Convexity and uniqueness guarantees for CHESRA-generated strain energy functions

Establish whether the low-complexity hyperelastic strain energy functions generated by the Cardiac Hyperelastic Evolutionary Symbolic Regression Algorithm (CHESRA) satisfy mathematical convexity conditions and yield unique solutions to the associated elastic boundary value problems under relevant loading scenarios.

Background

Although the CHESRA-derived SEF satisfy several desirable properties (material frame indifference, material symmetry, stress-free undeformed state), the authors could not provide formal guarantees of convexity or uniqueness for boundary value problems using these SEF. Such guarantees are important for well-posedness, numerical stability, and the reliable deployment of these models in 3‑D finite element simulations for cardiac digital twins.

The authors suggest that future work could enforce mathematical convexity conditions to guarantee unique minimal-energy solutions, indicating that the theoretical validation of CHESRA-generated models remains an unresolved issue.