Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequences

This repository contains the implementation to reproduce the numerical experiments of the paper Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequences

Installation

Please make sure you have installed the requirements before executing the python scripts.

pip install numpy
pip install matplotlib
pip install pytorch
pip install pandas
pip install filelock 

Neural network training: Ensemble and retraining

In the source folder run

 python train_networks.py 'experiment' 'training_type' 'sampling_method' 'input_dimension' 'max_learning_iterations'

experiment: name of the experiment type

• BSPDE, for the Black-Scholes PDE problem
• airfoil, for the airfoil problem
• projectile for the projectile motion problem
• sum_sines, for sum of sines problem

training_type: name of the training procedure:

• ensemble, to perform an ensemble training
• retrain, to perform a retraining of the best performing network

! Note: only do a retraining once the corresponding MC ensemble training is finished. Everything else will lead to FileNotFound errors.

sampling_method: Sampling method for training and test set:

• QMC, for the Sobol-based Quasi-Monte Carlo sampling
• MC, for the standard Monte-Carlo sampling

input_dimension: integer to indicate the input space dimension

! Note: for every 'training_type' only the data for input dimensions specified in the experiments of the paper are available. Everything else will lead to FileNotFound errors.

max_learning_iterations: integer to indicate the maximum amount of learning iterations

The results are stored in data/<experiment>/results.