  We derive conditions in which inverse problems posed under an information
field theory (IFT) framework have unique solutions. While the theorems here
apply to IFT inverse problems in general, we place a special focus on the
problem of identifying model-form error. Due to the continued increase in
popularity of physics-informed methods, tools which can validate the form of
the physics chosen under a physics-informed framework are desirable. Using IFT,
we pose the problem of identifying model-form error as a Bayesian inverse
problem. The IFT framework lets us define a physics-informed prior over fields,
where a parameter, which we call the trust, measures our belief in the physical
model by scaling the spread of this prior. In principle, smaller values of
trust cause the prior to appear flat, representing a larger degree of
uncertainty about the physics. To detect model-form error, we infer the trust
as part of an inverse problem and study the limiting behavior. Using the
Gaussian random field interpretation of IFT, we show how identifying the trust
becomes a well-posed inverse problem. We provide an example where the physics
are assumed to be the Poisson equation and study the effect of model-form error
on the trust. We find that a correct model leads to infinite trust, and under
model-form error, physics which are closer to the ground truth lead to larger
values of the trust.
