Methods of operating membrane processes, such as seawater purification processes, are described herein. The methods generally include flowing seawater into a membrane purification process; recovering purified seawater and concentrated seawater from the membrane purification process; sensing operating parameters of the membrane purification process; determining a state of the membrane purification process from the operating parameters using a physical model; using a statistical model to resolve a time dependence of the state of the membrane purification process; using a recursive statistical process to update the statistical model; using the updated statistical model to predict a future state of the membrane purification process; comparing the predicted future state of the membrane purification process to a threshold state; and predicting a remaining time before the membrane purification process reaches the threshold state.