Mathematical and Computational Methods for Machine Learning

  1. "Normalization effects on deep neural networks", (with Jiahui Yu), 2023, AIMS Journal on Foundations of Data Science, 2023, Volume 5, Issue 3: pp. 389-465, [ArXiv preprint], [CODE].
  2. "PDE-constrained Models with Neural Network Terms: Optimization and Global Convergence", (with Justin Sirignano and Jonathan MacArt), 2023, Journal of Computational Physics, Volume 481, 15 May 2023, 112016, [ArXiv preprint].
  3. "Online Adjoint Methods for Optimization of PDEs", (with Justin Sirignano), Applied Mathematics and Optimization, 85, Article number: 18 (2022). [ArXiv preprint].
  4. "Asymptotics of Reinforcement Learning with Neural Networks", (with Justin Sirignano), Stochastic Systems, Vol. 12, No. 1, March 2022, pp. 2-29, [ArXiv preprint].
  5. "Normalization effects on shallow neural networks and related asymptotic expansions", (with Jiahui Yu), 2021, AIMS Journal on Foundations of Data Science , ,June 2021, Vol. 3, Issue 2, pp. 151-200. [ArXiv preprint], [CODE].
  6. "Mean field analysis of deep neural networks", (with Justin Sirignano), 2021, Mathematics of Operations Research, Vol. 47, No. 1, pp. 120-152, [ArXiv preprint].
  7. "Mean field analysis of neural networks: a law of large numbers", (with Justin Sirignano), 2020, SIAM Journal on Applied Mathematics, Vol. 80, Issue 2, pp. 725--752. [ArXiv preprint].
  8. "Stochastic gradient descent in continuous time: a central limit theorem", (with Justin Sirignano), 2019, Stochastic Systems , Volume 10, Issue 2, pp. 99-191, [ArXiv preprint].
  9. "Mean field analysis of neural networks: A central limit theorem", (with Justin Sirignano), 2020, Stochastic Processes and their Applications , Volume 130, Issue 3, March 2020, pp. 1820-1852, [ArXiv preprint].
  10. "Scaling Limit of Neural Networks with the Xavier Initialization and Convergence to a Global Minimum ", (with Justin Sirignano), 2019, [ArXiv preprint], unpublished technical note, available on arxiv.
  11. "DGM: A deep learning algorithm for solving partial differential equations", (with Justin Sirignano), 2018, Journal of Computational Physics , Vol. 375, pp. 1339--1364, [ArXiv preprint].
  12. "Stochastic gradient descent in continuous time", (with Justin Sirignano), 2017, SIAM Journal on Financial Mathematics, Vol. 8, Issue 1, pp. 933--961, [ArXiv preprint]