TY - GEN A1 - Villani, P. A1 - Unger, Jörg F. A1 - Weiser, M. T1 - Adaptive Gaussian Process Regression for Bayesian inverse problems T2 - arxiv.org N2 - We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on optimizing both the positioning and simulation accuracy of training data in order to reduce the computational cost of simulating training data without compromising the fidelity of the posterior distributions of parameters. The method interleaves a goal-oriented active learning algorithm selecting evaluation points and tolerances based on the expected impact on the Kullback-Leibler divergence of surrogated and true posterior with a Markov Chain Monte Carlo sampling of the posterior. The performance benefit of the adaptive approach is demonstrated for two simple test problems. T2 - ALGORITMY 2024 Central-European Conference on Scientific Computing CY - High Tatra Mountains, Slovakia DA - 15.03.2024 KW - Active learning KW - Bayesian inverse problems KW - Gaussian Process Regression (GPR) KW - Parameter identification KW - Surrogate models PY - 2024 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-600408 DO - https://doi.org/10.48550/arXiv.2404.19459 SN - 2331-8422 SP - 1 EP - 12 PB - Cornell University CY - Ithaca, NY AN - OPUS4-60040 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -