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.

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

**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.

**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.

**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.

**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.

**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.

**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.

- Modeling and Design
- Statistical Advances
- Computational Advances
- Robustness and Sensitivity

**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

Advances in Neural Information Processing Systems, 34.

Advances in Neural Information Processing Systems, 34.

In Tutorials in Operations Research: Emerging Optimization Methods and Modeling Techniques with Applications (pp. 227-254). INFORMS.

arXiv preprint arXiv:2106.07191.

arXiv preprint arXiv:2106.02263.

Stochastic Systems.

In International Conference on Machine Learning.

Under review. Submitted to Operations Research.

In International Conference on Machine Learning.

In International Conference on Artificial Intelligence and Statistics (pp. 3331-3339). PMLR.

In Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency (pp. 648-665).

Association for Uncertainty in Artificial Intelligence (UAI).

The Journal of Physical Chemistry A

arXiv preprint arXiv:2110.06897.

arXiv preprint arXiv:2102.09042.

arXiv preprint arXiv:2108.08979. Submitted to the Elsevier Journal for Applied and Computational Harmonic Analysis.

Under review. Submitted to Journal of Machine Learning Research.

Work in progress

Work in progress

Journal of Scientific Computing (Springer) 91, 30, (2022).

Chaos 32, 083140 (2022).

The Journal of Chemical Physics 157, 21, 10.1063/5.0122990 (2022).

The Journal of Chemical Physics, in revision.

Conference on Neural Information Processing System (NeurIPS), 2022.

Conference on Neural Information Processing System (NeurIPS), 2022.

Stochastic System, 2022.

Management Science, 2022.

International Conference on Machine Learning (ICML), 2022.

Biometrika, 2022.

Conference on Neural Information Processing System (NeurIPS), 2022.

International Conference on Artificial Intelligence and Statistics (AISTATS), 2022.

Mathematics of Operation Research, 2022.

Journal of Chemical Theory and Computation.

Journal of Computational Physics, 456 (2022), pp. 111025.

Statistics and Computing, 32 (2022).

Submitted to Comptes Rendus Mathematique (2022).

Submitted to SIAM Journal on Uncertainty Quantification (2022).

Submitted to Annals of Statistics (2022).

Submitted to Annals of Statistics (2022).

PNAS (2022).

Journal of the Mechanics and Physics of Solids (2022).

Journal of the Mechanics and Physics of Solids (2022).

Matter (2022).

Conference on Uncertainty in Artificial Intelligence (UAI), 2022.

In the final stages of preparation.

In preparation.

In preparation.

In progress

To be submitted.

Submitted to International Conference on Learning Representations (ICLR), 2023.

Submitted to International Conference on Learning Representations (ICLR), 2023.

In preparation.