This also makes me think of "inverse problems", in the context of mathematics, physics.
E.g. a forward problem might be to solve some PDE to simulate the state of a system from some known initial conditions.
The inverse problem could be to try to reverse engineer what the initial conditions were given the observed state of the system.
Inverse problems are typically much harder to deal with, and much harder to solve. E.g. perhaps they don't have a unique solution, or the solution is a highly discontinuous function of the inputs, which amplifies any measurement errors. In practice this can be addressed by regularisation aka introducing strong structural assumptions about what the expected solution should be like. This can be quite reasonable from a Bayesian perspective.
E.g. a forward problem might be to solve some PDE to simulate the state of a system from some known initial conditions.
The inverse problem could be to try to reverse engineer what the initial conditions were given the observed state of the system.
Inverse problems are typically much harder to deal with, and much harder to solve. E.g. perhaps they don't have a unique solution, or the solution is a highly discontinuous function of the inputs, which amplifies any measurement errors. In practice this can be addressed by regularisation aka introducing strong structural assumptions about what the expected solution should be like. This can be quite reasonable from a Bayesian perspective.
https://en.wikipedia.org/wiki/Inverse_problem#Mathematical_c...