Käänteismallinnus

Käänteismallinnus, or inverse modeling, is a process used to infer the causes or underlying parameters of a system by analyzing its observed effects. Instead of predicting an output from known inputs, as in forward modeling, käänteismallinnus seeks to determine the inputs or parameters that would produce a specific, observed output. This is often achieved by iteratively adjusting model parameters and comparing the model's output to the actual measurements. When the discrepancy between the model's prediction and the observation is minimized, the parameters used are considered a good representation of the real-world system.

This technique finds applications across numerous scientific and engineering disciplines. In geophysics, for instance, käänteismallinnus is used to determine the internal structure of the Earth by analyzing seismic wave data. In medical imaging, it helps reconstruct images of internal organs from projection data obtained by techniques like CT scans. In environmental science, it can be used to estimate pollution sources based on atmospheric concentration measurements. The process typically involves defining a mathematical model of the phenomenon, an objective function to quantify the difference between model predictions and observations, and an optimization algorithm to find the parameter values that minimize this difference. Challenges in käänteismallinnus often include non-uniqueness, where multiple sets of parameters might produce similar results, and the potential for noise in the observational data to lead to inaccurate inversions.