An apparatus (100, 200) configured for controlling an operation of a continuously operating dynamical system in engineered processes and machines, comprising: an input interface configured to receive a state trajectory, that is a sequence of states, of the system; a memory configured to store a model (104, 208a) describing dynamics of the system including a combination of at least one differential equation and a closure model; a processor configured to: update the closure model using reinforcement learning, RL, having a value function reducing a difference between a shape of the received state trajectory and a shape of state trajectory estimated using the model with the updated closure model, wherein a shape of the state trajectory is a series of states of the system as a function of time; and determine a control command based on the model with the updated closure model; and an output interface configured to transmit the control command to an actuator of the system to control the operation of the system; wherein the differential equation of the model defines a reduced order model of the system having a number of parameters less than a physical model of the system according to a partial differential equation, PDE, and wherein the reduced order model is an ordinary differential equation, ODE, wherein the updated closure model is a nonlinear function of a state of the system capturing a difference in behavior of the system according to the ODE and the PDE; wherein the partial differential equation, PDE, is a Boussinesq equation; wherein the updated closure model includes a gain, wherein the processor is configured to determine the gain reducing an error between a state of the system estimated with the model having the updated closure model with the updated gain and an actual state of the system; wherein the actual state of the system is a measured state. an input interface configured to receive a state trajectory, that is a sequence of states, of the system; a memory configured to store a model (104, 208a) describing dynamics of the system including a combination of at least one differential equation and a closure model; a processor configured to: update the closure model using reinforcement learning, RL, having a value function reducing a difference between a shape of the received state trajectory and a shape of state trajectory estimated using the model with the updated closure model, wherein a shape of the state trajectory is a series of states of the system as a function of time; and determine a control command based on the model with the updated closure model; and an output interface configured to transmit the control command to an actuator of the system to control the operation of the system; wherein the differential equation of the model defines a reduced order model of the system having a number of parameters less than a physical model of the system according to a partial differential equation, PDE, and wherein the reduced order model is an ordinary differential equation, ODE, wherein the updated closure model is a nonlinear function of a state of the system capturing a difference in behavior of the system according to the ODE and the PDE; wherein the partial differential equation, PDE, is a Boussinesq equation; wherein the updated closure model includes a gain, wherein the processor is configured to determine the gain reducing an error between a state of the system estimated with the model having the updated closure model with the updated gain and an actual state of the system; wherein the actual state of the system is a measured state. update the closure model using reinforcement learning, RL, having a value function reducing a difference between a shape of the received state trajectory and a shape of state trajectory estimated using the model with the updated closure model, wherein a shape of the state trajectory is a series of states of the system as a function of time; and determine a control command based on the model with the updated closure model; and an output interface configured to transmit the control command to an actuator of the system to control the operation of the system; wherein the differential equation of the model defines a reduced order model of the system having a number of parameters less than a physical model of the system according to a partial differential equation, PDE, and wherein the reduced order model is an ordinary differential equation, ODE, wherein the updated closure model is a nonlinear function of a state of the system capturing a difference in behavior of the system according to the ODE and the PDE; wherein the partial differential equation, PDE, is a Boussinesq equation; wherein the updated closure model includes a gain, wherein the processor is configured to determine the gain reducing an error between a state of the system estimated with the model having the updated closure model with the updated gain and an actual state of the system; wherein the actual state of the system is a measured state.