Controller and control method for internal combustion engine

A controller for an internal combustion engine, the controller being configured to control an internal combustion engine that is mounted on a vehicle and includes a filter configured to trap particulate matter in exhaust gas discharged from a plurality of cylinders and fuel injection valves provided for the respective cylinders, wherein

• the controller comprises processing circuitry, and
• the processing circuitry is configured to execute:
• on condition that an execution request for a regeneration process of the filter is made, a dither control process of operating the fuel injection valves such that at least one of the cylinders is a lean combustion cylinder, in which an air-fuel ratio is leaner than a stoichiometric air-fuel ratio, and at least another one of the cylinders is a rich combustion cylinder, in which an air-fuel ratio is richer than the stoichiometric air-fuel ratio;
• and
• a deposition amount calculating process of calculating a deposition amount, which is an amount of particulate matter trapped by the filter, 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.