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I have added a test function to validate the Automatic differentiation implemented by TensorFlow. This test computes the Jacobians of the 3D power spectrum of the N-body simulation both by Automatic differentiation and finite differences.
The two derivatives are comparable with a tolerance error of 0.1 .
Sadly this test is a bit slow (it spends about 6/7 minutes).
I also have added a notebook with a plot to compare the two Jacobians.
https://github.com/DifferentiableUniverseInitiative/flowpm/blob/Nbody_jacobian/notebooks/num_theo_jacobian.ipynb