weakl 0.0.1

A package implementing physics-informed kernels in dimensions 1 and 2

WeaKL

WeaKL is a Python package for constructing kernel methods with weak physical information as introduced in the paper
Forecasting time series with constraints (2025) by Nathan Doumèche, Francis Bach, Eloi Bedek, Claire Boyer, Gérard Biau, and Yannig Goude.

Features

• Build kernels tailored to weak information
• Compatible with NumPy and PyTorch backends
• GPU support via PyTorch for accelerated computation

Installation

You can install the package via pip:

pip install weakl

Resources

• Tutorial: https://github.com/claireBoyer/tutorial-piml
• Source code: https://github.com/NathanDoumeche/weakl
• Bug reports: https://github.com/NathanDoumeche/weakl/issues

Citation

To cite this package:

@article{doumèche2025forecastingtimeseriesconstraints,
  title={Forecasting time series with constraints}, 
  author={Nathan Doumèche and Francis Bach and Éloi Bedek and Gérard Biau and Claire Boyer and Yannig Goude},
  year={2025},
  journal={arXiv:2502.10485},
  url={https://arxiv.org/abs/2502.10485}
}

Minimum examples

Training an additive model

import pandas as pd
from weakl.utils import device, dataset_load
from weakl.additive_model import 

# Download the dataset on the French electricity load
data = dataset_load()

# Defining the additive model
features_weakl = {
"features": ["Load_d1", "temperature_smooth_950", "temperature",
            "temperature_max_smooth_990", 'temperature_min_smooth_950',
            'toy',  'day_type_week', 'day_type_jf', 'Load_d7','time'],
"features_type":['linear','regression','regression','regression','regression', 
            'regression','categorical7','linear','linear','linear']
}

features_weakl["masked"] = features_weakl["features_type"].copy()

# Setting the hyperparameters of the model
m_list = ['Linear', 10, 10, 10, 10, 10, 4, 'Linear', 'Linear', 'Linear']
alpha_list = torch.tensor([1.0000e-30, 1.0000e-30, 1.0000e-05, 1.0000e-03, 1.0000e-03, 1.0000e-04, 1.0000e-08, 1.0000e-30, 1.0000e-30, 1.0000e-30, 1.0000e-30],
       device=device)
s_list = ['*', 2, 2, 2, 2, 2, 0, '*', '*', '*']

hyperparameters = {"m_list": m_list,
                   "s_list": s_list,
                   "alpha_list": alpha_list}

# Training the model
dates_test = {
"begin_train": "2013-01-08 00:00:00+00:00",
"end_train": "2022-09-01 00:00:00+00:00",
"end_test": "2023-02-28 00:00:00+00:00"
}

data_hourly = half_hour_formatting(data, dates_test, features_weakl)
cov_hourly = cov_hourly_m(m_list, data_hourly)
sobolev_matrix = Sob_matrix(alpha_list, s_list, m_list)*len(data_hourly[0][0])
M_stacked = torch.stack([sobolev_matrix for i in range(48)])

# Evaluating the RMSE
perf_test, fourier_vectors_test, perf_h_test = WeakL(data, hyperparameters, cov_hourly, M_stacked, criterion=criterion)
print("The RMSE of the model is "+ str(perf_test.cpu().numpy()))

Learning the hyperparameters of the additive model by grid search

Training a model with time adaption