  Starting from the observation that artificial neural networks are uniquely
suited to solving optimisation problems, and most physics problems can be cast
as an optimisation task, we introduce a novel way of finding a numerical
solution to wide classes of differential equations. We find our approach to be
very flexible and stable without relying on trial solutions, and applicable to
ordinary, partial and coupled differential equations. We apply our method to
the calculation of tunnelling profiles for cosmological phase transitions,
which is a problem of relevance for baryogenesis and stochastic gravitational
wave spectra. Comparing our solutions with publicly available codes which use
numerical methods optimised for the calculation of tunnelling profiles, we find
our approach to provide at least as accurate results as these dedicated
differential equation solvers, and for some parameter choices even more
accurate and reliable solutions. In particular, we compare the neural network
approach with two publicly available profile solvers, \texttt{CosmoTransitions}
and \texttt{BubbleProfiler}, and give explicit examples where the neural
network approach finds the correct solution while dedicated solvers do not. We
point out that this approach of using artificial neural networks to solve
equations is viable for any problem that can be cast into the form
$\mathcal{F}(\vec{x})=0$, and is thus applicable to various other problems in
perturbative and non-perturbative quantum field theory.
