B. Adcock, J.M. Cardenas and N.D. A unified framework for learning with nonlinear model classes from arbitrary linear samples. Proceedings of the 41st International Conference on Machine Learning (ICML 2024), pp. 169–202.
J.M. Cardenas, B. Adcock and N.D. CS4ML: A general framework for active learning with arbitrary data based on Christoffel functions. Advances in Neural Information Processing Systems 36 (NeurIPS 2023, spotlight).
B. Adcock, N.D. and S. Moraga. Optimal deep learning of holomorphic operators between Banach spaces. Advances in Neural Information Processing Systems 37 (NeurIPS 2024, spotlight).
S. Brugiapaglia, N.D., S. Karam and W. Wang. Physics-informed deep learning and compressive collocation for high-dimensional diffusion-reaction equations: practical existence theory and numerics. Journal of Machine Learning Research 26(275), 1–51 (2025).
B. Adcock, S. Brugiapaglia, N.D. and S. Moraga. Near-optimal learning of Banach-valued, high-dimensional functions via deep neural networks. Neural Networks 181, 106761 (2025).
B. Adcock, S. Brugiapaglia, N.D. and S. Moraga. On efficient algorithms for computing near-best polynomial approximations to high-dimensional, Hilbert-valued functions from limited samples. Memoirs of the European Mathematical Society, Vol. 13 (2024).
A. DeLise and N.D. Active Learning for Conditional Generative Compressed Sensing. Preprint (2026).
B. Adcock, S. Brugiapaglia, N.D. and S. Moraga. On efficient algorithms for computing near-best polynomial approximations to high-dimensional, Hilbert-valued functions from limited samples. Memoirs of the European Mathematical Society, Vol. 13 (2024).
B. Adcock, S. Brugiapaglia, N.D. and S. Moraga. Learning smooth functions in high dimensions: from sparse polynomials to deep neural networks. In Numerical Analysis Meets Machine Learning, Handbook of Numerical Analysis, Vol. 25, pp. 1–52 (2024).
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, pp. 9–77 (2022).
B. Adcock, N.D. and S. Moraga. Optimal approximation of infinite-dimensional holomorphic functions II: recovery from i.i.d. pointwise samples. Journal of Complexity 89, 101933 (2025).
S. Brugiapaglia, N.D., S. Karam and W. Wang. Physics-informed deep learning and compressive collocation for high-dimensional diffusion-reaction equations: practical existence theory and numerics. Journal of Machine Learning Research 26(275), 1–51 (2025).
B. Adcock, S. Brugiapaglia, N.D. and S. Moraga. Near-optimal learning of Banach-valued, high-dimensional functions via deep neural networks. Neural Networks 181, 106761 (2025).
B. Adcock, N.D. and S. Moraga. Optimal approximation of infinite-dimensional holomorphic functions. Calcolo 61, 12 (2024).
B. Adcock, J.M. Cardenas and N.D. An adaptive sampling and domain learning strategy for multivariate function approximation on unknown domains. SIAM Journal on Scientific Computing 45(1), A200–A225 (2023).
G. Novakovsky, N.D., M.W. Libbrecht, W.W. Wasserman and S. Mostafavi. Obtaining genetics insights from deep learning via explainable artificial intelligence. Nature Reviews Genetics 24, 125–137 (2023).
B. Adcock, J.M. Cardenas and N.D. CAS4DL: Christoffel adaptive sampling for function approximation via deep learning. Sampling Theory, Signal Processing, and Data Analysis 20, 21 (2022).
N.D., H. Tran and C. Webster. On the strong convergence of forward-backward splitting in reconstructing jointly sparse signals. Set-Valued and Variational Analysis 30, 543–557 (2022).
B. Adcock, N.D. and Q. Xu. Improved recovery guarantees and sampling strategies for TV minimization in compressive imaging. SIAM Journal on Imaging Sciences 14(3), 1149–1183 (2021).
B. Adcock and N.D. The gap between theory and practice in function approximation with deep neural networks. SIAM Journal on Mathematics of Data Science 3(2), 624–655 (2021).
H. Zabeti, N.D., A.H. Safari, N. Sedaghat, M.W. Libbrecht and L. Chindelevitch. INGOT-DR: an interpretable classifier for predicting drug resistance in M. tuberculosis. Algorithms for Molecular Biology 16, 17 (2021).
N.D., H. Tran and C. Webster. A mixed ℓ1 regularization approach for sparse simultaneous approximation of parameterized PDEs. ESAIM: Mathematical Modelling and Numerical Analysis 53(6), 2025–2045 (2019).
A. Chkifa, N.D., H. Tran and C. Webster. Polynomial approximation via compressed sensing of high-dimensional functions on lower sets. Mathematics of Computation 87(311), 1415–1450 (2018).
N.D., C. Webster and G. Zhang. Explicit cost bounds of stochastic Galerkin approximations for parameterized PDEs with random coefficients. Computers & Mathematics with Applications 71, 2231–2256 (2016).
B. Adcock, N.D. and S. Moraga. Optimal deep learning of holomorphic operators between Banach spaces. Advances in Neural Information Processing Systems 37 (NeurIPS 2024, spotlight).
B. Adcock, J.M. Cardenas and N.D. A unified framework for learning with nonlinear model classes from arbitrary linear samples. Proceedings of the 41st International Conference on Machine Learning (ICML 2024), pp. 169–202.
J.M. Cardenas, B. Adcock and N.D. CS4ML: A general framework for active learning with arbitrary data based on Christoffel functions. Advances in Neural Information Processing Systems 36 (NeurIPS 2023, spotlight).
B. Adcock, S. Brugiapaglia, N.D. and S. Moraga. Deep neural networks are effective at learning high-dimensional Hilbert-valued functions from limited data. Proceedings of Machine Learning Research, MSML 2021, pp. 1–36.
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 Physical 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 (WABI 2020), LIPIcs Vol. 172, pp. 2:1–2:18 (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).
N.D., S. Moraga, S. Brugiapaglia, B. Adcock. Effective deep neural network architectures for learning high-dimensional Banach-valued functions from limited data. 8th International Conference on Computational Harmonic Analysis 2022 (ICCHA2022).
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).
N.D. Sparse reconstruction techniques for solutions of high-dimensional parametric PDEs. Ph.D. dissertation, University of Tennessee (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.