 TV-Reg FWI + gradient 0.631 24.76 0.794
3 InversionNet + gradient 0.602 23.24 0.74
4 L-BFGS FWI + gradient 0.503 19.58 0.578
Spec Ranges (4 parameters)
Parameter Min Max Unit
starting_velocity_model_error -3.6 5.4 -
source_wavelet_error -2.4 3.6 -
anelastic_attenuation_(q) -120.0 180.0 -
source_location_error -24.0 36.0 m
Submit Reconstruction View Details →
Hidden 5 scenes

Fully blind server-side evaluation — no data download.

What you get & how to use

What you get: No data downloadable. Algorithm runs server-side on hidden measurements.

How to use: Package algorithm as Docker container / Python script. Submit via link.

What to submit: Containerized algorithm accepting y + H, outputting x_hat + corrected spec.

Hidden Leaderboard
# Method Score PSNR SSIM
1 TV-Reg FWI + gradient 0.600 23.8 0.761
2 InversionNet + gradient 0.597 23.48 0.75
3 VelocityGAN + gradient 0.592 23.78 0.761
4 L-BFGS FWI + gradient 0.448 18.01 0.5
Spec Ranges (4 parameters)
Parameter Min Max Unit
starting_velocity_model_error -2.1 6.9 -
source_wavelet_error -1.4 4.6 -
anelastic_attenuation_(q) -70.0 230.0 -
source_location_error -14.0 46.0 m
Submit Algorithm View Details →

Blind Reconstruction Challenge

Challenge

Given measurements with unknown mismatch and spec ranges (not exact params), reconstruct the original signal. A method must be evaluated on all three tiers for a complete score. Scored on a composite metric: 0.4 × PSNR_norm + 0.4 × SSIM + 0.2 × (1 − ‖y − Ĥx̂‖/‖y‖).

Input

Measurements y, ideal forward model H, spec ranges

Output

Reconstructed signal x̂

Spec DAG — Forward Model Pipeline

P → D

P Propagation
D Detector

Mismatch Parameters

Symbol Parameter Description Nominal Perturbed
s_v starting_velocity_model_error Starting velocity model error (-) 0.0 3.0
s_w source_wavelet_error Source wavelet error (-) 0.0 2.0
a_a anelastic_attenuation_(q) Anelastic attenuation (Q) (-) 0.0 100.0
s_l source_location_error Source location error (m) 0.0 20.0

Credits System

40%
Platform Profit Pool
Revenue allocated to benchmark rewards
30%
Winner Share
Top algorithm receives from pool
$100
Min Withdrawal
Minimum payout threshold
Spec Primitives Reference (11 primitives)
P Propagation

Free-space or medium propagation kernel (Fresnel, Rayleigh-Sommerfeld).

M Mask / Modulation

Spatial or spatio-temporal amplitude modulation (coded aperture, SLM pattern).

Π Projection

Geometric projection operator (Radon transform, fan-beam, cone-beam).

F Fourier Sampling

Sampling in the Fourier / k-space domain (MRI, ptychography).

C Convolution

Shift-invariant convolution with a point-spread function (PSF).

Σ Summation / Integration

Summation along a physical dimension (spectral, temporal, angular).

D Detector

Sensor readout with gain g and noise model η (Gaussian, Poisson, mixed).

S Structured Illumination

Patterned illumination (block, Hadamard, random) applied to the scene.

W Wavelength Dispersion

Spectral dispersion element (prism, grating) with shift α and aperture a.

R Rotation / Motion

Sample or gantry rotation (CT, electron tomography).

Λ Wavelength Selection

Spectral filter or monochromator selecting a wavelength band.