pypielm

PyPIELM: A Unified and Reproducible Framework for Physics-Informed Extreme Learning Machines.

Physics-Informed Extreme Learning Machines (PIELMs) solve PDEs by embedding differential operators into the ELM training objective. The hidden-layer weights are sampled randomly and frozen; only the output weights are determined analytically (ridge regression, RRQR, or Bayesian solve), making training orders of magnitude faster than gradient-based PINNs.

This package provides:

• 26+ PIELM variants and 4 PINN baselines under a unified fit/predict/score API.

• PyTorch-native implementation with autograd PDE operators and GPU support.

• Universal data adapters (CSV, NPZ, PINNacle, PDEBench, torch.utils.data.Dataset).

• YAML-driven reproducible experiment configs and a CLI entry point.

• Publication-quality visualisation helpers.

Example:

from pypielm.data import auto_load
from pypielm.models import CorePIELM
from pypielm.pde.operators import AnalyticLaplacian

ds    = auto_load("poisson.dat", source="pinnacle")
model = CorePIELM(hidden_dim=300, ridge_lambda=1e-8)
model.fit(ds, pde_operator=AnalyticLaplacian())
print(model.score(ds.X_test, ds.y_test))  # relative L²