  Physics-Informed Neural Networks (PINNs) offer a promising approach to
solving differential equations and, more generally, to applying deep learning
to problems in the physical sciences. We adopt a recently developed transfer
learning approach for PINNs and introduce a multi-head model to efficiently
obtain accurate solutions to nonlinear systems of ordinary differential
equations with random potentials. In particular, we apply the method to
simulate stochastic branched flows, a universal phenomenon in random wave
dynamics. Finally, we compare the results achieved by feed forward and
GAN-based PINNs on two physically relevant transfer learning tasks and show
that our methods provide significant computational speedups in comparison to
standard PINNs trained from scratch.
