A brake system control method determines vehicle operating conditions, compares the conditions to an allowable range, and uses a neural network to predict an expected coefficient of friction when the conditions are within the range. When the conditions fall outside of the range, the method determines an amount of required braking force using a constant coefficient of friction, and calculates the required braking force using the expected coefficient of friction when the conditions are within the range. The vehicle operating conditions include a vehicle speed, brake pressure, modeled brake rotor temperature, and apply state. The expected coefficient is multiplied by a constant or a calculated correction factor. A vehicle has an engine, transmission, and braking system, with a controller and an algorithm for predicting a coefficient of friction for two brake rotors, calculating a hydraulic brake pressure, and for applying the braking system using the hydraulic brake pressure.