We develop an adaptive scheme in the kinetic Monte Carlo simulations, where the adsorption and activation energies of all elementary steps, including the effects of other adsorbates, are evaluated "on-the-fly" by employing the neural network potentials. The configurations and energies evaluated during the simulations are stored for reuse when the same configurations are sampled in a later step. The present scheme is applied to hydrogen adsorption and diffusion on the Pd(111) and Pt(111) surfaces and the CO oxidation reaction on the Pt(111) surface. The effects of interactions between adsorbates, i.e., adsorbate-adsorbate lateral interactions, are examined in detail by comparing the simulations without considering lateral interactions. This study demonstrates the importance of lateral interactions in surface diffusion and reactions and the potential of our scheme for applications in a wide variety of heterogeneous catalytic reactions.