A FEM-Based Neural Network Framework for Inverse Parameter Identification in the Stokes Equations

Kurzfassung

This thesis investigates the use of differentiable neural network surrogates for efficient inverse analysis and optimal sensor placement in PDE-constrained problems. A physics-informed surrogate model is developed and validated against classical numerical methods. Its applicability to parameter identification is demonstrated, with particular emphasis on computational efficiency and reconstruction accuracy. Furthermore, uncertainty quantification is incorporated to assess the reliability of parameter estimates and identify suitable sensor locations. The results demonstrate the potential of differentiable surrogate models to accelerate inverse problems and support uncertainty-based sensor placement.