Parameter inference problem

The parameter inference problem corresponds to the inverse modeling of a system. The aim is to determine the parameters of a mathematical model based on observation values.

According to the model equation , a subset of the model variables as well as the relations and thus the definition of the function are known. The parameter inference problem thus has the signature of . ${\displaystyle \{{\mathcal {V}}\}=f(\{{\mathcal {R}}\},\{{\mathcal {V}}\},\{p\})}$ ${\displaystyle \{{\mathcal {V}}\}}$ ${\displaystyle \{{\mathcal {R}}\}}$ ${\displaystyle f:p\rightarrow V}$ ${\displaystyle f^{-1}:V\rightarrow p}$

Problem reduction

If the function cannot be inverted, the solution can be approximated if there is an evaluation function . Then the parameter inference problem can be reduced to an optimization problem . ${\displaystyle f}$ ${\displaystyle f^{-1}}$ ${\displaystyle c:V,p\rightarrow \mathbb {R} }$

Common candidates for the scoring function are methods of similarity analysis or the mean square deviation . ${\displaystyle c}$

Application examples

The physical properties, so the parameters of the mathematical model of a GaAs - MESFET could with optimization algorithms are determined.

See also

• Inference (logic)
• Inferential statistics

literature

1. ↑ Albert Tarantola. Inverse Problem Theory. Society of Industrial and Applied Mathematics, 2004
2. ↑ Gerd Gottwald and Werner Wiesbeck. The Conjugate Gradient Method in Comparison with the Evolution Optimization for Solving Nonlinear Problems. Proc. of the 21th Europ. Microwave Conference, pages 1544-1549, 1992