Reliable algorithmic differentiation techniques offer great promise for the inverse design of materials and functionals as well as the propagating uncertainties from functionals to DFT quantities of interest. We recently developed a differentiation framework for plane-wave density-functional theory (DFT) that combines the strengths of algorithmic differentiation (AD) and density-functional perturbation theory (DFPT) within the Density-functional ToolKit (DFTK, https://dftk.org). In our resulting AD-DFPT framework [1] derivatives of any DFT output quantity with respect to any input parameter (e.g.
geometry, density functional or pseudopotential) can be computed accurately without deriving gradient expressions by hand. I provide some hands-on examples employing these capabilities targeting, e.g. the inverse design of a semiconductor band gap, the learning of exchange-correlation functional parameters, or the propagation of DFT parameter uncertainties to relaxed structures.
[1] https://arxiv.org/abs/2509.07785
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