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ABSTRACT We present a detailed model atmosphere analysis of 14001 DA white dwarfs from the Montreal White Dwarf Database with ultraviolet photometry from the GALEX mission. We use the 100 pc sample, where the extinction is negligible, to demonstrate that there are no major systematic differences between the best-fitting parameters derived from optical only data and the optical + UV photometry. GALEX FUV and NUV data improve the statistical errors in the model fits, especially for the hotter white dwarfs with spectral energy distributions that peak in the UV. Fitting the UV to optical spectral energy distributions also reveals UV-excess or UV-deficit objects. We use two different methods to identify outliers in our model fits. Known outliers include objects with unusual atmospheric compositions, strongly magnetic white dwarfs, and binary white dwarfs, including double degenerates and white dwarf + main-sequence systems. We present a list of 89 newly identified outliers based on GALEX UV data; follow-up observations of these objects will be required to constrain their nature. Several current and upcoming large-scale spectroscopic surveys are targeting >105 white dwarfs. In addition, the ULTRASAT mission is planning an all-sky survey in the NUV band. A combination of the UV data from GALEX and ULTRASAT and optical data on these large samples of spectroscopically confirmed DA white dwarfs will provide an excellent opportunity to identify unusual white dwarfs in the solar neighbourhood.