cymbal-tapered-v1
Bowed, belled and hammered bronze disk lathed to a tapered thickness, struck with a drum stick, geometrically nonlinear: radiated pressure. Challenge specification. results.json. Generated 2026-09-17T20:36:16+00:00.
Errors are relative to the reference solution cymbal-solutions/vonkarman-modal/vk-g4-w600-a600-m2, chosen by rule partial-order-agreement. Rows are sorted by the primary metric. Submissions are named as repository/submission.
| Submission | Solution | Method | waveform_l2 (primary) | spectrogram_l2 | Time (s) | Hardware | Claimed more accurate than | Output |
|---|---|---|---|---|---|---|---|---|
| vonkarman-modal cymbal-solutions · Jeremy Magland | vk-g4-w600-a600-m2 (reference) | Marguerre shallow shell (Airy form) on a Cartesian grid masked to the disk, modal method on shell modes built from Bogner-Fox-Schmit plate modes with variable thickness, Gautschi-type integrator exact in the linear part, retarded Rayleigh-type integral with cubic fractional delays{"grid_spacing_m": 0.004, "cells": 8112, "n_dof": 33268, "transverse_modes": 600, "basis_even_in_y": false, "airy_modes": 600, "oversampling": 2, "dt_s": 1.0416666666666666e-05, "highest_transverse_mode_hz": 14584.7} | 0 | 0 | 1.36e+03 | Intel(R) Xeon(R) w5-3435X (32 threads), numpy/scipy for the setup; coupling tensor and time stepping on NVIDIA RTX 6000 Ada Generation (PyTorch 2.14.0+cu130) | vk-g4-w400-a400-m2 | wav fields code viz |
| vonkarman-modal cymbal-solutions · Jeremy Magland | vk-g4-w400-a400-m2 | Marguerre shallow shell (Airy form) on a Cartesian grid masked to the disk, modal method on shell modes built from Bogner-Fox-Schmit plate modes with variable thickness, Gautschi-type integrator exact in the linear part, retarded Rayleigh-type integral with cubic fractional delays{"grid_spacing_m": 0.004, "cells": 8112, "n_dof": 33268, "transverse_modes": 400, "basis_even_in_y": false, "airy_modes": 400, "oversampling": 2, "dt_s": 1.0416666666666666e-05, "highest_transverse_mode_hz": 12904.8} | 1.599 | 1.307 | 479 | Intel(R) Xeon(R) w5-3435X (32 threads), numpy/scipy for the setup; coupling tensor and time stepping on NVIDIA RTX 6000 Ada Generation (PyTorch 2.14.0+cu130) | vk-g8-w400-a400-m2 | wav code viz |
| vonkarman-modal cymbal-solutions · Jeremy Magland | vk-g8-w400-a400-m2 | Marguerre shallow shell (Airy form) on a Cartesian grid masked to the disk, modal method on shell modes built from Bogner-Fox-Schmit plate modes with variable thickness, Gautschi-type integrator exact in the linear part, retarded Rayleigh-type integral with cubic fractional delays{"grid_spacing_m": 0.008, "cells": 2024, "n_dof": 8500, "transverse_modes": 400, "basis_even_in_y": false, "airy_modes": 400, "oversampling": 2, "dt_s": 1.0416666666666666e-05, "highest_transverse_mode_hz": 16678.6} | 1.644 | 1.342 | 399 | Intel(R) Xeon(R) w5-3435X (32 threads), numpy/scipy for the setup; coupling tensor and time stepping on NVIDIA RTX 6000 Ada Generation (PyTorch 2.14.0+cu130) | vk-g8-w200-a200-m2 | wav code viz |
| vonkarman-modal cymbal-solutions · Jeremy Magland | vk-g8-w200-a200-m2 | Marguerre shallow shell (Airy form) on a Cartesian grid masked to the disk, modal method on shell modes built from Bogner-Fox-Schmit plate modes with variable thickness, Gautschi-type integrator exact in the linear part, retarded Rayleigh-type integral with cubic fractional delays{"grid_spacing_m": 0.008, "cells": 2024, "n_dof": 8500, "transverse_modes": 200, "basis_even_in_y": false, "airy_modes": 200, "oversampling": 2, "dt_s": 1.0416666666666666e-05, "highest_transverse_mode_hz": 10644.3} | 1.955 | 1.751 | 72.5 | Intel(R) Xeon(R) w5-3435X (32 threads), numpy/scipy for the setup; coupling tensor and time stepping on NVIDIA RTX 6000 Ada Generation (PyTorch 2.14.0+cu130) | wav code viz |
Reference selection
Candidates are the maximal elements of each submission's asserted order. The score is the number of asserted pairs from other submissions whose order is preserved by the primary error to this candidate. Ties are broken first by the convergence gap (the primary error between the candidate and the nearest solution of its own submission asserted to be less accurate; smaller means a tighter convergence claim), then by the mean primary error to the other candidates.
| Candidate | Pairs preserved | Convergence gap | Mean error to other candidates | Violated pairs |
|---|---|---|---|---|
| cymbal-solutions/vonkarman-modal/vk-g4-w600-a600-m2 | 0/0 | 1.599 | 0 |
Order check against the chosen reference
All asserted accuracy orderings are preserved by both metrics under the chosen reference.
Pairwise errors (row vs column as reference)
waveform_l2
| cymbal-solutions/vonkarman-modal/vk-g4-w600-a600-m2 | cymbal-solutions/vonkarman-modal/vk-g4-w400-a400-m2 | cymbal-solutions/vonkarman-modal/vk-g8-w400-a400-m2 | cymbal-solutions/vonkarman-modal/vk-g8-w200-a200-m2 | |
|---|---|---|---|---|
| cymbal-solutions/vonkarman-modal/vk-g4-w600-a600-m2 | 0 | 1.25 | 1.24 | 1.16 |
| cymbal-solutions/vonkarman-modal/vk-g4-w400-a400-m2 | 1.6 | 0 | 1.38 | 1.25 |
| cymbal-solutions/vonkarman-modal/vk-g8-w400-a400-m2 | 1.64 | 1.42 | 0 | 1.26 |
| cymbal-solutions/vonkarman-modal/vk-g8-w200-a200-m2 | 1.96 | 1.64 | 1.6 | 0 |
spectrogram_l2
| cymbal-solutions/vonkarman-modal/vk-g4-w600-a600-m2 | cymbal-solutions/vonkarman-modal/vk-g4-w400-a400-m2 | cymbal-solutions/vonkarman-modal/vk-g8-w400-a400-m2 | cymbal-solutions/vonkarman-modal/vk-g8-w200-a200-m2 | |
|---|---|---|---|---|
| cymbal-solutions/vonkarman-modal/vk-g4-w600-a600-m2 | 0 | 1.01 | 1.01 | 1.03 |
| cymbal-solutions/vonkarman-modal/vk-g4-w400-a400-m2 | 1.31 | 0 | 1.09 | 1.1 |
| cymbal-solutions/vonkarman-modal/vk-g8-w400-a400-m2 | 1.34 | 1.13 | 0 | 1.06 |
| cymbal-solutions/vonkarman-modal/vk-g8-w200-a200-m2 | 1.75 | 1.45 | 1.36 | 0 |