# Impact Study of Numerical Discretization Accuracy on Parameter Reconstructions and Model Parameter Distributions

arXiv: https://arxiv.org/abs/2305.02663 · HTML: https://mlsanity.com/paper/2305.02663/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 53 references that are in the map.
- First posted on arXiv 4 May 2023.

## Builds on (most cited first, 5 of 5)

- [Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction](https://mlsanity.com/paper/1809.06674/) (2018)
- [Automatic tempered posterior distributions for Bayesian inversion problems](https://mlsanity.com/paper/2107.11614/) (2021)
- [Bayesian Active Learning for Structured Output Design](https://mlsanity.com/paper/1911.03671/) (2019)
- [Using Gaussian process regression for efficient parameter reconstruction](https://mlsanity.com/paper/1903.12128/) (2019)
- [Bayesian Target-Vector Optimization for Efficient Parameter Reconstruction](https://mlsanity.com/paper/2202.11559/) (2022)

## Abstract (arXiv)

In optical nano metrology numerical models are used widely for parameter reconstructions. Using the Bayesian target vector optimization method we fit a finite element numerical model to a Grazing Incidence X-Ray fluorescence data set in order to obtain the geometrical parameters of a nano structured line grating. Gaussian process, stochastic machine learning surrogate models, were trained during the reconstruction and afterwards sampled with a Markov chain Monte Carlo sampler to determine the distribution of the reconstructed model parameters. The numerical discretization parameters of the used finite element model impact the numerical discretization error of the forward model. We investigated the impact of the polynomial order of the finite element ansatz functions on the reconstructed parameters as well as on the model parameter distributions. We showed that such a convergence study allows to determine numerical parameters which allows for efficient and accurate reconstruction results.