A controller executes a dither control process and a deposition amount calculating process. In the dither control process, on condition that an execution request for a regeneration process of the filter is made, fuel injection valves are operated such that at least one of the cylinders is a lean combustion cylinder, and at least another one of the cylinders is a rich combustion cylinder. In the deposition amount calculating process, a deposition amount is calculated such that, as compared to a case in which a target value of an average value of an exhaust air-fuel ratio in a predetermined period by the dither control process is a first air-fuel ratio, a decrease amount per unit time of the deposition amount is calculated to be a great value in a case in which the target value is a second air-fuel ratio, which is leaner than the first air-fuel ratio.