Unpolarized TMD extraction with Deep Neural Networks*

We introduce a physics-informed deep neural network (DNN) framework to extract unpolarized transverse-momentum–dependent parton distribution functions (TMDs) directly from fixed-target Drell–Yan data (E288, E605). The key idea is to embed the DNN as the integrand inside the TMD factorization convolution, so that learning occurs at the level of the physical integral rather than through a pre-chosen parametric ansatz. This "integrand-level" training enforces QCD kinematic constraints by construction and enables data-driven reconstruction of the TMD without model bias from functional forms. In this talk I will outline the formulation, training strategy, and validation (including closure tests) and show how the method recovers the k⊥ structure consistent with the measured spectra while remaining flexible across x and Q. I will also discuss uncertainty propagation within the learning loop and compare to traditional fits. Beyond TMDs, I will highlight how this paradigm generalizes to other QCD inverse problems—most notably generalized parton distributions (GPDs)—by replacing the relevant convolution kernels while retaining the same physics-constrained learning principle.