  In this article we address the question whether it is possible to learn the
differential equations describing the physical properties of a dynamical
system, subject to non-conservative forces, from observations of its realspace
trajectory(ies) only. We introduce a network that incorporates a difference
approximation for the second order derivative in terms of residual connections
between convolutional blocks, whose shared weights represent the coefficients
of a second order ordinary differential equation. We further combine this
solver-like architecture with a convolutional network, capable of learning the
relation between trajectories of coupled oscillators and therefore allows us to
make a stable forecast even if the system is only partially observed. We
optimize this map together with the solver network, while sharing their
weights, to form a powerful framework capable of learning the complex physical
properties of a dissipative dynamical system.
