  The real time evolution of a scalar field in 0+1 dimensions is investigated
on a complex time contour. The path integral formulation of the system has a
sign problem, which is circumvented using the Complex Langevin equation.
Measurement of the boundary terms allow for the detection of correct results
(for contours with small real time extents) or incorrect results (at large real
time extents), as confirmed by comparison to exact results calculated using
diagonalization of the Hamiltonian. We introduce a constant matrix kernel in
the Complex Langevin equation, which is optimized with the requirement that
distributions of the fields on the complexified manifold remain close to the
real manifold. We observe that reachable real times are roughly twice as large
with the optimal kernel. We also investigate field dependent kernels
represented by a neural network for a toy model as well as for the scalar
field, providing promising first results.
