This talk presents a reduced-order modeling approach for efficiently solving parameter identification problems governed by parabolic PDEs. Building on recent advances in adaptive model reduction for elliptic problems, the reduced forward operator is constructed adaptively during optimization, combining parameter reduction with state space reduction via a reduced basis (RB) approach. To ensure reliability, the iteratively regularized Gauss?Newton method (IRGNM) is integrated into an error-aware trust-region strategy. Accuracy and efficiency are demonstrated through numerical experiments on dynamic reaction-diffusion systems.