We introduce a neural-network-based machine learning method to predict the effective spin-orbit coupling (SOC) strength in hole quantum dot arrays from standard charge stability diagrams. Specifically, we study a $2\times 2$ Ge hole quantum dot array described by a generalized spin-orbit coupled Hubbard model that incorporates random site- and bond-dependent disorder in all system parameters, including onsite potentials, Coulomb interaction strengths, interdot tunneling amplitudes, as well as the direction and angle of the SOC-induced spin rotations accompanying interdot tunneling. We train the neural network on numerically simulated charge stability diagrams from nearest-neighbor pairs of quantum dots for different chemical potentials and out-of-plane magnetic fields, and show that this enables us to predict the SOC-induced spin-flip tunneling amplitudes — and, thus, the effective SOC strength — with high fidelity ($R^2\approx 0.94$) even when all other Hubbard model parameters are unknown. Furthermore, our neural network can also predict the other Hubbard model parameters with high fidelity, demonstrating that neural-network-based approaches can be a powerful tool for the automated characterization of hole spin qubit arrays.

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