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              <p>From the vasculature of animals to the porous media making up batteries, the core task of flow networks is to transport solutes and perfuse all cells or media equally with resources. Yet, living flow networks have a key advantage over porous media: they are adaptive and self-organise their geometry for homogeneous perfusion throughout the network. Here, we show that artificial flow networks with an initial random geometry and inhomogeneous perfusion profile can be re-organised towards more homogeneous perfusion by flowing through them a reactive chemical that erodes the network walls. Flowing a pulse of cleaving enzyme through a network patterned into an erodible hydrogel, with initial channels disparate in width, we observe a homogenisation in channel resistances. Experimental observations are matched with numerical simulations of the diffusion-advection-sorption dynamics of an eroding enzyme within a network. Analysing transport dynamics theoretically, we show that homogenisation only occurs if the pulse of the eroding enzyme lasts longer than the time it takes any channel to equilibrate to the pulse concentration. The equilibration time scale derived analytically is in agreement with simulations. Last, we show both numerically and experimentally that erosion leads to the homogenisation of complex networks containing loops. Erosion being an omnipresent reaction, our results pave the way for a very versatile self-organised increase in the performance of porous media.</p>
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