Elliptic boundary-value problems with localised features (e.g., re-entrant corner singularities, internal layers, or material interfaces) require concentrating resolution where the solution is hardest to approximate. In isogeometric analysis (IGA), this is often addressed by h-refinement and adaptive strategies guided by error indicators; however, r-adaptivity offers a fixed degree of freedom (DOF) alternative by redistributing DOF without changing mesh topology. In this talk, we present a differentiable r-adaptive IGA framework where the solution field is represented by tensor-product B-splines, while selected geometric/parametric quantities—interior knot locations—are treated as trainable parameters θ. For each θ, the field coefficients are obtained via a standard Galerkin IGA solution of the weak formulation, ensuring stability and strong enforcement of the essential boundary conditions. The adaptation is driven by minimizing a loss functional L(θ) composed of the strong-form PDE residual and interface flux jumps, evaluated on the Galerkin solution. Gradients ∇θL are computed via automatic differentiation, using implicit differentiation of the linear solve to propagate sensitivities without backpropagating through solver iterations/factorization. This differentiable r-adaptive approach connects with recent neural and deep-learning-driven r-adaptive methodologies. We test the approach on a 1D Helmholtz interface problem with discontinuous material coefficients, where the method successfully redistributes knots to resolve non-uniform oscillations and sharp gradients at material interfaces. We also consider the 2D Laplace problem on an L-shaped domain, showing that knot relocation automatically clusters resolution near singularities, yielding substantially improved accuracy compared with uniform discretisations with the same number of DOFs.