IBM Double Pendulum Chaotic Dataset — data/
⚠ DATA UNAVAILABLE — upstream CDN defunct (verified 2026-04-22)
dax-cdn.cdn.appdomain.cloud resolves as NXDOMAIN: IBM shut down the DAX
(Data Asset eXchange) platform and its CDN around 2023. The tarball URL in
download.sh is permanently dead. data.csv is not present.
To reconstruct data.csv manually:
- Obtain the tarball
double-pendulum-chaotic.tar.gzfrom an alternative source (e.g. a mirror, archive.org, or direct contact with the authors at IBM Research AI). - Place it at
benchmarks/dynamical_systems/ibm_double_pendulum/data/double-pendulum-chaotic.tar.gz. - Re-run
ONLY_VIDEO=0 bash download.sh— the script detects the local tarball and skips the download step.
Source
IBM Data Asset eXchange (DAX), "Double Pendulum Chaotic" v2.0.1.
- Landing page: https://developer.ibm.com/exchanges/data/all/double-pendulum-chaotic/
- Project homepage: https://ibm.github.io/double-pendulum-chaotic-dataset/
- Tarball (primary):
https://dax-cdn.cdn.appdomain.cloud/dax-double-pendulum-chaotic/2.0.1/double-pendulum-chaotic.tar.gz - Paper: Asseman, Kornuta & Ozcan, Learning beyond simulated physics, NeurIPS 2018 MDSD workshop. https://openreview.net/pdf?id=HylajWsRF7
- License: CDLA-Sharing-1.0 (https://cdla.io/sharing-1-0/)
Redistribution is permitted under CDLA-Sharing-1.0. We therefore rebuild
data.csv by downloading the upstream tarball on demand; the raw tarball and
the generated data.csv / data_all_videos.csv are gitignored per
/data/yiming/real-sr/.gitignore.
Usage
./download.sh # defaults to ONLY_VIDEO=0 -> data.csv is video 0
ONLY_VIDEO=5 ./download.sh # use video 5 as data.csv instead
ONLY_VIDEO=all ./download.sh # make data.csv = all 21 videos concatenated
The script always writes data_all_videos.csv (full 21-video concatenation)
alongside the single-video data.csv.
File layout (regenerated; gitignored)
double-pendulum-chaotic.tar.gz— upstream tarball (~hundreds of MB).dpc_raw/— extracted tarball tree. Contains.../original/dpc_dataset_csv/{0..20}.csv(the 21 full-length marker-position CSVs we use) and.../train_and_test_split/…(IBM's 4-in / 200-out train/validation/test split, which we do not consume here).data.csv— benchmark entry data (one video by default).data_all_videos.csv— all 21 videos concatenated, with avideo_idcolumn.
Upstream CSV format (per the Asseman 2018 notebook example)
Each original/dpc_dataset_csv/<k>.csv is headerless, whitespace-separated,
with 6 float columns per row:
x_red y_red x_green y_green x_blue y_blue
Rows are consecutive video frames at 400 Hz. Coordinates are in image pixels multiplied by 5 (IBM upscales the video 5× before pattern-matching to get sub-pixel resolution; the multiplication is preserved in the stored CSV — see Sec. 2.3 of Asseman 2018). Red = pivot (the fixed hinge), green = first datum (tip of upper arm), blue = second datum (tip of lower arm).
Derived columns we add
download.sh writes the following column order to data.csv:
| col | name | role | units | source |
|---|---|---|---|---|
| 0 | theta1_ddot_fd |
output | rad/s² | 2nd centred finite difference of theta1 |
| 1 | theta1 |
input | rad | atan2(x_green - x_red, y_green - y_red) |
| 2 | theta2 |
input | rad | atan2(x_blue - x_green, y_blue - y_green) |
| 3 | omega1 |
input | rad/s | 1st centred finite difference of theta1 |
| 4 | omega2 |
input | rad/s | 1st centred finite difference of theta2 |
| 5 | theta2_ddot_fd |
input | rad/s² | 2nd centred finite difference of theta2 |
| 6 | H_mpernorm |
input | J/kg (proxy) | see below — per-unit-mass Hamiltonian with m1 = m2 = 1 |
| 7 | x_red |
input | pixels × 5 | upstream (IBM) |
| 8 | y_red |
input | pixels × 5 | upstream (IBM) |
| 9 | x_green |
input | pixels × 5 | upstream (IBM) |
| 10 | y_green |
input | pixels × 5 | upstream (IBM) |
| 11 | x_blue |
input | pixels × 5 | upstream (IBM) |
| 12 | y_blue |
input | pixels × 5 | upstream (IBM) |
| 13 | frame_idx |
input | count | row index within a video |
| 14 | t_seconds |
input | s | frame_idx / 400 |
| 15 | video_id |
input | int 0..20 | source-video index |
All upstream columns are preserved unchanged. The derived columns are documented finite-difference estimates of the kinematic quantities — they are not fits.
Angle convention
With image coordinates (x right, y down), the downward vertical is the direction of increasing y. We define
theta1 = atan2(x_green - x_red , y_green - y_red)
theta2 = atan2(x_blue - x_green, y_blue - y_green)
so that theta = 0 when the arm hangs straight down, theta > 0 when it swings
to the right of the image, and theta is measured independently for each arm
from the downward vertical. This matches the convention used in the simple
double-pendulum Lagrangian (Levien & Tan 1993, Wikipedia) consumed by
formulas/hamiltonian.py, formulas/eom_theta1.py and formulas/eom_theta2.py.
The paper's alpha = atan2(...) convention (from horizontal, for the first
arm only) and our convention differ only by a constant offset; either can be
recovered from the stored marker positions.
Finite-difference conventions (defaults; not paper-prescribed)
The Asseman 2018 paper does not prescribe a derivative estimator. We use the simplest defensible centred-difference scheme:
omega_i = (theta_{i+1} - theta_{i-1}) / (2 * dt)
alpha_i = (theta_{i+1} - 2 theta_i + theta_{i-1}) / dt^2
dt = 1 / 400 s
Endpoints are dropped. Angles are np.unwraped before differentiation so that
multi-revolution swings do not inject 2π artefacts. These O(dt²) schemes are
noise-amplifying by a factor O(1/dt) ≈ 400 for velocities and O(1/dt²) ≈ 1.6e5
for accelerations, so reference scores on theta1_ddot_fd / theta2_ddot_fd
are bounded from below by tracker noise, not by model fit. See
description.md for a full discussion.
Hamiltonian-proxy caveat
The paper does not report the bob masses m1, m2. We therefore compute
H_mpernorm = H(theta1, theta2, omega1, omega2; l1=0.091, l2=0.070, g=9.81,
m1 = 1, m2 = 1)
as a proxy. Absolute energy values are meaningful only up to an unknown scale;
formulas/hamiltonian.py matches this convention. A searcher that finds
H(theta, omega; l1, l2, g) * k for any constant k > 0 has found the same
answer.
Reproducibility notes
- IBM shut down the DAX platform (~2023);
dax-cdn.cdn.appdomain.cloudreturns NXDOMAIN as of 2026-04-22. The only recovery path is a manual copy of the tarball (see the "DATA UNAVAILABLE" notice at the top of this file). - The CDLA-Sharing-1.0 license requires that any redistribution of the data, including derivatives, be under the same license and with attribution. This benchmark entry attributes Asseman, Kornuta & Ozcan (IBM Research AI, 2018).