A vehicle system includes an electronic control unit. The electronic control unit is configured to execute a first program, a second program, and a third program. The first program is configured to recognize an object present around a vehicle, the second program is configured to store information related to the recognized object as time-series map data, and the third program is configured to predict a future position of the object based on the stored time-series map data. The first program and the third program are configured to be (i) first, individually optimized based on first training data corresponding to output of the first program and second training data corresponding to output of the third program, and (ii) then, collectively optimized based on the second training data corresponding to the output of the third program.