<p>The Hirota–Miwa equation is one of the most celebrated fully discrete integrable systems. By introducing bilinear operators of trigonometric-type, we propose a novel variant of the Hirota–Miwa equation, which can be regarded as an integrable discretization of the Kadomtsev–Petviashvili-I (KPI) equation. It turns out that this new equation admits a number of physically significant solutions, including solitons, lumps, breathers, and periodic wave solutions. As far as we know, it is the first time that lump solutions have been reported in the context of fully discrete integrable systems. In addition, the numerical periodic wave solutions are computed by employing deep learning techniques. Finally, the reduction procedure is considered, which yields a trigonometric-type discrete Korteweg–de Vries (KdV) equation and a trigonometric-type discrete Boussinesq equation.</p>