Research
Research Interest
Numerical Analysis
Finite Elements Method
Compressed Sensing
Uncertainty Quantification
High-dimensional Approximation Theory
Machine Learning
Sampling strategies
Data Science
News
Miny-simposium "Learning Deep Neural Networks and Sparse Approximations from Limited Data fro High-Dimensional Problems in Computational Science and Engineering" at SIAM CSE23. See the information here for part I! See the information here for part II
Miny-simposium "Deep Learning and Sparse Approximation for High-Dimensional Problems in Data Science at SIAM MDS22". See the information here for pat I! See the information here for part II!
Best poster Award SIAM CSE21. See the news here!
SIAM Student Chapter at SFU. See the website here!
Book Chapters
B. Adcock, J. M. Cardenas, N. Dexter and S. Moraga, Towards optimal sampling for learning sparse approximations in high dimensions(preview) High Dimensional Optimization and Probability, Springer Optimization and Its Applications, Vol 191. pp 9-77. Springer, Cham. Preprint: arXiv:2202.02360
Publications
Ben Adcock, Juan M. Cardenas, Nick Dexter, A unified framework for learning with nonlinear model classes from arbitrary linear samples (2023). Preprint: arXiv:2311.14886
Ben Adcock, Juan M. Cardenas, Nick Dexter, CS4ML: A general framework for active learning with arbitrary data based on Christoffel functions . Thirty-seventh Conference on Neural Information Processing Systems. Preprint: arXiv.2306.00945
Ben Adcock, Juan M. Cardenas, Nick Dexter, CAS4DL: Christoffel Adaptive Sampling for function approximation via Deep Learning . Sampl. Theory Signal Process. Data Anal. 20, 21 (2022). Preprint: arXiv.2208.12190
Ben Adcock, Juan M. Cardenas, Nick Dexter, Sebastian Moraga, The quest for optimal sampling strategies for learning sparse approximations in high dimensions. Published by International Conference on Computational Harmonic Analysis 2021 (ICCHA-2021). Preprint: [PDF] from univie.ac.at
Ben Adcock, Juan M. Cardenas, Nick Dexter, An Adaptive sampling and domain learning strategy for multivariate function approximation on unknown domains. SIAM J. Sci. Comput. 45(1):A200-A:225, 2023 .Preprint: arXiv:2202.00144
B. Adcock, J. M. Cardenas, N. Dexter and S. Moraga, Towards optimal sampling for learning sparse approximations in high dimensions(preview) High Dimensional Optimization and Probability, Springer Optimization and Its Applications, Vol 191. pp 9-77. Springer, Cham. Preprint: arXiv.2202.02360
Juan M. Cardenas and Manuel Solano. A high order unfitted hybridizable discontinuous Galerkin method for linear elasticity Center for Research in Mathematical Engineering (CI2MA). IMA J. Numer. Anal. 2023. Preprint. ArXiv Preprint: arXiv:2202.03410
Ben Adcock, Juan M. Cardenas. Near-Optimal Sampling Strategies for Multivariate Function Approximation on General Domains. SIAM J. Math. Data Sci. 2(3):607-630. Preprint: arXiv:1908.01249
Thesis
Juan M. Cardenas. Adaptive sampling strategies for function approximation in high dimensions. Phd. D. in Applied Mathetematics Thesis, Simon Fraser University, 2023. Supervisor: Ben Adcock
Juan M. Cardenas. A Discontinuous Hybridizable Galerkin Method for Linear Elasticity in Curved Domains. Mathematical Civil Engineering Thesis, University of Concepcion, 2018. Supervisor: Manuel Solano
Upcomming Events
The Twelfth International Conference on Learning Representations (ICLR 2024) - Vienna, Austria. May 7-11, 2024.
SIAM Annual Meeting (AN24) 2024 - Spokane, U.S. July 8-12, 2024.
the Forty-first International Conference on Machine Learning (ICML 2024) - Viena, Austria. July 21-27, 2024.
SIAM Conference on Mathematics of Data Science (MDS24) - Atlanta, U.S. October 21-25, 2024.
The Thirty-eight Annual conference on Neural Information Processing Systems (NeurIPS 2024) - Vancouver, B.C., Canada, December 9-14, 2024.
The 39th Annual AAAI Conference on Artificial Intelligence (AAAI 2025) - Philadelphia, P.A., U.S. February 2025.
SIAM Conference on Computational Science and Engineering (CSE25) - Forth Worth, Texas, U.S. March 3-7, 2025.
SIAM International Conference on Data Mining (SDM25) - Alexandria, Virginia, U.S. May 1- 3, 2025.
The Third Joint SIAM/CAIMS Annual Meetings (AN25) - Montreal, Quebec, Canada. July 28- August 1, 2025.
Talks and Posters
"An Adaptive Sampling Strategy for Multifidelity Uncertainty Quantification" - SIAM Conference on Uncertainty Quantification (UQ24). Trieste, Italy, February 27- March 1, 2024. (Talk)
"An adaptive sampling strategy to approximate partial differential equations from noisy data" - Seventh Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE 2024). Concepcion, Chile, January 14-19, 2024. (Talk)
"CS4ML: A general framework for active learning with arbitrary data based on Christoffel functions" - Thirty-seventh Annual Conference on Neural Information Processing Systems (NeurIPS 2023). New Orleans, U.S., December 10-16, 2023. (Poster)
"CAS4DL: Christoffel Adaptive Sampling for Deep Learning in Scientific Computing Applications" - SIAM Conference in Computing Science and Engineering (CSE23) - Amsterdam, Netherlands, February 26 - March 3, 2023. (Talk)
"CAS4DL: Christoffel Adaptive Sampling for Deep Learning in Data-Scarce Applications" - SIAM Conference on Mathematics of Data Science (MDS22) - San Diego, California, U.S. - September 26-30, 2022. (Talk)
"The quest for optimal sampling strategies for learning sparse approximations in high dimensions" - International Conference on Computational Harmonic Analysis - Munich, Germany - September 13-17, 2021.(Talk)
"Adaptive sampling and domain learning strategies for multivariate function approximation on known and unknown domains" - Canadian Applied and Industrial Mathematics Society Annual Meeting 2019 - University of Waterloo, Waterloo, Canada - June 21-24, 2019. (Talk)
"Adaptive sampling and domain learning strategies for multivariate function approximation on known and unknown domains" - SIAM Conference on Computational Science and Engineering - Forth Worth, Texasm, U.S. - March 1-5, 2021. (Poster)
"Optimal sampling of a multivariate function on a irregular domain" - SIAM Pacific North West Conference - Seattle University, Washington, U.S. - October 18-20, 2019. (Talk)
"Optimal sampling of a multivariate function on a irregular domain" - Canadian Applied and Industrial Mathematics Society Annual Meeting 2019 - Whistler Conference Center, Whistler, B.C., Canada - June 9-13, 2019. (Talk)
"Hibridized Discontinuous Galerkin method for linear elasticity in curved comains" - XXXI Jornada de Matematica de la Zona Sur - Universidad Austral de Chile, Valdivia, Chile - April 25-27, 2018.(Talk)
Past Events
SIAM Conference on Uncertainty Quantification (UQ24) - February 27-March 1, 2024. Trieste, Italy.
Thirty-seventh Conference on Neural Information Processing Systems (NeurIPS) 2023 - New Orleans, U.S. December 10-16, 2023.
Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE) 2024 - Concepcion, Chile. January 15-19, 2024.
10th International Congress on Industrial and Applied Mathematics (ICIAM 2023) - Waseda University, Tokyo, Japan. August 20-25, 2023.
4th Biennial Meeting of SIAM Pacific Northwest Section 2023 - Bellingham, WA,, U.S. October 13-15, 2023.
Foundations of Computational Mathematics (FoCM) 2023 - Paris, France. June 12-21, 2023.
CAIMS Annual Meeting 2023 - New Brunswick, Canada. June 12-15, 2023.
SIAM International Conference on Data Mining (SDM23) - Minneapolis,U.S. April 27-29, 2023.
SIAM Conference on Computational Science and Engineering (CSE23) - Amsterdam, The Netherlands. February 26-March 3, 2023.
Canadian Mathematical Society winter meeting (CMS) 2022 - Toronto, Canada. December 2-5, 2022.
SIAM Conference on Mathematics of Data Science (MDS22) - San Diego, California, US - September 26-30, 2022.
Focus Program on Data Science, Approximation Theory, and Harmonic Analysis - Workshop on Neural Networks and Deep Learning - FIELDS, University of Toronto, Toronto, Ontario, Canada - June 6 -10, 2022.
ICCHA 2021 - Munich, Germany - September 13-17, 2021.
CAIMS Anual Meeting 2021 - Waterloo, Ontario, Canada - June 21-24, 2021.
SIAM Conference on Computational Science and Engineering (CSE21) - Fort Worth, Texas, U.S. - March 1-5, 2021.
SIAM PNW Conference - Seattle University, Seattle, WA, U.S.- October 18-20, 2019.
PIMS CRG Summer School: Deep Learning for Computational Mathematics - Simon Fraser University, BC, Canada - July 22-25, 2019.
CAIMS Anual Meeting - Whistler Conference Center, Whistler, BC, Canada - June 9-13, 2019.
PIMS Mini-course on High Dimensional Data in Uncertainty Quantification of PDEs - Simon Fraser University, BC, Canada - March 4-5, 2019.
2018 Pacific Northwest Numerical Analysis Seminar - University of British Columbia, BC, Canada - October 13 2018.
XXXI Jornada de Matematica de la Zona Sur - Universidad Austral de Chile, Valdivia, Chile - April 25-27, 2018.
WONAPDE - Universidad de Concepcion, Concepcion, Chile - January 11-15, 2016.
Collaborators
The cover photo was taken at Canal de Tenglo, Puerto Montt, Chile.