In this study, a set of 2D simulations was initially performed to assess the sensitivity of the topology optimizations results to variations in effective parameters. Then, two separate 3D simulations were carried out using two sets of parameters, selected based on the findings of the 2D simulations, leading to two distinct patterns for the preferred flow and conductive pathways. The geometries for the 2D and 3D cases are depicted in Fig. . The inverse design process started with an initial uniform design variable (γ) set to 0.5, and the porosity of the material value was considered to be 0.5. The ratio of ohmic and kinetic resistances was set to vary as δ ∈ {1.0, 25.0} to have an order of magnitude of difference, the same as for the liquid and solid conductivity ratio to vary as τ ∈ {0.005, 0.1, 0.5}. Moreover, the dimensionless applied current density was adjusted to vary as λ ∈ {0.1, 5.0}, controlling the level of the kinetics nonlinearity in the Butler-Volmer equation (Eq. 30) . The RAMP parameter (q α in Eq. 38) was set to 2.0, and the filtered design variable γ was computed with a filter radius of r = 0.01 in the PDE filter (Eq. 36). The optimization was performed for 150 iterations after which no significant change in the objective functions was observed. Additionally, two 3D cases were simulated using different applied current densities and liquid/solid ratios, the results of which were transformed into TPMS structures. The simulations were carried out using the parameter sets of [τ = 0.005, λ = 5] and [τ = 0.5, λ = 1], where all the other parameters were kept the same, and the ratio of ohmic and kinetic resistances was set as δ = 1.