FPGA acceleration of Bayesian model based analysis for time-independent problems

Inverse problems in plasma physics commonly face a tradeoff between approximated real-time schemes or post-processed rigorous uncertainty handling. Bayesian analysis allows parameter and uncertainty estimation as well as joint analysis of multiple diagnostics in a strict mathematical way. It also improves the inference from correlated measurements but with long processing times. For linear and non-linear problems, many optimal and sub-optimal Bayesian online algorithms are available but generally targeted at dynamic systems and introducing some level of approximation. Given plasma physics time-independent non-linear inverse problems, several Wendelstein 7-X diagnostics use a Bayesian inference framework. This research focuses on accelerating this type of mathematically intense standard Bayesian analysis for such inverse problems. We show a significant acceleration for the estimation of electron density and temperature profiles. The approach maintains a floating-point double precision while reducing the processing time useful in applications where a reliable error estimation is required together with a fast processing time.