cfd-chaotic-advection

# Chirikov Standard Map Lyapunov Spectrum **Maximal Lyapunov exponent** Λ(K) for the Chirikov standard map on T², computed with a custom CUDA Benettin kernel on **NVIDIA RTX 5090** (sm_120). > Part of the [bigcompute.science](https://bigcompute.science) CFD conjecture program — GPU-accelerated exploration of open questions in fluid mixing and dynamical systems. ## Quick Start ```python from datasets import load_dataset ds = load_dataset("cahlen/cfd-chaotic-advection", "deep_sweep", split="train") row = ds[1200] print(f"K={row['K']:.4f}, mean Λ={row['mean_lyapunov']:.6f}") ``` ## What's In This Dataset Each row is one coupling parameter K on a uniform grid in [0, K_max]: | Column | Type | Description | |--------|------|-------------| | `k_index` | int | Grid index | | `K` | float | Standard map coupling parameter | | `mean_lyapunov` | float | Mean maximal Lyapunov exponent over ICs | | `std_lyapunov` | float | Standard deviation across ICs | | `min_lyapunov` | float | Minimum over ICs | | `max_lyapunov` | float | Maximum over ICs | | `fraction_positive` | float | Fraction of ICs with Λ > 0 | ### Configurations | Config | n_k | n_ic | n_iters | K_max | Trajectories | Wall time | |--------|-----|------|---------|-------|--------------|-----------| | `deep_sweep` | 2048 | 8192 | 50000 | 5.0 | 16,777,216 | 116.6 s | | `standard_sweep` | 512 | 4096 | 20000 | 5.0 | 2,097,152 | 5.9 s | | `smoke_test` | 64 | 512 | 5000 | 2.0 | 32,768 | ~1 s | Certifying logs are in `logs/`. Claim-validation artifacts in `validation/` (convergence at $K=5$, `convergence_k5_gpu.json`). Metadata in `metadata.json`. ### Validation artifacts | File | Description | |------|-------------| | `validation/convergence_k5_gpu.json` | GPU mean Λ at $K=5$ for 5k–100k iterations (65,536 ICs) | | `validation/lyapunov_k2_ic65536_iter*.csv` | Per-iteration-count sweeps at $K=0$ and $K=5$ only | Generated by `validate_claims.py` — see [finding claim-validation table](https://bigcompute.science/findings/cfd-standard-map-chaos-onset/). ## Key Results (deep_sweep) - Λ(0) = 0 (integrable limit validated) - At literature K_crit ≈ 0.971635406: mean Λ ≈ 0.0446, >99.9% ICs positive - At K = 5: mean Λ ≈ 0.956 - Zero NaN/Inf across all trajectories ## Reproduction ```bash git clone https://github.com/cahlen/idontknow.git cd idontknow ./scripts/experiments/cfd-chaotic-advection/run.sh 2048 8192 50000 5.0 ``` CUDA kernel: [cahlen/bigcompute-cuda-kernels](https://huggingface.co/cahlen/bigcompute-cuda-kernels) (`cfd-chaotic-advection/standard_map_lyapunov.cu`) ## Related - Experiment: [bigcompute.science/experiments/cfd-chaotic-advection](https://bigcompute.science/experiments/cfd-chaotic-advection/) - Finding: [Standard Map Chaos Onset](https://bigcompute.science/findings/cfd-standard-map-chaos-onset/) ## Citation ```bibtex @misc{humphreys2026cfdchaoticadvection, author = {Humphreys, Cahlen}, title = {Chirikov Standard Map Lyapunov Spectrum (GPU-Computed)}, year = {2026}, publisher = {Hugging Face}, howpublished = {\\url{https://huggingface.co/datasets/cahlen/cfd-chaotic-advection}} } ``` Human–AI collaborative research. Not peer-reviewed. All code and data open for verification.