In this talk, we present a low rank numerical optimization-based approach for the stability of specific physical systems. The main problem consists in finding the largest eigenvalue of a specific partial differential operator, modeling battery lifetime, and this is achieved via a suitable rank adaptive method. Secondly, a parameters estimation for parametrized systems to impose criticality conditions via numerical optimization is considered. Numerical results confirm the effectiveness of the proposed approach. This talk is part of a research activity within the project PRIN PNRR 2022 P20228C2PP (CUP: F53D23010020001) BAT-MEN (BATtery Modeling, Experiments & Numerics).