  We present a deep learning-based reduced order model (DL-ROM) for predicting
the fluid forces and unsteady vortex patterns. We consider flow past a sphere
to examine the accuracy of our DL-ROM predictions. The proposed methodology
relies on a three-dimensional convolutional recurrent autoencoder network (3D
CRAN) to extract the low-dimensional flow features from full-order snapshots.
The low-dimensional features are evolved in time using a long short-term
memory-based recurrent neural network and reconstructed back to the full-order
as flow voxels. These 3D voxels are introduced as static and uniform query
probes in the point cloud domain to reduce the unstructured mesh complexity
while providing convenience in 3D CRAN training. We analyze a novel procedure
to recover the interface description and the force quantities from the 3D flow
voxels. The 3D CRAN methodology is first applied to an external flow past a
static sphere at a single Reynolds number of Re = 300. We provide an assessment
of the computing requirements in terms of the memory usage, training costs, and
testing times associated with the 3D CRAN framework. Subsequently, variable
Re-based flow information is infused in one 3D CRAN to learn a complicated
symmetry-breaking flow regime (280 < Re < 460) for the flow past a sphere.
Effects of transfer learning are analyzed for training this complicated 3D flow
regime on a relatively smaller time series dataset. The 3D CRAN framework
learns the flow regime nearly 20 times faster than the parallel full-order
model and predicts unsteady flows with an excellent to good accuracy. Based on
the predicted flow fields, the network demonstrates an R2 accuracy of 98.58%
for drag and 76.43% for lift over the sphere in the chosen flow regime. The
proposed framework aligns with the development of a digital twin for 3D
unsteady flow field with variable Re effects.
