@misc{HartmannRichterSchuetteetal., author = {Hartmann, Carsten and Richter, Lorenz and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Variational characterization of free energy: theory and algorithms}, series = {Entropy}, volume = {19}, journal = {Entropy}, number = {11}, issn = {1099-4300}, doi = {10.3390/e19110626}, pages = {27}, language = {en} } @misc{HartmannKebiriNeureitheretal., author = {Hartmann, Carsten and Kebiri, Omar and Neureither, Lara and Richter, Lorenz}, title = {Variational approach to rare event simulation using least-squares regression}, series = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, volume = {29}, journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, number = {6}, issn = {1089-7682}, doi = {10.1063/1.5090271}, pages = {16}, language = {en} } @misc{NueskenRichter, author = {N{\"u}sken, Nikolas and Richter, Lorenz}, title = {Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space}, series = {Partial Differential Equations and Applications}, volume = {2}, journal = {Partial Differential Equations and Applications}, number = {4}, issn = {2662-2971}, doi = {10.1007/s42985-021-00102-x}, language = {en} } @misc{RichterBoustatiNueskenetal., author = {Richter, Lorenz and Boustati, Ayman and N{\"u}sken, Nikolas and Ruiz, Francisco and Akyildiz, {\"O}mer Deniz}, title = {VarGrad: A Low-Variance Gradient Estimator for Variational Inference}, series = {34th Conference on Neural Information Processing Systems (NeurIPS 2020), Vancouver, Canada}, journal = {34th Conference on Neural Information Processing Systems (NeurIPS 2020), Vancouver, Canada}, doi = {10.48550/arXiv.2010.10436}, pages = {12}, language = {en} } @incollection{HartmannRichter, author = {Hartmann, Carsten and Richter, Lorenz}, title = {Transgressing the boundaries: towards a rigorous understanding of deep learning and its (non-)robustness}, series = {Artificial Intelligence - Limits and Prospects}, booktitle = {Artificial Intelligence - Limits and Prospects}, editor = {Klimczak, Peter and Petersen, Christer}, publisher = {transcript Verlag}, address = {Bielefeld}, isbn = {978-3-8376-5732-6}, doi = {10.14361/9783839457320-004}, pages = {43 -- 82}, language = {en} } @article{HartmannRichter, author = {Hartmann, Carsten and Richter, Lorenz}, title = {Nonasymptotic Bounds for Suboptimal Importance Sampling}, series = {SIAM/ASA Journal on Uncertainty Quantification}, volume = {12}, journal = {SIAM/ASA Journal on Uncertainty Quantification}, number = {2}, publisher = {Society for Industrial \& Applied Mathematics (SIAM)}, issn = {2166-2525}, doi = {10.1137/21M1427760}, pages = {309 -- 346}, language = {en} }