Check my google scholar page

Many of my papers are available on arXiv

Some representative papers in selected areas:

Machine Learning

EG Tabak, E Vanden-Eijnden, Density estimation by dual ascent of the log-likelihood, Comm.  Math. Sci. 8 (1), 217-233 (2010) [link]
 

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

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]

Multiscale Modeling and HMM

E Vanden-Eijnden, Fast Communications: Numerical techniques for multi-scale dynamical systems with stochastic effects, Comm. Math. Sci. 1 (2), 385-391 (2003) [link]

W E, D Liu, E Vanden‐Eijnden, Analysis of multiscale methods for stochastic differential equations, Comm. Pure App. Math. 58 (11), 1544-1585 (2005) [link]

W E, B Engquist, X Li, W Ren, E Vanden-Eijnden, Heterogeneous multiscale methods: a review, Comm. Comp. Phys. 2 (3), 367-450 (2007)

A Abdulle, W E, B Engquist, E Vanden-Eijnden, The heterogeneous multiscale method, Acta Numerica 21, 1-87 (2012) [link]

Rare Events Modeling and Simulation

E Vanden-Eijnden, FA Tal, Transition state theory: Variational formulation, dynamical corrections, and error estimates, J. Chem. Phys. 123 (18), 184103 (2005)


W E, E Vanden-Eijnden, Towards a theory of transition paths, J. Stat. Phys. 123 (3), 503 (2006)

P Metzner, C Schütte, E Vanden-Eijnden, Transition path theory for Markov jump processes, SIAM Multiscale Modeling & Simulation 7 (3), 1192-1219 (2009)

W E, E Vanden-Eijnden, Transition-path theory and path-finding algorithms for the study of rare events. Ann. Rev. Phys. Chem. 61, 391-420 (2010)

M Cameron, E Vanden-Eijnden, Flows in complex networks: theory, algorithms, and application to Lennard–Jones cluster rearrangement, J. Stat. Phys.  156 (3), 427-454 (2014)

Tobias Grafke, Tobias Schäfer, Eric Vanden-Eijnden, Long term effects of small random perturbations on dynamical systems: Theoretical and computational tools, pp. 17-55 in: Recent Progress and Modern Challenges in Applied Mathematics, Modeling and Computational Science, Springer, New York, NY (2017)

T Grafke, E Vanden-Eijnden, Numerical computation of rare events via large deviation theory, Chaos: An Interdisciplinary Journal of Nonlinear Science 29 (6), 063118 (2019)

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)
 

String Method

W E, W Ren, E Vanden-Eijnden, String method for the study of rare events, Phys. Rev. B 66, 052301 (2002)

W E, W Ren, E Vanden-Eijnden, Finite temperature string method for the study of rare events, J. Phys. Chem. 109 (14), 6688-6693 (2005)

L Maragliano, A Fischer, E Vanden-Eijnden, G Ciccotti, String method in collective variables: Minimum free energy paths and isocommittor surfaces, J. Chem. Phys.  125 (2), 024106 (2006)
 

W E, W Ren, E Vanden-Eijnden,  Simplified and improved string method for computing the minimum energy paths in barrier-crossing events, J. Chem. Phys. 126, 164103 (2007)

L Maragliano, E Vanden-Eijnden, On-the-fly string method for minimum free energy paths calculation, Chem. Phys. Lett.  446 (1-3), 182-190 (2007)

E Vanden-Eijnden, M Venturoli, Revisiting the finite temperature string method for the calculation of reaction tubes and free energies, J. Chem. Phys.  130 (19), 05B605 (2009)

Minimum Action Method

W E, W Ren, E Vanden-Eijnden, Minimum action method for the study of rare events, Comm. Pure App. Math. 57 (5), 637-656 (2004)

M Heymann, E Vanden‐Eijnden, The geometric minimum action method: A least action principle on the space of curves, Comm. Pure App. Math. 61 (8) 1052-1117 (2008)

T Grafke, R Grauer, T Schäfer, E Vanden-Eijnden, Arclength parametrized Hamilton’s equations for the calculation of instantons, SIAM Multiscale Modeling & Simulation 12 (2), 566-580 (2014)
 

Enhanced Sampling

L Maragliano, E Vanden-Eijnden, A temperature accelerated method for sampling free energy and determining reaction pathways in rare events simulations, Chem. Phys. Lett. 426 (1-3), 168-175 (2006)

L Maragliano, E Vanden-Eijnden, Single-sweep methods for free energy calculations, J. Chem. Phys. 128 (18), 184110 (2008)

E Vanden-Eijnden, M Venturoli, Markovian milestoning with Voronoi tessellations,  J. Chem. Phys. 130 (19), 194101 (2009)

E Vanden-Eijnden, M Venturoli, Exact rate calculations by trajectory parallelization and tilting, J. Chem. Phys.  131 (4), 044120 (2009)

C Schütte, F Noé, J Lu, M Sarich, E Vanden-Eijnden, Markov state models based on milestoning,  J. Chem. Phys. 134 (20), 05B609 (2011)

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)

Fluids Dynamics and Geophysical Flows

W E W, E Vanden-Eijnden, Asymptotic theory for the probability density functions in Burgers turbulence, Phys. Rev. Lett. 83 (13), 2572 (1999).

AJ Majda, I Timofeyev, E Vanden Eijnden, A mathematical framework for stochastic climate models, Comm. Pure App. Math. 54 (8), 891-974 (2001)

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

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)