Herrmann, L. et al. (2020). Deep neural network expression of posterior expectations in Bayesian PDE inversion*The main part of the paper was written while LH was at the Seminar for Applied Mathematics, ETH Zürich, Rämistrasse 101, CH–8092 Zürich, Switzerland, and during the postdoctoral stay of JZ to the Department of Aeronautics and Astronautics, MIT, 02139 Cambridge, MA, USA. JZ is supported by the Swiss National Science Foundation under Early Postdoc.Mobility Fellowship 184530. CS acknowledges stimulating discussions at the RICAM WS on Optimization under uncertainty in November 2019 at RICAM, Linz, Austria, and at the WIAS WS on Deep Learning for PDEs at the Weierstrass Institute Berlin, Germany, 2–6 December 2019.. Inverse problems. p. . [Online].