ANSRE: ANalysis and Synthesis of Rare Events



This website is created in support of a Multi-University Research Initiative (MURI) sponsored by the Air Force, under award number FA9550-20-1-0397, to analyze, understand, and synthesize rare but consequential events.

Earthquakes, tsunamis, volcanic eruptions; pandemics, stock market crashes, currency crises---all these are events that seldom occur within the ordinary spatial and/or temporal scales of a system, and yet have an enormous impact when they do occur. In Air Force applications, rare events of interest include aircraft engine failures, fatigue, and fracture in aero-structural components, lightning or bird strikes on aerospace vehicles, and countless more. The impact of these events lends practical urgency to the development of a comprehensive mathematical theory for the modeling, prediction, and prevention of rare events.

Our goal is to develop a comprehensive framework that can be used to systematically study rare events in a wide range of settings, and we will develop the mathematical and computational tools necessary to apply our framework. While these developments are intended to be foundational and general, they are grounded in---and will be applied to---realistic applications in materials science, environmental engineering, mean-field phenomena, and networks.

Key Investigators

Jose Blanchet

Professor of Management Science and Engineering

William M. Keck Faculty Scholar

Stanford University

Research Interest: Applied probability, Computational finance, MCMC, Queueing theory, Rare-event analysis, Simulation methodology, and Risk theory.

Personal Website

Wei Cai

Professor of Mechanical Engineering

Professor (by courtesy) of Materials Science and Engineering

Stanford University

Research Interest: Predicting mechanical strength of materials through theory and simulations of defect microstructures across atomic, mesoscopic and continuum scales. Developing new atomistic simulation methods for long time-scale processes, such as crystal growth and self-assembly. Introducing magnetic field in quantum simulations of electronic structure and transport.

Personal Website

Maria Cameron

Associate Professor of Mathematics

Affiliate Associate Professor of Computer Science

University of Maryland

Research Interest: Numerical methods for solving mathematical problems arising in natural sciences including geophysics, chemical physics, and biology, spliting between Hamilton-Jacobi solvers for nonlinear PDEs and greedy graph algorithms for analysis of complex networks.

Personal Website

Youssef Marzouk

Professor of Aeronautics and Astronautics

Director of Aerospace Computational Design Laboratory

Co-director of MIT Center for Computational Science and Engineering

Massachusetts Institute of Technology

Research Interest: Intersection of computation and statistical inference with physical modeling, including new methodologies for uncertainty quantification, Bayesian modeling and computation, data assimilation, experimental design, and machine learning in complex physical systems.

Personal Website

Evan Reed

Associate Professor of Materials Science and Engineering

Charles Lee Powell Faculty Scholar

Stanford University

Research Interest: Theory and modeling of nanoscale materials for electronics and energy applications, and materials at conditions of extreme temperatures, pressures, and fields. His work to date has focused on 2D materials, high pressure shock wave compression, THz radiation generation, phase change materials, materials informatics approaches, energetic materials, and photonic crystals.

Personal Website

Zhigang Suo

Allen E. and Marilyn M. Puckett Professor of Mechanics and Materials

Member of the US National Academy of Engineering

Harvard University

Research Interest: Mechanical behavior of materials and structures. Basic processes include fracture, deformation, polarization, and diffusion, driven by various thermodynamic forces (e.g., stress, electric field, electron wind, chemical potential). Applications are concerned with microelectronics, large-area electronics, soft materials, active materials, and lithium-ion batteries.

Personal Website

Vahid Tarokh

Rhodes Family Professor of Electrical and Computer Engineering

Bass Connections Endowed Professor

Professor of Mathematics

Duke University

Research Interest: Representation, modeling, inference and prediction from data such as determining how different people will respond to exposure to certain viruses, predicting rare events from small amounts of data, formulation and calculation of limits of learning from observations, and prediction of a macaque monkey's future actions from its brain waves.

Personal Website



Kickoff Meeting

  • Zhigang Suo: Fractures, Fatigue and Cracking Applications Thrust. Slides

  • Vahid Tarokh: Multidimensional Dimensional Extremes Thrust. Slides

  • Evan Reed: Chemical Reactions and Large-Scale Simulations Thrust. Slides

  • Youssef Marzouk: High Dimensional Learning for Conditioning Thrust. Slides

  • Maria Cameron: Large Deviations Computations Thrust. Slides

  • Jose Blanchet: Model Misspecification and Robustness Thrust. Slides



Modified Frank Wolfe in Probability Space

Kent, C., Li, J., Blanchet, J., & Glynn, P. W. (2021)
Advances in Neural Information Processing Systems, 34.

Adversarial Regression with Doubly Non-negative Weighting Matrices

Le, T., Nguyen, T., Yamada, M., Blanchet, J., & Nguyen, V. A. (2021)
Advances in Neural Information Processing Systems, 34.

Statistical Analysis of Wasserstein Distributionally Robust Estimators

Blanchet, J., Murthy, K., & Nguyen, V. A. (2021)
In Tutorials in Operations Research: Emerging Optimization Methods and Modeling Techniques with Applications (pp. 227-254). INFORMS.

Distributionally Robust Martingale Optimal Transport

Zhou, Z., Blanchet, J., & Glynn, P. W. (2021)
arXiv preprint arXiv:2106.07191.

Unbiased Optimal Stopping via the MUSE

Zhou, Z., Wang, G., Blanchet, J., & Glynn, P. W. (2021)
arXiv preprint arXiv:2106.02263.

Efficient Steady-State Simulation of High-Dimensional Stochastic Networks

Blanchet, J., Chen, X., Si, N., & Glynn, P. W. (2021)
Stochastic Systems.

Sequential Domain Adaptation by Synthesizing Distributionally Robust Experts

Taskesen, B., Yue, M. C., Blanchet, J., Kuhn, D., & Nguyen, V. A. (2021)
In International Conference on Machine Learning.

Robustifying Conditional Portfolio Decisions via Optimal Transport

Nguyen, V. A., Zhang, F., Blanchet, J., Delage, E., & Ye, Y. (2021)
Under review. Submitted to Operations Research.

Testing Group Fairness via Optimal Transport Projections

Si, N., Murthy, K., Blanchet, J., & Nguyen, V. A. (2021)
In International Conference on Machine Learning.

Finite-Sample Regret Bound for Distributionally Robust Offline Tabular Reinforcement Learning

Zhou, Z., Bai, Q., Zhou, Z., Qiu, L., Blanchet, J., & Glynn, P.W. (2021)
In International Conference on Artificial Intelligence and Statistics (pp. 3331-3339). PMLR.

A Statistical Test for Probabilistic Fairness

Taskesen, B., Blanchet, J., Kuhn, D., & Nguyen, V. A. (2021)
In Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency (pp. 648-665).

Generative Archimedean Copulas

Ng, Y., Hasan, A., Elkhalil, K., & Tarokh, V. (2021)
Association for Uncertainty in Artificial Intelligence (UAI).

Atomic-Level Features for Kinetic Monte Carlo Models of Complex Chemistry from Molecular Dynamics Simulations

Dufour-Décieux, V., Freitas, R., & Reed, E. J. (2021).
The Journal of Physical Chemistry A

Machine Learning For Elliptic PDEs: Fast Rate Generalization Bound, Neural Scaling Law and Minimax Optimality

Lu, Y., Chen, H., Lu, J., Ying, L., & Blanchet, J. (2021).
arXiv preprint arXiv:2110.06897.

Deep Extreme Value Copulas for Estimation and Sampling

Hasan, A., Elkhalil, K., Pereira, J. M., Farsiu, S., Blanchet, J. H., & Tarokh, V. (2021).
arXiv preprint arXiv:2102.09042.

Computing Committors in Collective Variables via Mahalanobis Diffusion Maps

Evans, L., Cameron, M. K., & Tiwary, P. (2021).
arXiv preprint arXiv:2108.08979. Submitted to the Elsevier Journal for Applied and Computational Harmonic Analysis.

Dropout Training is Distributionally Robust Optimal

Blanchet, J., Kang, Y., Olea, J. L. M., Nguyen, V. A., & Zhang, X.
Under review. Submitted to Journal of Machine Learning Research.

Data-driven Rare Event Simulation for Stochastic Dynamical Systems: A Koopman Approach

Zhang, B., Long, Q., White, J., Sahai., T, Marzouk, Y.
Work in progress

Transport Maps Induce Riemannian Manifold Langevin Dynamics

Zhang, B., Brennan, M., Spiliopoulos, K., Marzouk, Y.
Work in progress

An Efficient Jet Marcher for Computing the Quasipotential for 2D SDEs

Packal, N., Cameron, M.
Journal of Scientific Computing (Springer) 91, 30, (2022).

Most Probable Escape Paths in Periodically Driven Nonlinear Oscillators

Cilenti, L., Cameron, M., Balachandran, B.
Chaos 32, 083140 (2022).

Computing Committors via Mahalanobis Diffusion Maps with Enhanced Sampling Data

Evans, L., Cameron, M., Tiwary, P.
The Journal of Chemical Physics 157, 21, 10.1063/5.0122990 (2022).

Predicting Molecule Size Distribution in Hydrocarbon Pyrolysis Using Random Graph Theory

Dufour-Décieux, V., Moakler, C., Cameron, M., Reed, E. J.
The Journal of Chemical Physics, in revision.

Inference and Sampling for Archimax Copulas

Ng, Y., Hasan A., Tarokh, V.
Conference on Neural Information Processing System (NeurIPS), 2022.

Tikhonov Regularization is Optimal Transport Robust under Martingale Constraints

Li, J., Lin, S., Blanchet, J., Nguyen, V. A.
Conference on Neural Information Processing System (NeurIPS), 2022.

Smoothed Variable Sample-size Accelerated Proximal Methods for Nonsmooth Stochastic Convex Programs

Jalilzadeh, A., Shanbhag, U., Blanchet, J., Glynn, P. W.
Stochastic System, 2022.

Distributionally Robust Mean-variance Portfolio Selection with Wasserstein Distances

Blanchet, J., Chen, L., Zhou, X.
Management Science, 2022.

Distributionally Robust Q-Learning

Liu, Z., Bai, Q., Blanchet, J., Dong, P., Xu, W., Zhou, Z., Zhou, Z.
International Conference on Machine Learning (ICML), 2022.

Confidence Regions in Wasserstein Distributionally Robust Estimation

Blanchet, J., Murthy, K., Si, N.
Biometrika, 2022.

Sobolev Acceleration and Statistical Optimality for Learning Elliptic Equations via Gradient Descent

Lu, Y., Blanchet, J., Ying, L.
Conference on Neural Information Processing System (NeurIPS), 2022.

A Class of Geometric Structures in Transfer Learning: Minimax Bounds and Optimality

Zhang, X., Blanchet, J., Ghosh, S., Squillante, M.
International Conference on Artificial Intelligence and Statistics (AISTATS), 2022.

Optimal Transport-based Distributionally Robust Optimization: Structural Properties and Iterative Schemes

Blanchet, J., Murthy, K., Zhang, F.
Mathematics of Operation Research, 2022.

Temperature Extrapolation of Molecular Dynamics Simulations of Complex Chemistry to Microsecond Timescales Using Kinetic Models: Applications to Hydrocarbon Pyrolysis

Dufour-Décieux, V., Ransom, B., Sendek, A. D., Freitas, R., Blanchet, J., Reed, E. J.
Journal of Chemical Theory and Computation.

A Koopman Framework for Rare Event Simulation in Stochastic Differential Equations

Zhang, B., Sahai, T.,Marzouk, Y.
Journal of Computational Physics, 456 (2022), pp. 111025.

Geometry-informed Irreversible Perturbations for Accelerated Convergence of Langevin Dynamics

Zhang, B., Marzouk, Y., Spiliopoulos, K.
Statistics and Computing, 32 (2022).

Computing Eigenfunctions of the Multidimensional Ornstein-Uhlenbeck Operator

Zhang, B., Sahai, T., Marzouk, Y.
Submitted to Comptes Rendus Mathematique (2022).

Conditional Sampling with Monotone GANs

Baptista, R., Hosseini, B., Kovachki, N., Marzouk, Y.
Submitted to SIAM Journal on Uncertainty Quantification (2022).

On Minimax Density Estimation via Measure Transport

Wang, S, Marzouk, Y.
Submitted to Annals of Statistics (2022).

Distributionally Robust Gaussian Process Regression and Bayesian Inverse Problems

Zhang, X., Blanchet, J., Marzouk, Y., Nguyen, V. A., Wang, S.
Submitted to Annals of Statistics (2022).

Self-assembled Nanocomposites of High Water Content and Load-bearing Capacity

Zhang, G., Kim, J., Hassan, S., Suo, Z.
PNAS (2022).

Polyacrylamide Hydrogels. VI. Synthesis-property Relation

Wang, Y., Nian, G., Kim, J., Suo, Z.
Journal of the Mechanics and Physics of Solids (2022).

Fracture Initiated from Corners in Brittle Soft Materials

Steck, J., Hassan, S., Suo, Z.
Journal of the Mechanics and Physics of Solids (2022).

High-throughput Experiments for Rare-event Rupture of Materials

Zhou, Y., Zhang, X., Yang, M., Pan, Y., Du, Z.,Blanchet, J.,Suo, Z. , Lu, T.
Matter (2022).

Modeling Extremes with d-max-decreasing Neural Networks

Hasan, A., Elkhalil, K., Ng, Y., Pereira, J., Farsiu, S., Blanchet, J., Tarokh, V.
Conference on Uncertainty in Artificial Intelligence (UAI), 2022.

Modeling the Fracture of Polymer Networks

Tao, M., Lavoie, S., Cameron, M., Suo, Z.
In the final stages of preparation.

Controllers Obtained Using Model Reduction and Transition Path Theory

Shah, A., Bentz, C., Yuan, J., Cameron, M.
In preparation.

Error Analysis for Target Measure Diffusion Maps

Sule, S., Evans, L., Cameron, M.
In preparation.

Quantifying Rare Transitions in Nonlinear Oscillators Using Analog Markov Chains and Transition Path Theory

Yuan, D., Moakler, C., Cilenti, L., Cameron, M., Balachandran, B.
In progress

Neural Network Accelerated Process Design of Polycrystalline Microstructures

Lin, J., Hasan, M., Acar, P., Blanchet, J., Tarokh, V.
To be submitted.

Minimax Optimal Kernel Operator Learning via Multilevel Training

Jin, J., Lu, Y., Blanchet, J., Ying, L.
Submitted to International Conference on Learning Representations (ICLR), 2023.

A Convergent Single-Loop Algorithm for Gromov Wasserstein in Graph Data

Li, J., Tang, J., Kong, L., Liu, H., Li, J., So, A. M., Blanchet, J.
Submitted to International Conference on Learning Representations (ICLR), 2023.

Statistical Consistency of Sampling and Density Estimation via Neural Differential Equations

Ren, R., Marzouk, Y., Wang, S., Zech, J.
In preparation.

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