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Starting from the observation that artificial neural networks are uniquelysuited to solving optimisation problems, and most physics problems can be castas an optimisation task, we introduce a novel way of finding a numericalsolution to wide classes of differential equations. We find our approach to bevery flexible and stable without relying on trial solutions, and applicable toordinary, partial and coupled differential equations. We apply our method tothe calculation of tunnelling profiles for cosmological phase transitions,which is a problem of relevance for baryogenesis and stochastic gravitationalwave spectra. Comparing our solutions with publicly available codes which usenumerical methods optimised for the calculation of tunnelling profiles, we findour approach to provide at least as accurate results as these dedicateddifferential equation solvers, and for some parameter choices even moreaccurate and reliable solutions. In particular, we compare the neural networkapproach with two publicly available profile solvers, \texttt{CosmoTransitions}and \texttt{BubbleProfiler}, and give explicit examples where the neuralnetwork approach finds the correct solution while dedicated solvers do not. Wepoint out that this approach of using artificial neural networks to solveequations 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 inperturbative and non-perturbative quantum field theory.

Solving differential equations with neural networks: Applications to the calculation of cosmological phase transitions