A system a method for controlling an operation of HVAC system is provided. The system comprises at least one processor; and memory having instructions stored thereon that, when executed by the at least one processor, cause the system to receive data indicative of the operation of the HVAC system and optimize a cost function to reduce a difference between a full thermal state of the conditioned environment simulated from the received data based on a physical model of airflow including a partial differential equation (PDE) and a thermal state of the conditioned environment reconstructed by an observer using a reduced order model (ROM) of airflow including an ordinary differential equation (ODE) from values of the full thermal state at a set of locations, wherein optimization of the cost function is a multivariable optimization of a structure of the observer and a structure of the ODE.