Since the turn of the century, astronomers have been exploiting the rich
information afforded by combining stellar kinematic maps and imaging in an
attempt to recover the intrinsic, three-dimensional (3D) shape of a galaxy. A
common intrinsic shape recovery method relies on an expected monotonic
relationship between the intrinsic misalignment of the kinematic and
morphological axes and the triaxiality parameter. Recent studies have, however,
cast doubt about underlying assumptions relating shape and intrinsic kinematic
misalignment. In this work, we aim to recover the 3D shape of individual
galaxies using their projected stellar kinematic and flux distributions using a
supervised machine learning approach with mixture density network (MDN). Using
a mock dataset of the EAGLE hydrodynamical cosmological simulation, we train
the MDN model for a carefully selected set of common kinematic and photometric
parameters. Compared to previous methods, we demonstrate potential improvements
achieved with the MDN model to retrieve the 3D galaxy shape along with the
uncertainties, especially for prolate and triaxial systems. We make specific
recommendations for recovering galaxy intrinsic shapes relevant for current and
future integral field spectroscopic galaxy surveys.

利用混合密度网络 (MDN) 的监督式机器学习方法，使用投影星体运动学和通量分布，恢复了个体星系的三维形状，并展示了 MDN 模型在获取三维星系形状及其不确定性方面相比以往方法的潜在改进，尤其是对纵椭圆和三轴系统。针对现有和未来的积分场光谱星系调查，给出了获取星系内在形状的具体建议。