  In this paper, we systematically study the integrability and data-driven
solutions of the nonlocal mKdV equation. The infinite conservation laws of the
nonlocal mKdV equation and the corresponding infinite conservation quantities
are given through Riccti equation. The data driven solutions of the zero
boundary for the nonlocal mKdV equation are studied by using the multi-layer
physical information neural network algorithm, which including kink soliton,
complex soliton, bright-bright soliton and the interaction between soliton and
kink-type. For the data-driven solutions with non-zero boundary, we study kink,
dark, anti-dark and rational solution. By means of image simulation, the
relevant dynamic behavior and error analysis of these solutions are given. In
addition, we discuss the inverse problem of the integrable nonlocal mKdV
equation by applying the physics-informed neural network algorithm to discover
the parameters of the nonlinear terms of the equation.
