We aim to constrain the equation of state of nuclear matter by comparing calculations with the $\mathrm{SMASH}$ transport model to directed and elliptic flow measurements for protons and deuterons performed by the HADES collaboration in a systematic way. A momentum-dependent term is included in the potential for which we show that it is needed to describe flow data. We further incorporate a simple symmetry potential in the transport model and present constraints on the stiffness of the equation of state of nuclear matter at saturation density and on the symmetry potential. The constraints are obtained by performing a Bayesian analysis such that we can also provide an uncertainty for the estimated parameters. The posterior distribution is obtained by Markov chain Monte Carlo sampling for which we emulate the transport model with a Gaussian process to lower computational costs. We find that a relatively stiff equation of state is favoured in our analysis with a small uncertainty whereas the constraints obtained for the symmetry potential are rather loose.

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• Equations of state of nuclear matter
• Relativistic heavy-ion collisions
• Transport in heavy-ion collisions