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For questions pertaining to methods to estimate input parameters based upon output data.

7 votes
Accepted

Inverse advection-diffusion problem, solving for a drift coefficient with experimental data?

There is another approach called the adjoint method, which is commonly used in inverse problems for PDE and which is quite easy to generalize to other problems. This is going to be long. Your observa …
Daniel Shapero's user avatar
1 vote

Algorithm for finding initial conditions of differential equations given trajectory

As Christian Clason alluded to in his comment, you have reinvented the ensemble Kalman filter! The Kalman filter is an algorithm for estimating, from imperfect measurements, the true state of a system …
Daniel Shapero's user avatar