We develop a physics-informed neural network (PINN) to evaluate closure terms for turbulence and chemical source terms in the Sandia turbulent nonpremixed flames. The approach relies on temperature, major species, and velocity point measurements to develop closure for the transport of momentum and the thermo-chemical state, through principal components (PCs). The PCs are derived using principal component analysis (PCA) implemented on the measured thermo-chemical scalars. With the solution for the PCs, the number of governing equations and associated closure terms is reduced relative to the solution of the measured species and temperature. The PINNs are trained on two flame conditions, the so-called Sandia flames D and F, and are validated on an additional flame, flame E. In addition to the radial and axial spatial coordinates, the Reynolds number is prescribed as an additional input parameter. A relatively shallow network attached to the PINNs is used to relate the unconditional means of the PCs to the source terms in their transport equations. The results show that PCs, species, the mixture fraction, and the axial and radial velocity components can adequately be represented with PINNs compared to experimental statistics. Moreover, PINNs are able to reconstruct closure terms associated with turbulence and scalar transport, including the averaged PCs' chemical source terms.