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Multi-Integral-Importance-Sampling

Implementation of Multi-Integral Importance Sampling for integration and for solving PDEs via the Deep Ritz method.

This repository implements Multi-Integral Importance Sampling (MIIS) to the Deep Ritz Method for solving Partial Differential Equations (PDEs), for the purpose of reducing the loss estimator variance and the gradient variance.

The repository is structured as follows:

1. MIIS

  • DeepRitz-MIIS-VarianceComparison.py:
    • Main execution script.
    • Runs the training loop for the neural network.
    • Performs the variance comparison using different integration rules: the standard Monte Carlo, the standard Importance Sampling, and Multi-Integral Importance Sampling.

2. transport_maps_examples

This folder provides examples of how conditional Normalizing Flows (using FlowJAX) can be used as transport maps to match target densities.

Xalbador Otxandorena - xalbaotxandorena@gmail.com