TODO. Various techniques in “running networks backwards”, definition later.
Prior regularisations for ill-posed inverse problems.
My focus is more on inverse problems.
Adler, Jonas, and Ozan Öktem. 2018. “Learned Primal-Dual Reconstruction.” IEEE Transactions on Medical Imaging 37 (6): 1322–32.
Anantha Padmanabha, Govinda, and Nicholas Zabaras. 2021. “Solving Inverse Problems Using Conditional Invertible Neural Networks.” Journal of Computational Physics 433 (May): 110194.
Ardizzone, Lynton, Jakob Kruse, Sebastian Wirkert, Daniel Rahner, Eric W. Pellegrini, Ralf S. Klessen, Lena Maier-Hein, Carsten Rother, and Ullrich Köthe. 2019. “Analyzing Inverse Problems with Invertible Neural Networks.” arXiv:1808.04730 [Cs, Stat], February.
Bao, Gang, Xiaojing Ye, Yaohua Zang, and Haomin Zhou. 2020. “Numerical Solution of Inverse Problems by Weak Adversarial Networks.” Inverse Problems 36 (11): 115003.
Borgerding, Mark, and Philip Schniter. 2016. “Onsager-Corrected Deep Networks for Sparse Linear Inverse Problems.” arXiv:1612.01183 [Cs, Math], December.
Chang, Bo, Lili Meng, Eldad Haber, Lars Ruthotto, David Begert, and Elliot Holtham. 2018. “Reversible Architectures for Arbitrarily Deep Residual Neural Networks.” In arXiv:1709.03698 [Cs, Stat].
Depina, Ivan, Saket Jain, Sigurdur Mar Valsson, and Hrvoje Gotovac. 2021. “Application of Physics-Informed Neural Networks to Inverse Problems in Unsaturated Groundwater Flow.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 0 (0): 1–16.
Franklin, Joel N. 1970. “Well-Posed Stochastic Extensions of Ill-Posed Linear Problems.” Journal of Mathematical Analysis and Applications 31 (3): 682–716.
Genzel, Martin, Jan Macdonald, and Maximilian März. 2020. “Solving Inverse Problems With Deep Neural Networks – Robustness Included?” arXiv:2011.04268 [Cs, Math], November.
Haber, Eldad, and Lars Ruthotto. 2018. “Stable Architectures for Deep Neural Networks.” Inverse Problems 34 (1): 014004.
Holl, Philipp, Vladlen Koltun, Kiwon Um, and Nils Thuerey. 2020. “Phiflow: A Differentiable PDE Solving Framework for Deep Learning via Physical Simulations.” In NeurIPS Workshop.
Holl, Philipp, Nils Thuerey, and Vladlen Koltun. 2020. “Learning to Control PDEs with Differentiable Physics.” In ICLR, 5.
Jo, Hyeontae, Hwijae Son, Hyung Ju Hwang, and Eun Heui Kim. 2020. “Deep Neural Network Approach to Forward-Inverse Problems.” Networks & Heterogeneous Media 15 (2): 247.
Kawar, Bahjat, Gregory Vaksman, and Michael Elad. 2021. “SNIPS: Solving Noisy Inverse Problems Stochastically.” In.
Khodayi-Mehr, Reza, and Michael M. Zavlanos. 2019. “VarNet: Variational Neural Networks for the Solution of Partial Differential Equations.” arXiv:1912.07443 [Physics, Stat], December.
Li, Housen, Johannes Schwab, Stephan Antholzer, and Markus Haltmeier. 2020. “NETT: Solving Inverse Problems with Deep Neural Networks.” Inverse Problems 36 (6): 065005.
Lu, Lu, Xuhui Meng, Zhiping Mao, and George Em Karniadakis. 2021. “DeepXDE: A Deep Learning Library for Solving Differential Equations.” SIAM Review 63 (1): 208–28.
Lucas, Alice, Michael Iliadis, Rafael Molina, and Aggelos K. Katsaggelos. 2018. “Using Deep Neural Networks for Inverse Problems in Imaging: Beyond Analytical Methods.” IEEE Signal Processing Magazine 35 (1): 20–36.
Lunz, Sebastian, Carola Schoenlieb, and Ozan Öktem. 2018. “Adversarial Regularizers in Inverse Problems.” In, 10.
Mahendran, Aravindh, and Andrea Vedaldi. 2015. “Understanding Deep Image Representations by Inverting Them.” In 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 5188–96.
Mowlavi, Saviz, and Saleh Nabi. 2021. “Optimal Control of PDEs Using Physics-Informed Neural Networks.” arXiv:2111.09880 [Physics], November.
Ogawa, T., Y. Kosugi, and H. Kanada. 1998. “Neural Network Based Solution to Inverse Problems.” In 1998 IEEE International Joint Conference on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36227), 3:2471–2476 vol.3.
Rackauckas, Christopher, Yingbo Ma, Vaibhav Dixit, Xingjian Guo, Mike Innes, Jarrett Revels, Joakim Nyberg, and Vijay Ivaturi. 2018. “A Comparison of Automatic Differentiation and Continuous Sensitivity Analysis for Derivatives of Differential Equation Solutions.” arXiv:1812.01892 [Cs], December.
Simonyan, Karen, Andrea Vedaldi, and Andrew Zisserman. 2014. “Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps.” arXiv:1312.6034 [Cs], April.
Spantini, Alessio, Antti Solonen, Tiangang Cui, James Martin, Luis Tenorio, and Youssef Marzouk. 2015. “Optimal Low-Rank Approximations of Bayesian Linear Inverse Problems.” SIAM Journal on Scientific Computing 37 (6): A2451–87.
Tait, Daniel J., and Theodoros Damoulas. 2020. “Variational Autoencoding of PDE Inverse Problems.” arXiv:2006.15641 [Cs, Stat], June.
Wei, Qi, Kai Fan, Lawrence Carin, and Katherine A. Heller. 2017. “An Inner-Loop Free Solution to Inverse Problems Using Deep Neural Networks.” arXiv:1709.01841 [Cs], September.
Williams, Christopher, Stefan Klanke, Sethu Vijayakumar, and Kian M. Chai. 2009. “Multi-Task Gaussian Process Learning of Robot Inverse Dynamics.” In Advances in Neural Information Processing Systems 21, edited by D. Koller, D. Schuurmans, Y. Bengio, and L. Bottou, 265–72. Curran Associates, Inc.
Yosinski, Jason, Jeff Clune, Anh Nguyen, Thomas Fuchs, and Hod Lipson. 2015. “Understanding Neural Networks Through Deep Visualization.” arXiv:1506.06579 [Cs], June.
Zhang, Dongkun, Ling Guo, and George Em Karniadakis. 2020. “Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks.” SIAM Journal on Scientific Computing 42 (2): A639–65.