Thermophotovoltaics (TPVs) rely on selective thermal emitters to tailor the blackbody radiation at high temperatures into band-matching emission for photovoltaic cells, resulting in power-conversion efficiencies surpassing the Shockley-Queisser limit. The selectivity of the thermal emitter must cover three orders of magnitude range of wavelengths, spreading from visible to the far infrared, which requires the superposition of multiple transformation theories of optics and degrees of freedom anisotropic geometries. It is extremely challenging to realize such high-dimensional complex metasurface design using conventional computational photonics. Here we develop a deep neural network-based Bayesian optimization (DeepBO) framework to screen a 16-dimensional design space of 10^43 candidates, and realize a record-high spectral efficiency of 69% for the TPV emitter. We show that the neural network combined with Bayesian linear regression is an efficient and robust surrogate model which scales linearly with the size of data. We also reveal the underlying physical mechanisms of the geometric design of the TPV emitters using primary component analysis (PCA). We anticipate the DeepBO framework is a useful tool for data-intensive complex geometric design for photonics research community.