Researching interests:
Inverse problems are concerned with determining (usually numerically) causes for desired or observed effects,  which is a type of problems frequently arising in science and engineering. The property that makes inverse problems mathematically challenging is their “ill-posedness”, which renders traditional numerical methods inherently unstable. This means that a solution to an inverse problem might neither exist nor be unique, and even if some generalized concept of solution is introduced, then this solution depends in a discontinuous way on the data.

Theoretical aspects where I have been active include conditional stability and parameter identification in partial differential equations, regularization schemes in non-Hilbert setting, uncertainty qualification in Bayesian approach and filter based methods.

Selected Publications:

[1] Bao, Gang; Lu, Shuai; Rundell, William and Xu, Boxi: A recursive algorithm for multifrequency acoustic inverse source problems. SIAM J. Numer. Anal. 53 (2015), no. 3, 1608–1628.

[2] Hömberg, Dietmar; Lu, Shuai; Sakamoto, Kenichi and Yamamoto, Masahiro: Parameter identification in non-isothermal nucleation and growth processes. Inverse Problems 30 (2014), no. 3, 035003, 24 pp.

[3] Lu, Shuai; Mathé, Peter: Heuristic parameter selection based on functional minimization: optimality and model function approach. Math. Comp. 82 (2013), no. 283, 1609–1630.

[4] Zhong, Min; Lu, Shuai; Cheng, Jin: Multiscale analysis for ill-posed problems with semi-discrete Tikhonov regularization. Inverse Problems 28 (2012), no. 6, 065019, 19 pp.

[5] Lu, Shuai; Pereverzev, Sergei V.:  Multi-parameter regularization and its numerical realization. Numer. Math. 118 (2011), no. 1, 1–31.

Monograph

[1] Shuai Lu and Sergei V Pereverzev: Regularization Theory for Ill-posed Problems Selected Topics.
Walter de Gruyter GmbH, Berlin/Boston, Inverse and Ill-Posed Problems Series 58