A method for operating an industrial system, an apparatus, a computer program product, a computer-readable medium and method for synchronizing a system model with a real system, wherein a) a system model including at least one device model configured to calculate simulated output values and/or state values from simulated input values using mathematical functions and which is expanded with at least one mathematical function inverse to the at least one mathematical function is provided, b) at least one real output value and/or state value is provided, c) the at least one real output value and/or state value is supplied to the expanded device model, d) via the functions, at least one input value is back-calculated from the at least one real output value and/or state value, and e) the at least one back-calculated input value and/or a derived value is used to synchronize the system model with the real system.