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

Data driven solutions and parameter discovery of the nonlocal mKdV equation via deep learning method