A hollow triangular rod-type valley-Hall photonic topological insulator is proposed, and two tandem residual deep neural networks are built for multimodal inverse design of the structure. One of them is a tandem multilayer perceptron, and the other is a composite tandem network based on variational auto-encoder. The former is used to inversely infer the value of the structural sizes, and the latter is used to predict the structural image of the lattice from demanded design targets. Residual connections are included in both networks to speed up the training convergence as well as avoid vanishing gradient problem. Based on an arbitrary inversely designed lattice, domain walls between two photonic topological insulators with different topology are constructed, and full-wave simulations on the transmission properties are conducted. Numerical results show that robust topologically protected wave propagation is supported along the domain wall with little backscattering, demonstrating that the proposed methods are valid.