Page 187 - Artificial Intelligence for Computational Modeling of the Heart

Chapter 4 Data-driven reduction of cardiac models 159

Figure 4.27. Visualization of the cylinder bending results for networks trained for different time steps (10dt, 20dt, 30dt,
40dt, 50dt, 75dt, and 100dt). In (A) the final deformation color-coded by the point-wise error is illustrated and the mean
error can be seen in (B). While the network produced accurate results up to 20dt, the error increased for larger time
steps due to an apparent artificial stiffening.

system was implemented, which reduces the number of training
samples required to simulate arbitrary motions. Furthermore, in
this framework the forces applied to the mesh vertices are used as
input for the motion model. As a result, FEM solvers can be used
to compute the forces at each time step, incorporating changes
to material model and boundary conditions without having to re-
train the AI model. The method was tested by simulating the com-
pression of a bar using a Neo-Hookean material response instead
of the Holzapfel–Ogden law. In all configurations TLED was un-
stable at a time step of 10dt. Through AI acceleration, conversely,
excellent results with a sub-millimeter accuracy in retrieving the
ground truth motion could be achieved.
While these results are promising, the geometries and mo-
tions used as test scenarios are simple and do not reflect real-
world problems. Extension to more complex configurations will
be subject of future work. Furthermore, although the approach
was capable of accurately predicting the deformations up to a
time step of 20dt, for large time steps an artificial stiffening and