Implementation of the Emulator-based Component Analysis

TL;DR

This paper introduces a PyTorch implementation of emulator-based component analysis for solving ill-posed nonlinear inverse problems by reducing dimensionality using an approximate emulator of the forward model.

Contribution

The paper provides a novel PyTorch-based implementation of emulator-based component analysis for inverse problems, enabling efficient dimensionality reduction and solution approximation.

Findings

Effective dimensionality reduction in inverse problems

Implementation demonstrates practical use with a Python class

Facilitates approximate solutions using emulators

Abstract

We present a PyTorch-powered implementation of the emulator-based component analysis used for ill-posed numerical non-linear inverse problems, where an approximate emulator for the forward problem is known. This emulator may be a numerical model, an interpolating function, or a fitting function such as a neural network. With the help of the emulator and a data set, the method seeks dimensionality reduction by projection in the variable space so that maximal variance of the target (response) values of the data is covered. The obtained basis set for projection in the variable space defines a subspace of the greatest response for the outcome of the forward problem. The method allows for the reconstruction of the coordinates in this subspace for an approximate solution to the inverse problem. We present an example of using the code provided as a Python class.