Preserving general physical properties in model reduction of dynamical systems via constrained?optimization projection

Model-reduction techniques aim to reduce the computational complexity of simulating dynamical systems by applying a (Petrov–)Galerkin projection process that enforces dynamics evolve in low-dimensional subspace original state space. Frequently, resulting reduced-order model (ROM) violates intrinsic physical properties full-order (e.g., global conservation, Lagrangian structure, state-variable bounds) because does not generally ensure preservation these properties. However, many applications, ensuring ROM preserves such can enable retain meaning and lead improved accuracy stability In this work, we present general constrained-optimization formulation for projection-based reduction be used as template enforce satisfy specific on kinematics dynamics. We introduce formulations at both time-continuous (i.e., ODE) level, which leads constrained Galerkin projection, time-discrete least-squares Petrov–Galerkin context linear multistep schemes. demonstrate ability proposed equip ROMs with desired energy conservation bounds total variation.