CV

CV

Positions

• Assistant Professor of Mathematics, University of Wisconsin-Madison 2019-present
• Postdoctotal Fellow, Lawrence Berkeley National Lab 2017-2019
• Visiting Assistant Professor, University of California, Irvine 2015-2017

Education

• Ph.D. in Applied Mathematics MIT June 2015
• Thesis : Fast and Scalable Solvers for the Helmholtz Equation .
• Advisor: Laurent Demanet.
• Master in Numerical Analysis and PDE's École Polytechnique August 2010
• Internship topic: Coupling of Thermo-Hydraulic codes.
• Advisor: Annalisa Ambrosso.
• Diploma, Ingénieur Polytechnicien, École Polytechnique August 2010
• Internship topic: Spectral methods for Navier-Stokes.
• Advisor: Oscar Bruno.
• 3 years of Mathematical Engineering studies, Universidad de Chile , 2004-2006

Funding

• WARF Fall Research Competition (sole PI) 2020
• NFS DMS grant 2012292 (sole PI) 2020
• MIT International Science and Technology Initiatives grant (co-PI) 2017

Publications

• M. Li, L. Demanet and L. Zepeda-Núñez, Accurate and Robust Deep Learning Framework for Solving Wave-Based Inverse Problems in the Super-Resolution Regime submitted.
• T. Bui-Thanh, Q. Li, and L. Zepeda-Núñez, Bridging and Improving Theoretical and Computational Electric Impedance Tomography via Data Completion, submitted to SISC.
• Y. Peng, L. Lin, L. Ying, and L. Zepeda-Núñez, Efficient Long-Range Convolutions for Point Clouds, submitted to JCP.
• M. Li, L. Demanet and L. Zepeda-Núñez, Wide-band butterfly network: stable and efficient inversion via multi-frequency neural networks submitted to SIAM MMS.
• L. Zepeda-Núñez, Y. Chen, J. Zhang, W. Jia, L. Zhang, and L. Lin Deep Density: circumventing the Kohn-Sham equations via symmetry preserving neural networks submitted to JCP.
• J. Zhang, L. Zepeda-Núñez, Y. Yao, and L. Lin Learning the mapping $\mathbf{x} 􏰡\rightarrow \sum_{i=1}^n x_i^2$ : the cost of finding the needle in a haystack Commun. Appl. Math. Comput., 2020.
• M. Taus, L. Zepeda-Núñez, R. Hewett, and L. Demanet L-Sweeps: A scalable, parallel preconditioner for the high-frequency Helmholtz equation, J. Comput. Phys., 420:109706, 2020.
• C. Mejuto-Zaera, L. Zepeda-Núñez, M. Lindsey, N. Tubman, B. Whaley, and L. Lin Efficient hybridization Fitting for dynamical mean-field theory viasemi-definite relaxation, Phys. Rev. B 101, 035143, 2020.
• Y. Fan, J. Feliu-Faba, L. Lin, L. Ying, L. Zepeda-Núñez A multiscale neural network based on hierarchical nested bases, Res. Math. Sci. 6, 21 (2019).
• Y. Fan, L. Lin, L. Ying, L. Zepeda-Núñez A multiscale neural network based on hierarchical matrices, Multiscale Model. Simul., 17(4), 1189–1213, 2019.
• L. Lin, L. Zepeda-Núñez Projection based embedding theory for solving Kohn-Sham density functional theory, Multiscale Model. Simul., 17(4), 1274--1300, 2019.
• L. Zepeda-Núñez, A. Scheuer, R. Hewett, L. Demanet, The method of polarized traces for the 3D Helmholtz equation, Geophysics 2019 84:4, T313-T333 .
• J. Fang, J. Qian, L. Zepeda-Núñez , H. Zhao, A hybrid approach to solve the high-frequency Helmholtz equation with source singularity, J. Comput. Phys., 371:261–279, 2018.
• M. Taus, L. Zepeda-Núñez, R. Hewett, L. Demanet, Pollution-free and fast hybridizable discontinuous Galerkin solvers for the high-frequency Helmholtz equation. SEG Tech. Program Expand. Abstr., 2017.
• J. Fang, J. Qian, L. Zepeda-Núñez , H. Zhao, Learning Dominant Wave Directions For Plane Wave Methods For High-Frequency Helmholtz Equations, Res. Math. Sci., 4(1):9, May 2017.
• A. Scheuer, L. Zepeda-Núñez, R. Hewett and L. Demanet, A short note on a pipelined polarized-trace algorihtm for 3D Helmholtz, SEG Tech. Program Expand. Abstr., 2016.
• M. Taus, L. Zepeda-Núñez and L. Demanet, A short note on a fast and high-order Hybridazable Discontinuous Galerkin solver for the 2D high-frequency Helmholtz equation, SEG Tech. Program Expand. Abstr., 2016.
• L. Zepeda-Núñez and H. Zhao, Fast alternating bi-directional preconditioner for the 2D high-frequency Lippmann-Schwinger equation, SIAM J. Sci. Comput., 38(5):B866–B888, 2016.
• L. Zepeda-Núñez and L. Demanet, Nested domain decomposition with polariced traces for the 2D Helmholtz Equation, SIAM J. Sci. Comput., 40(3):B942–B981, 2018.
• L. Zepeda-Núñez and L. Demanet, A short note on the nested-sweep polarized traces method for the 2D Helmholtz equation, SEG Tech. Program Expand. Abstr., 2015.
• L. Zepeda-Núñez and L. Demanet, The method of polarized traces for the 2D Helmholtz equation, J. Comput. Phys., 308:347–388, 2016.
• A. Schiemenz, W. Lewis, L. Zepeda-Núñez, A. El-Sabaa, R. Coates, Improved imaging resolution using a hybrid l-BFGS - truncated Newton method in FWI: application to the Bruce 3D field data, SEG Tech. Program Expand. Abstr., 2014.
• L. Zepeda-Núñez, R. Hewett, L. Demanet, Preconditioning the 2D Helmholtz equation with polarized traces, SEG Tech. Program Expand. Abstr., 2014.
• L. Zepeda-Núñez, R. J. Hewett, M. Rao, L. Demanet, Time-stepping beyond CFL: a locally one-dimensional scheme for acoustic wave propagation, SEG Tech. Program Expand. Abstr., 2013.

Teaching

• UCI, MATH 2B Single-variable Calculus II, spring 2017 : instructor
• UCI, MATH 2D Multi-variable Calculus, winter 2017 : instructor
• UCI, MATH 2A Single-variable Calculus I, fall 2016 : instructor
• UCI, MATH 3A Introduction to Linear Algebra, spring 2016 : instructor
• UCI, MATH 3A Introduction to Linear Algebra, winter 2016 : instructor
• UCI, MATH 105 LA Numerical Analysis Laboratory, fall 2015 : instructor
• MIT, 18.04 Complex variable with applications, fall 2014 : recitation instructor
• École Polytechnique, MAP431 Analyse numérique et optimisation, fall 2009 : tuteur
• Universidad de Chile, MA26B Matemáticas Aplicadas (now MA2002 ) spring 2006 : recitation instructor

Mentoring

• MIT Summer Research Program (MSRP) 2012: Served as a supervisor to Mauricio Flores (now at U. Minnesota) who worked on travel times estimation by spectral deconvolution.
• Summer Internship at ICG/MIT 2014 : Served as a supervisor to Thomas Gillis and Adrien Scheuer (now at Université Catholique de Louvain) who developed a 2D-3D fourth order fast Helmholtz solver.
• Summer Internship at ICG/MIT 2015 : Served as a supervisor to :
  • Adrien Scheuer (now at Université Catholique de Louvain and École Central de Nantes) who developed a parallel Helmholtz solver based on the method of polarized traces;
  • Leo Lébrat (now at INSA Toulouse) who developed a PETSC extension for Pysit;
  • Ian Mcbrearty (now at University fo Winsconsin-Madison) who developed an FWI code for variable density acoustic models.
• Summer Internship at ICG/MIT 2016 : Served as a supervisor to :
  • Adrien Scheuer (now at Université Catholique de Louvain and École Central de Nantes) who developed a highly efficient Helmholtz solver based on the method of polarized traces;

Professional Organizations

• Member, Society for Industrial and Applied Mathematics (SIAM), 2011-Present.
• Member, Society of Exploration in Geophysics (SEG), 2012- Present.

Student Organizations

• President, SIAM MIT student chapter, 2014-Present
• Organizer, Single Person Applied Math Seminar, 2011-2012

Awards

• MIT Presidential Fellowship, Cambridge, MA, USA 2010
• Egide Fellowship from French government for Master’s studies, Paris, France. 2009
• Summer Undergraduate Research Fellowship (SURF) Caltech Pasadena, CA, USA. 2009
• Foundation of Ecole Polytechnique Fellowship, Paris, France. 2007
• Excellence Fellowship, Universidad de Chile, Santiago de Chile, Chile. 2005
• Entrance Excellence Fellowship, Universidad de Chile, Santiago de Chile, Chile. 2004
• Silver Medal, Ibero-American Physics Olympiads, Havana, Cuba. 2003