A Robust Scientific Machine Learning for Optimization: A Novel Robustness Theorem

TL;DR

This paper introduces a robustness test for multiobjective scientific machine learning-based optimization methods, ensuring their reliability while reducing computational costs compared to traditional rigorous approaches.

Contribution

It proposes a new robustness test for SciML optimization that guarantees results respect the universal approximator theorem and is computationally efficient.

Findings

The robustness test confirms SciML optimization results are reliable.

The methodology is validated through benchmark comparisons.

It achieves similar robustness guarantees with less computational effort.

Abstract

Scientific machine learning (SciML) is a field of increasing interest in several different application fields. In an optimization context, SciML-based tools have enabled the development of more efficient optimization methods. However, implementing SciML tools for optimization must be rigorously evaluated and performed with caution. This work proposes the deductions of a robustness test that guarantees the robustness of multiobjective SciML-based optimization by showing that its results respect the universal approximator theorem. The test is applied in the framework of a novel methodology which is evaluated in a series of benchmarks illustrating its consistency. Moreover, the proposed methodology results are compared with feasible regions of rigorous optimization, which requires a significantly higher computational effort. Hence, this work provides a robustness test for guaranteed robustness in applying SciML tools in multiobjective optimization with lower computational effort than the existent alternative.