jimchen2/pendulum-cjepa-new

Pendulum video / time-series dataset

Silent H.264 MP4s of a nonlinear physical pendulum, with frame-aligned CSVs.

Physics

theta'' = -(gravity / length) * sin(theta) - damping * theta'

gravity is in m/s², length in meters, damping in s⁻¹. Integration uses fourth-order Runge-Kutta (RK4), with multiple substeps per video frame. omega_rad_s is angular velocity and alpha_rad_s2 angular acceleration. energy_j_per_kg is mechanical energy per unit mass relative to the lowest position. It is conserved for zero damping, and decays when damping is positive. The integration is numerical, so conservation is approximate.

Illumination is independently controlled: light(t) = mean + amplitude * sin(2*pi*frequency*t + phase). The orange disk marks parallel-ray light, not a finite-distance emitter. The shadow is the exact ground projection of the circular bob and ideal thin rod, ignoring decorative drawing stroke thickness.

The physical rod length defaults to 1 meter. The drawing uses a fixed length of 8 visual world units so it resembles the earlier image dataset. bob_x_m / bob_y_m are physical coordinates relative to the pivot; bob_x_world / bob_y_world, shade, and mid are drawing-world coordinates. Do not interpret shadow labels as meters.

Files

• videos/train/, videos/test/: clean, caption-free MP4s.
• timeseries/clip_XXXX.csv: one label row per decoded video frame.
• index.csv: video-level paths, splits, configuration, and physical parameters.
• metadata.json: timing, model, renderer, and generation settings.
• preview.mp4, preview.png: annotated three-condition comparison (demo set only).
• frames/clip_XXXX/: optional PNGs, enabled with --save-frames.

Frame n corresponds to CSV row frame=n, at time_s=n/fps. For duration 12 seconds and 30 fps there are 360 frames; the last sampled instant is 11.9666667 seconds. The encoded movie still lasts exactly 12 seconds. Non-integral duration*fps is rounded; metadata records the actual duration. All splits are whole-video splits, never adjacent-frame splits.

Examples

python -m pip install numpy pillow imageio imageio-ffmpeg

# Three comparison clips: undamped, damped, and damped with moving light.
python simulate_pendulum_videos.py --demo-set --output pendulum_demo --zip

# A reproducible dataset with varied initial states, damping, and lighting.
python simulate_pendulum_videos.py --randomize --num-videos 50 \
  --duration 10 --fps 30 --size 256 --seed 42 --output pendulum_50 --zip

# One custom physical trajectory; optionally also export PNG frames.
python simulate_pendulum_videos.py --theta0 40 --omega0 0 --damping 0.15 \
  --length 1 --light-angle 90 --light-amplitude 20 --light-frequency 0.08 \
  --duration 12 --fps 30 --save-frames --output my_pendulum

Choose a new or empty output folder. imageio-ffmpeg supplies FFmpeg, so a separate system installation is not necessary. The script has no dependency on the earlier image generator. All videos are silent.

The three demo profiles are illustrative, not a representative ML benchmark. The second and third profiles intentionally share the exact same pendulum trajectory, with different illumination. Their graph traces coincide; nested stroke widths show both colors without changing any plotted values. For training, use --randomize and many videos. Randomized ranges are initial angle ±15–40°, initial angular velocity ±0.2 rad/s, damping 0–0.35 s⁻¹, light mean 70–110°, light amplitude 0–15°, and light frequency 0.04–0.12 Hz. Physical gravity and length remain the user-selected values for the entire batch.

CSVs preserve raw quantities rather than fitting normalization across splits. Original supplied code's copyright notice is preserved; see LICENSE.

C-JEPA smoke-test export

cjepa_slots.pkl has the exact nested structure expected by src/train/train_causalwm_from_clevrer_slot.py: {split: {video_key: float32[T, 4, slot_dim]}} for train and val. The four slots are deterministic simulator-state slots (bob/rod, light, shadow, scene). They verify C-JEPA data loading and prediction, but they are not learned visual slots. For visual learning, train or fine-tune an object-centric encoder on the MP4 files and replace this pickle with its extracted slots.