Publications
Preprints
B. Adcock, S. Brugiapaglia, N.D., S. Moraga, On efficient algorithms for computing near-best polynomial approximations to high-dimensional, Hilbert-valued functions from limited samples. Submitted (2022).
B. Adcock, J.M. Cardenas, N.D. An adaptive sampling and domain learning strategy for multivariate function approximation on unknown domains. Submitted (2022).
H. Zabeti, N. D., I. Lau, L. Unruh, B. Adcock and L. Chindelevitch. Group Testing Large Populations for SARS-CoV-2. Submitted (2021).
Preprint Book Chapters
B. Adcock, J. M. Cardenas, N.D. and S. Moraga, Towards optimal sampling for learning sparse approximations in high dimensions. High Dimensional Optimization and Probability, Springer. Accepted (2021).
Refereed Journal Publications
B. Adcock, N. D., Q. Xu. Improved recovery guarantees and sampling strategies for TV minimization in compressive imaging. SIAM Journal on Imaging Sciences (2021).
B. Adcock, N. D. The gap between theory and practice in function approximation with deep neural networks. SIAM Journal on Mathematics of Data Science (2021).
N. D., H. Tran, C. Webster. On the strong convergence of forward-backward splitting in reconstructing jointly sparse signals. Set-Valued and Variational Analysis (2021).
B. Adcock, S. Brugiapaglia, N.D., S. Moraga. Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data. Proceedings of Machine Learning Research, MSML (2021).
H. Zabeti, N. D., A.H. Safari, N. Sedaghat, M. Libbrecht, L. Chindelevitch, INGOT-DR: an interpretable classifier for predicting drug resistance in M. tuberculosis, Accepted, Algorithms for Molecular Biology, (2021).
N. D., H. Tran, C. Webster. A mixed ℓ1 regularization approach for sparse simultaneous approximation of parameterized PDEs. ESAIM: Mathematical Modelling and Numerical Analysis (2019).
A. Chkifa, N. D., H. Tran, C. Webster. Polynomial approximation via compressed sensing of high-dimensional functions on lower sets. Mathematics of Computation (2016).
N. D., C. Webster, G. Zhang. Explicit cost bounds of stochastic Galerkin approximations for parameterized PDEs with random coefficients. Computers & Mathematics with Applications (2016).
Refereed Conference Proceedings and Extended Abstracts
B. Adcock, S. Brugiapaglia, N.D., S. Moraga. Learning High-Dimensional Hilbert-Valued Functions With Deep Neural Networks From Limited Data. AAAI 2021 Spring Symposium on Combining Artificial Intelligence and Machine Learning with Physics Sciences (2021).
H. Zabeti, N.D., A. H. Safari, N. Sedaghat, M. Libbrecht, L. Chindelevitch. An interpretable classification method for predicting drug resistance in M. tuberculosis. 20th International Workshop on Algorithms in Bioinformatics (2020).
N.D., H. Tran, C. Webster. Reconstructing high-dimensional Hilbert-valued functions via compressed sensing. 13th International conference on Sampling Theory and Applications (2019).
Conference Abstracts
N.D., S. Moraga, S. Brugiapaglia, B. Adcock. Deep Neural Network Approximation of High-Dimensional Hilbert-Valued Functions From Limited Data. Online International Conference on Computational Harmonic Analysis (2021).
J.M. Cardenas, N.D., S. Moraga, B. Adcock. The quest for optimal sampling strategies for learning sparse approximations in high dimensions. Online International Conference on Computational Harmonic Analysis (2021).
Thesis
Sparse Reconstruction Techniques for Solutions of High-Dimensional Parametric PDEs. (Ph.D. dissertation, 2018).
The cover photo was taken at Moraine Lake in Banff National Park in Alberta, Canada. In the warmer months, the water is a brilliant blue-green due to glacial rock flour.