This article presents a novel method for the exact inversion of partially coherent dynamical electron scattering data to retrieve picometer-scale atomic structure information. The challenge lies in reconstructing the phase distribution of electron waves from intensity measurements, which is complicated by the nonlinear nature of high-energy electron diffraction and the presence of thermal diffuse scattering (TDS) in thick specimens. The proposed method employs a fully differentiable, parametrized approach using neural network concepts, incorporating physical quantities such as atom positions, types, and thermal displacements. This allows for the inversion of psychographic data by accounting for the atomistic nature of the specimen and thermal effects, using a frozen phonon model to treat TDS accurately. The method is validated using experimental and simulated data from 4D scanning transmission electron microscopy (STEM) of a ferroelectric material, PbZr0.2Ti0.8O3. The approach reduces the number of unknowns by four orders of magnitude compared to existing methods, enabling the retrieval of atomic positions with picometer precision and the determination of chemical composition through gradient analysis. The method also allows for the direct measurement of temperature as a differentiable parameter, enhancing the sensitivity to atomic number contrast. The study demonstrates the ability to accurately retrieve ferroelectric displacements and distinguish between different atom types in mixed columns, providing a robust framework for the inversion of partially coherent electron scattering data in nanostructures. The results highlight the importance of incorporating physical constraints and thermal effects in the reconstruction process, leading to more accurate and reliable atomic structure determination.This article presents a novel method for the exact inversion of partially coherent dynamical electron scattering data to retrieve picometer-scale atomic structure information. The challenge lies in reconstructing the phase distribution of electron waves from intensity measurements, which is complicated by the nonlinear nature of high-energy electron diffraction and the presence of thermal diffuse scattering (TDS) in thick specimens. The proposed method employs a fully differentiable, parametrized approach using neural network concepts, incorporating physical quantities such as atom positions, types, and thermal displacements. This allows for the inversion of psychographic data by accounting for the atomistic nature of the specimen and thermal effects, using a frozen phonon model to treat TDS accurately. The method is validated using experimental and simulated data from 4D scanning transmission electron microscopy (STEM) of a ferroelectric material, PbZr0.2Ti0.8O3. The approach reduces the number of unknowns by four orders of magnitude compared to existing methods, enabling the retrieval of atomic positions with picometer precision and the determination of chemical composition through gradient analysis. The method also allows for the direct measurement of temperature as a differentiable parameter, enhancing the sensitivity to atomic number contrast. The study demonstrates the ability to accurately retrieve ferroelectric displacements and distinguish between different atom types in mixed columns, providing a robust framework for the inversion of partially coherent electron scattering data in nanostructures. The results highlight the importance of incorporating physical constraints and thermal effects in the reconstruction process, leading to more accurate and reliable atomic structure determination.