OPTIMIZATION METHODS IN INVERSE PROBLEMS – OPTIMIZATION APPROACHES FOR DETERMINING THE SOURCE FUNCTION
Abstract
This paper explores optimization methods for solving inverse problems, specifically focusing on determining unknown source functions in parabolic partial differential equations. The study discusses problem formulation, regularization techniques, numerical optimization algorithms, parameterization strategies, and uncertainty quantification. Applications in heat conduction, geophysics, medical imaging, and environmental monitoring are examined. Emerging hybrid approaches combining classical optimization and machine learning are also highlighted. The methods presented ensure stable and physically meaningful reconstruction of sources in ill-posed problems.
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