### Preprints

- Yiping Lu, Haoxuan Chen, Jianfeng Lu, Lexing Ying, and Jose Blanchet,
*Machine learning for Elliptic PDEs: Fast rate generalization bound, neural scaling law and minimax optimality*(2021) [arXiv:2110.06897] - with Felix Otto and Lihan Wang,
*Optimal artificial boundary conditions based on second-order correctors for three dimensional random elliptic media*(2021) [arXiv:2109.01616] - with Thomas Barthel and Gero Friesecke,
*On the closedness and geometry of tensor network state sets*(2021) [arXiv:2108.00031] - with Kevin Stubbs,
*Finite second moment implies Chern triviality in non-periodic insulators*(2021) [arXiv:2107.10699] - with Guillaume Bal, Simon Becker, Alexis Drouot, Clotilde Fermanian Kammerer, and Alexander Watson,
*Edge state dynamics along curved interfaces*(2021) [arXiv:2106.00729] - with Yulong Lu,
*A priori generalization error analysis of two-layer neural networks for solving high dimensional Schrodinger eigenvalue problems*(2021) [arXiv:2105.01228] - with Yu Cao,
*Structure-preserving numerical schemes for Lindblad equations*(2021) [arXiv:2103.01194] - with Kevin Stubbs,
*Algebraic localization implies exponential localization in non-periodic insulators*(2021) [arXiv:2101.02626] - with Ziang Chen and Yingzhou Li,
*On the global convergence of randomized coordinate gradient descent for non-convex optimization*(2021) [arXiv:2101.01323] - with Terry Loring and Alex Watson,
*Locality of the windowed local density of states*(2021) [arXiv:2101.00272] - with Lihan Wang,
*Complexity of zigzag sampling algorithm for strongly log-concave distributions*(2020) [arXiv:2012.11094] - with Stefan Steinerberger,
*Neural collapse with cross-entropy loss*(2020) [arXiv:2012.08465] - with Shi Chen, Qin Li, and Stephen J. Wright,
*Manifold learning and nonlinear homogenization*(2020) [arXiv:2011.00568] - with Cody Murphey and Stefan Steinerberger,
*Fast localization of eigenfunctions via smoothed potentials*(2020) [arXiv:2010.15062] - with Katy Craig, Jian-Guo Liu, Jeremy Marzuola, and Li Wang,
*A proximal-gradient algorithm for crystal surface evolution*(2020) [arXiv:2006.12528] - with Zhenning Cai and Siyao Yang,
*Numerical analysis for inchworm Monte Carlo method: Sign problem and error growth*(2020) [arXiv:2006.07654] - Matthias Sachs, Deborshee Sen, Jianfeng Lu, and David Dunson,
*Posterior computation with the Gibbs zig-zag sampler*(2020) [arXiv:2004.04254] - Shahar Kovalsky, Noam Aigerman, Ingrid Daubechies, Michael Kazhdan, Jianfeng Lu, and Stefan Steinerberger,
*Non-convex planar harmonic maps*(2020) [arXiv:2001.01322] - with Jiequn Han, Yingzhou Li, Lin Lin, Jiefu Zhang, and Linfeng Zhang,
*Universal approximation of symmetric and anti-symmetric functions*(2019) [arXiv:1912.01765] - with Yu Cao and Lihan Wang,
*On explicit \(L^2\)-convergence rate estimate for underdamped Langevin dyanmics*(2019) [arXiv:1908.04746] - with Yulong Lu and Jim Nolen,
*Accelerating Langevin sampling with birth-death*(2019) [arXiv:1905.09863] - with Michael Holst, Houdong Hu, Jeremy L. Marzuola, Duo Song, and John Weare,
*Symmetric breaking in density functional theory due to Dirac exchange for a hydrogen molecule*(2019) [arXiv:1902.03497] - with Zhenning Cai and Kevin Stubbs,
*On discrete Wigner transforms*(2018) [arXiv:1802.05834] - with Stefan Steinerberger,
*Riesz energy on the torus: Regularity of minimizers*(2017) [arXiv:1710.08010] - with Felix Otto,
*An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus*(2015) [arXiv:1508.07172]