Gradient-based optimization combined with the adjoint method has been demonstrated to be an efficient way to design a nano-structure with a vast number of degrees of freedom. However, most inverse-designed photonic devices are applied as linear photonic devices. Here, we demonstrate the nonlinear optical response in inverse-designed integrated splitters fabricated on a SiN platform. The splitting ratio is tunable under different incident powers. The thermo-optical effect can be used as an effective approach for adjusting the nonlinear optical response threshold and modulation depth of the device. These promising results indicate the great potential of inverse-designed photonic devices in nonlinear optics and optical communications.