  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.
