  DeepWarp is an efficient and highly re-usable deep neural network (DNN) based
nonlinear deformable simulation framework. Unlike other deep learning
applications such as image recognition, where different inputs have a uniform
and consistent format (e.g. an array of all the pixels in an image), the input
for deformable simulation is quite variable, high-dimensional, and
parametrization-unfriendly. Consequently, even though DNN is known for its rich
expressivity of nonlinear functions, directly using DNN to reconstruct the
force-displacement relation for general deformable simulation is nearly
impossible. DeepWarp obviates this difficulty by partially restoring the
force-displacement relation via warping the nodal displacement simulated using
a simplistic constitutive model -- the linear elasticity. In other words,
DeepWarp yields an incremental displacement fix based on a simplified
(therefore incorrect) simulation result other than returning the unknown
displacement directly. We contrive a compact yet effective feature vector
including geodesic, potential and digression to sort training pairs of per-node
linear and nonlinear displacement. DeepWarp is robust under different model
shapes and tessellations. With the assistance of deformation substructuring,
one DNN training is able to handle a wide range of 3D models of various
geometries including most examples shown in the paper. Thanks to the linear
elasticity and its constant system matrix, the underlying simulator only needs
to perform one pre-factorized matrix solve at each time step, and DeepWarp is
able to simulate large models in real time.
