My research focuses on the mathematical and computational aspects of statistical mechanics, with applications to complex dynamical systems arising in molecular dynamics,  materials science, atmosphere-ocean science, fluids dynamics, and neural networks. More recently I have become interested in the mathematical foundations of machine learning (ML) and started to explore the exciting new prospects ML offer for scientific computing.  My work combines tools from probability theory, mathematical physics, numerical analysis, and optimization to uncover governing principles in complex systems and design efficient algorithms for their simulation.


Some recent papers

GM Rotskoff, E Vanden-Eijnden, Trainability and accuracy of neural networks: An interacting particle system approach, arXiv:1805.00915 (2018) [link]

G Dematteis, T Grafke, E Vanden-Eijnden, Rogue waves and large deviations in deep sea, Proc. Nat. Acad. USA  115 (5), 855-860 (2018) [link]

G Rotskoff, S Jelassi, J Bruna, E Vanden-Eijnden, Neuron birth-death dynamics accelerates gradient descent and converges asymptotically, International Conference on Machine Learning, 5508-5517 (2019) [link]

G Dematteis, T Grafke, E Vanden-Eijnden, Extreme event quantification in dynamical systems with random components, SIAM/ASA Journal on Uncertainty Quantification 7 (3), 1029-1059 (2019) [link]

GM Rotskoff, E Vanden-Eijnden, Dynamical Computation of the Density of States and Bayes Factors Using Nonequilibrium Importance Sampling,  Phys. Rev. Lett. 122 (15), 150602 (2019) [link]

G Dematteis, T Grafke, M Onorato, E Vanden-Eijnden, Experimental evidence of hydrodynamic instantons: the universal route to rogue waves, Phys. Rev. X 9 (4), 041057 (2019) [link]
 

Z Chen, GM Rotskoff, J Bruna, E Vanden-Eijnden, A Dynamical Central Limit Theorem for Shallow Neural Networks, arXiv:2008.09623 (2020) [link]

GM Rotskoff, E Vanden-Eijnden, Learning with rare data: Using active importance sampling to optimize objectives dominated by rare events, arXiv:2008.06334 (2020) [link]

SS Mannelli, E Vanden-Eijnden, L Zdeborová, Optimization and Generalization of Shallow Neural Networks with Quadratic Activation Functions, arXiv:2006.15459 (2020) [link]


Contact
Eric Vanden-Eijnden
Professor of Mathematics
Courant Institute of Mathematical Sciences, NYU
251, Mercer Street
New York, NY, 10012
Email: eve2 at cims.nyu.edu
Phone: (212) 998-3154
Fax: (212) 995-412