Symplectic Attention and Numerical Error Envelope Benchmark Dataset for Chaotic Double Pendulum with Multi-Precision BOINC Simulations

The data are released as a community resource to establish a statistical upper bound on the predictive capability of local attention features and to facilitate future comparative studies.Due to volunteer computing task completion variability, the actual number of successfully returned files is 4,933 (Group A), 5,562 (Group B), and 11,885 (Group C). The remaining work units did not complete within the campaign window; the achieved sample size is nonetheless sufficient for statistical closure as reported in the associated paper.Data Files and Organization: The .npz results is organized into three .zip files (group_A.zip, group_B.zip, group_C.zip) each containing individual .npz files named with the pattern <Group>_<5-digit_id>.npz.

Group A contains 4933 files (Float64 with Kahan compensation), Group B contains 6000 files (Float64 without Kahan), and Group C contains 12000 files (Float32). Each .npz file is a compressed NumPy archive that includes the following keys:'trajectories': A list of numpy arrays, each of shape (30000, 4) and dtype float32, storing the time series of angles and angular velocities (theta1, theta2, omega1, omega2) for the double pendulum.

Only one trajectory per file (since TRAJS_PER_WU=1), but the field is kept as a list for compatibility.'features': A dictionary with eight keys: 'ent_symp', 'Z_mean', 'Z_var', 'ent_gated', 'dev_gated', 'ent_multi_mean', 'ent_multi_var', 'dS_att'. Each value is a list containing a single numpy array of length equal to the number of sliding windows (typically 56) for that trajectory. These are the attention-based features described in the associated code.'targets': A list containing a single numpy array of the same length as the feature arrays, storing the envelope slope (target variable) for each window.'entropy_symp_seq': A list containing a single numpy array of window-wise symplectic attention entropy values.'entropy_multi_var_seq': A list containing a single numpy array of window-wise multi-head entropy variance.'y0_perturbed': A list of the initial condition vectors (theta1, theta2, omega1, omega2) actually used (including any perturbation for Group A).'perturb_labels': For Group A, a list of the Euclidean norm of the applied perturbation; for Groups B and C, this is a list of zeros (placeholders).'metadata': A dictionary containing simulation parameters (precision, group, dt, n_steps, window_size, step_size, mode, temperature, n_heads, use_quantile, do_inverse, seed).The analysis results (containing heatmaps and scatters for each groups' attention results) are saved in output.zipCode and Reproducibility: The repository includes all source code required in source_code.zip to generate and process the data:pipeline.py: Core computational module containing the symplectic integrator, energy calculations, attention feature extraction, envelope slope extraction, and statistical analysis functions (block-bootstrap, inverse decoder, symbolic regression).buda_main.py: BOINC work unit wrapper that reads input.json, calls pipeline functions, and writes output.npz.

This script is the entry point for volunteer computing tasks.make_workunits.py: Script that generates the input.json files for all work units, with configurable precision groups and perturbation settings.Dockerfile: Container environment definition and Python dependencies (numpy, scipy, scikit-learn, gplearn, matplotlib) for exact reproducibility.test.py: Full‑scale statistical analysis script that loads all generated .npz files, computes instantaneous and lagged correlations (Pearson and Spearman) for all eight attention features, and produces the heatmaps, scatter plots, and summary tables reported in the paper.This respository also includes the input files for workunits in workunits.zip