JuliaCon 2026

The Density-Functional ToolKit (DFTK) is a Julia package providing routines to compute
the electronic structure of a bulk material and related properties,
using plane-wave density functional theory (DFT).
Many material properties of interest can be expressed as derivatives of simulation outputs
wrt. input parameters, and typically only specific combinations are implemented by DFT codes,
as a result of great programming effort to hand-implement all the required derivative terms.
In DFTK however, derivatives of any output quantity wrt. any input parameter can be computed,
using algorithmic differentiation (AD) combined with density-functional perturbation theory (DFPT).
This results in a general AD-DFPT framework [1] that can only be used to compute both standard and novel derivatives,
with promising applications including gradient-based optimization and error propagation.

In the first part of this talk, I will discuss the key ideas behind this implementation,
showing how we offload tedious derivative computations to the AD framework,
while keeping the numerics under control thanks to the underlying DFPT solver.
The overall strategy is quite general, and should be applicable in other fields as well.
In the second part of this talk, I will present new research directions enabled by AD-DFPT.
In particular, I will focus on the propagation of model parameter uncertainty
and estimated numerical errors all the way to predicted physical quantities.