基础知识学习指南：
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本科阶段学习书籍：
----> Richard C. Aster, Brian Borchers, Clifford H. Thurber, Parameter Estimation and Inverse Problems, Second Edition, 2013. PDF（第一、二版）PDF（第三版） （有限维理论+算法；阅读基础：高等代数，数学分析）
----> Daniela Calvetti and Erkki Somersalo, Introduction to Bayesian Scientific Computing -- Ten Lectures on Subjective Computing, Springer, 2007. (贝叶斯计算；阅读基础：高等代数，数学分析)
----> Jari Kaipio, E. Somersalo, Statistical and Computational Inverse Problems, Applied Mathematical Sciences 160, 2004. (贝叶斯理论+算法；阅读基础：高等代数，数学分析，泛函分析)
----> Christopher M. Bishop, Pattern Recognition And Machine Learning, Springer, 2006 (贝叶斯观点下的机器学习；阅读基础：高等代数，数学分析，泛函分析)
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反问题相关的一些课程：
----> Welcome to Inverse Problems and Imaging (https://tristanvanleeuwen.github.io/IP_and_Im_Lectures/intro.html)
----> Professor Haizhao Yang, Mathematical Theory and Applications of Deep Learning (http://tmcc.whu.edu.cn/info/1262/2052.htm)
----> 金其年教授，反问题正则化理论，国家天元数学中部数学中心(https://www.bilibili.com/video/BV1wP4y1c71R?spm_id_from=333.337.search-card.all.click&vd_source=38dafb1e6cbb16d24205806362d6d103)
----> 李培军教授，Maxwell's Equation in Periodic Strucutres. (https://www.bilibili.com/video/BV1HF411V7vJ?spm_id_from=333.337.search-card.all.click&vd_source=38dafb1e6cbb16d24205806362d6d103)
----> (天元数学中心)深度学习与科学计算的结合：基础与提高(https://www.bilibili.com/video/BV1B3411j7of?spm_id_from=333.337.search-card.all.click&vd_source=38dafb1e6cbb16d24205806362d6d103)
----> Control, Machine Learning and Numerics by Professor Enrique Zuazua from FAU Germany(https://www.bilibili.com/video/BV1jL411H7W3?spm_id_from=333.999.0.0&vd_source=38dafb1e6cbb16d24205806362d6d103)
----> 龚伟教授，偏微分方程约束优化：理论与算法 短课程(https://www.bilibili.com/video/BV1nA411v7AF?spm_id_from=333.999.0.0&vd_source=38dafb1e6cbb16d24205806362d6d103)
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研究生阶段学习书籍：
反问题正则化理论基础：
----> Thorsten Hohage, Lecture Notes on Inverse problems, 2002. PDF (复习泛函分析的同时学习经典的正则化方法)
统计反问题理论基础：
----> 严加安，测度论讲义（第二版），科学出版社，2004 （整本） PDF，课后习题答案PDF
----> J. C. Robinson, Infinite-Dimensional Dynamical Systems, An Introduction to Dissipative Prabolic PDEs and the Theory of Global Attractors, Cambridge Texts in Applied Mathematics, 2001 （阅读1--7章 复习泛函分析，了解PDE的基本理论）
----> Giuseppe Da Prato, An Introduction to Infinite-Dimensional Analysis, Springer, 2006. (阅读1--3章)
----> Giuseppe Da Prato and Jerzy Zabczyk, Stochastic Equations in Infinite Dimensions, Second Edition, Cambridge University Press, 2014. （阅读2--4章 了解无穷维测度的基本理论）
----> Lawrence C. Evans, Partial Differential Equations, Second Edition, American Mathematical Society, 2010. （阅读5--7章 回顾线性PDE的基础）
----> E. D. nezza, G. Palatucci, E. Valdinoci, Hitchhiker's guide to the fractional Sobolev spaces, Bull. Sci. math. 136 (2012) 521-573 （简单学习分数次Sobolev空间）
----> Masoumeh Dashti and Andrew M. Stuart, The Bayesian Approach to Inverse Problem, Handbook of Uncertainty Quantification, Springer International Publishing Switzerland 2017. 与 A. M. Stuart, Inverse problems: A Bayesian perspective, Acta Numerica, 2010 （学习无穷维贝叶斯反演理论与算法）
统计反问题计算基础（基于有限元）：
----> Daniela Calvetti and Erkki Somersalo, Introduction to Bayesian Scientific Computing -- Ten Lectures on Subjective Computing, Springer, 2007. (整本书)
----> 刘继军，现代数值计算方法，科学出版社，2010 （阅读1--3章了解有限元方法的基本知识）
----> Juan Carlos De los Reyes, Numerical PDE-Constrained Optimization, Springer, 2015 (PDE约束下优化问题的基本理论)
----> T. Bui-Thanh, O. Ghattas, J. Martin, G. Stadler, A computational framework for infinite-dimensional Bayesian inverse problems Part I: The linearized case, with application to global seismic inversion, SIAM J. Sci. Comput, 35(6), 2013, A2494-A2523 （学习基于有限元离散的贝叶斯反演计算基本概念）
----> 学习Python编程，学习 https://uvilla.github.io/inverse17/ （熟悉网页上的程序）
统计反问题+机器学习（还没有书，可通过以下文章了解）：
----> Pelip Cucker, Steve Samle, On the mathematical foundations of learning, Bulletin of The American Mathematical Society, 39(1), 2001, 1-49.
----> Ernesto De Vito, Lorenzo Rosasco, Andrea Caponnetto et al., Learning from examples as an inverse problem, Journal of Machine Learning Research, 6, 2005, 883-904. (在核方法的框架下阐明了反问题与机器学习问题)
----> M. M. Dunlop, M. A. Girolami, A. M. Stuart, and A. L. Teckentrup; How Deep Are Deep Gaussian Processes? Journal of Machine Learning Research 19(54):1−46, 2018.
----> N. B. Kovachki, and A. M. Stuart; Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks. Inverse Problems, Vol. 35, Number 9, (2019).
----> K. Bhattacharya, B. Hosseini, N. B. Kovachki, A. M. Stuart; Model Reduction and Neural Networks for Parametric PDEs
----> F. Hoffmann, B. Hosseini, Z. Ren, A. M. Stuart; Consistency of Semi-Supervised Learning Algorithms on Graphs: Probit and One-Hot Methods, Journal of Machine Learning Research, 21(186):1−55, 2020.
----> M. M. Dunlop, D. Slepcev, A. M. Stuart, M. Thorpe; Large Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning Algorithms, Applied & Computational Harmonic Analysis, 49-2 (2020), pp. 655-697.
梯度流：
----> Filippo Santambrogio, Optimal Transport for Applied Mathematicans---Calculus of Variations, PDEs, and Modeling, Birkhauser, 2015
----> Luigi Ambrosio, Nicola Gigli, Giuseppe Savare, Gradient Flows --- in Metric Spaces and in the Space of Probability Measures, Second Edition, 2008
图神经网络：
----> Yao Ma, Jiliang Tang, Deep Learning on Graphs, 2020.
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注：书籍和论文可以在 http://gen.lib.rus.ec/ 上下载
