Towards a machine learning pipeline in reduced order modelling for inverse problems: neural networks for boundary parametrization, dimensionality reduction and solution manifold approximation

TL;DR

This paper introduces a non-intrusive model order reduction framework using neural networks to efficiently solve inverse PDE problems by boundary parametrization, dimensionality reduction, and solution manifold approximation, demonstrated on CFD cases.

Contribution

It presents a novel neural network-based pipeline for boundary parametrization and solution manifold approximation in inverse PDE problems, enhancing computational efficiency.

Findings

Effective boundary parametrization via neural networks.

Significant reduction in computational time for inverse problems.

Successful application to CFD test cases.

Abstract

In this work, we propose a model order reduction framework to deal with inverse problems in a non-intrusive setting. Inverse problems, especially in a partial differential equation context, require a huge computational load due to the iterative optimization process. To accelerate such a procedure, we apply a numerical pipeline that involves artificial neural networks to parametrize the boundary conditions of the problem in hand, compress the dimensionality of the (full-order) snapshots, and approximate the parametric solution manifold. It derives a general framework capable to provide an ad-hoc parametrization of the inlet boundary and quickly converges to the optimal solution thanks to model order reduction. We present in this contribution the results obtained by applying such methods to two different CFD test cases.