PolyaNet

A mathematically-informed neural operator for early warning of climate and geophysical crises.

PolyaNet embeds the arithmetic structure of the Pólya operator K(i,j) = Λ(gcd(i,j))/√(ij) directly into its architecture. The spectral properties of this operator (unbounded growth λ_max → ∞ on the critical line, lower bound supR N ≥ (log 2/128)·log N) are formally verified in Lean 4, making PolyaNet the first ENSO predictor with a machine-checked mathematical core.

Key results (NOAA ONI, 1950–2026; val 2011–2026)

Model	L6	L12
Persistence	0.323	−0.022
LSTM	0.252	−0.004
Transformer	0.351	0.386
PolyaNet	0.431	0.446

At the 12-month horizon — the window needed for real crisis prevention — baselines collapse while PolyaNet retains a robust signal.

Structure

• polyanet.py — PolyaLayer (Pólya kernel + Dirichlet convolutions, theorem-initialized) + validation V1–V3
• stress.py / stress2.py / stress3.py — synthetic, climate (ONI), seismic (USGS) stress tests
• train.py / train_seis.py — ENSO and seismic forecasting (S3, S4)
• bench.py — benchmark vs persistence/LSTM/Transformer (S5)
• lean/ — Lean 4 formalization (EigenvalueLimit.lean et al.)
• data/ — manually downloaded datasets (oni.data, query.csv)

Requirements

Python 3.10+, torch, numpy, pandas. Data: NOAA ONI (data/oni.data), USGS catalog (data/query.csv).

License

MIT