1. A computer-implemented method for reconstructing a 3D modeled object that represents a real object, the real object being a manufacturing product or part, from a 3D mesh and measured data representative of the real object, the method comprising: obtaining the measured data via one or more physical signal sensors based on a physical instance of the real object; selecting the 3D mesh from a template library; providing a set of deformation modes, a deformation mode being a parameterized deformation function of the 3D mesh, the parameterized deformation function of the 3D mesh being a set of functions that take the 3D mesh as input and output a deformed version of the input depending on values of respective parameters, the values of the respective parameters each varying in a respective continuum, the set of deformation modes comprising a subset representative of geometrical modes that includes a rigid mode and a 3D scaling mode, the set of deformation modes further comprising a subset representative of at least one physics mode; determining a composition of the set of deformation modes which optimizes a program that explores deformation modes and/or values of variable parameters of deformation modes, that rewards fit between the 3D mesh as deformed by the composition and the measured data, and that further rewards sparsity of deformation modes of the set of deformation modes involved in the determined composition; and applying the composition to the 3D mesh.