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Monolithic integrated mode converters with high integration are essential to photonic integrated circuits (PICs), and they are widely used in next-generation optical communications and complex quantum systems. It is expected that PICs will become more miniaturized, multifunctional, and intelligent with the development of micro/nano-technology. The increase in design space makes it difficult to realize high-performance device design based on traditional parameter sweeping or heuristic design, especially in the optimal design of reconfigurable PIC devices. Combining the mode coupling theory and adjoint calculation method, we proposed a design method for a switchable mode converter. The device could realize the transmission of TE0 mode and the conversion from TE0 to TE1 mode with a footprint of 0.9 × 7.5 μm2 based on the phase change materials (PCMs). We also found that the mode purity could reach 78.2% in both states at the working wavelength of 1.55 μm. The designed method will provide a new impetus for programmable photonic integrated devices and find broad application prospects in communication, optical neural networks, and sensing. [ABSTRACT FROM AUTHOR]