[@fgsimon2015], non-simple exclusion processes [@GJLR], semilinear SPDEs [@Gubinelli2016Hairer], or interacting diffusions [@Diehl2017]. From the BGP, it comes naturally that some suitably rescaled microscopic quantity, called *density fluctuation field* (see below for a precise meaning) subsequentially converges, as the size of the microscopic system goes to infinity, to random fields which are solutions ${{\mathcal Y}}$ of a generalized martingale problem for , where the singular non-linear drift $\nabla ( {{\mathcal Y}}^2(t,u))$ is a well-defined space-time distributional random field. Gonçalves and Jara in [@gj2014] (see also [@Gubinelli2013]) called them *energy solutions*. Recently, Gubinelli and Perkowski [@Gubinelli2015Energy] proved uniqueness of energy solutions to and as a significant consequence, the proof of the weak KPZ universality conjecture could be concluded for all the models mentioned above. We note that none of these models admits a microscopic Cole-Hopf transformation, which prevents the use of the methods of [@BerG].

Purposes of this work
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Our goal in this article is to go beyond the weak KPZ universality conjecture and to derive a new SPDE, namely, the KPZ equation with boundary conditions, from an interacting particle system in contact with stochastic reservoirs. Indeed, the presence of boundary conditions in evolution equations often lacks understanding from a physical 