In research on inverse problems, it's common to construct a synthetic data set from a known set of parameters and then test whether the inversion technique can reconstruct those parameters. In doing so, it's important to add appropriate levels of random noise to the synthetic data. Furthermore, if the method used to compute the synthetic data is based on a finite difference or finite element grid, it's also important to not use that same grid in the inversion process. Otherwise, the inversion process is really inverting the approximate numerical forward model. The phrase "inverse crime" has been used to describe this.
This phrase was in common use when I first became interested in these problems. I'm aware that it appears in the book Inverse Acoustic and Electromagnetic Scattering Theory by Colton and Kress, published in 1992. I'd be interested in any earlier uses of the phrase.