David Aristoff

Associate Professor, Colorado State University

Email: aristoff at math dot colostate dot edu

Associate Professor, Colorado State University

Email: aristoff at math dot colostate dot edu

Education

PhD, Mathematics, University of Texas, 2011
BA, Mathematics, University of Michigan, 2005

Positions held

2020-- Associate Professor, Colorado State University
2014-2020 Assistant Professor, Colorado State University
June-July 2018 Labex Bezout Visiting Professor, Ecole des Ponts ParisTech
2011-2014 Dunham Jackson Assistant Professor, University of Minnesota

Long-term visits

2017 IPAM semester program: Complex High-Dimensional Energy Landscapes
2015 ICERM semester workshop: Phase Transitions and Emergent Properties

Contracts and grants

2021-2024 Particles and Proxies for Sampling, NSF-DMS-2111277. Role: co-PI with Gideon Simpson.
2018-2021 Stochastic Methods for Complex Systems, NSF-DMS-1818726. Role: co-PI with Gideon Simpson.
2019-2020 High-performance weighted ensemble software for simulation of complex bio-events, NIH 2R01GM115805-05. Role: co-investigator.
2015-2019 Algorithms for Complex Systems, NSF-DMS-1522398.
Role: sole PI.
2021 Stochastic methods for complex systems, Simons collaboration grant #854435.
Role: declined for NSF grant.
2015 Complex Systems and Algorithms, Simons collaboration grant #355431.
Role: declined for NSF grant.

Open-source code

Weighted ensemble Julia package, WeightedEnsemble.jl, developed by Felix Jones and Gideon Simpson

Publications

*invited presentations

Teaching

Courses taught:
Course development:
Advising:

Service

University service at CSU:
Conference organization (minisymposium):
Grant refereeing: I served as a reviewer on NSF panels in Spring 2019 and Spring 2020.
Journal refereeing: I have been a reviewer for many journals including:
I am a Math Alliance member.

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Open-source code

Publications

- D. Aristoff and W. Bangerth. A benchmark for the Bayesian inversion of coefficients in partial differential equations arXiv:2102.07263
- R.J. Webber, D. Aristoff, and G. Simpson. A splitting method to reduce MCMC variance arXiv:2011.13899
- J.D. Russo, D. Aristoff, J. Copperman, G. Simpson, and D.M. Zuckerman. Unbiased estimation of equilibrium, rates, and committors from Markov state model analysis arXiv:2105.13402
- D. Aristoff. An ergodic theorem for the weighted ensemble method (2022) J. Appl. Prob. 59(1), 152--166
- D. Aristoff and D.M. Zuckerman. Optimizing weighted ensemble sampling of steady states (2020) SIAM Multiscale Model. Simul. 18(2), 646--673
- J. Copperman, D. Aristoff, D.E. Makarov, G. Simpson, and D.M. Zuckerman. Transient probability currents provide upper and lower bounds on non-equilibrium steady-state currents... (2019) J. Chem. Phys. 151, 174108
- D. Aristoff. Generalizing parallel replica dynamics: trajectory fragments, asynchronous computing, and PDMPs (2019) SIAM/ASA Journal on Uncertainty Quantification 7(2), 685--719
- D. Aristoff. Analysis and optimization of weighted ensemble sampling (2018) ESAIM: Mathematical Modelling and Numerical Analysis 52(2018), 1219--1238
- T. Wang, P. Plecháč, and D. Aristoff. Stationary averaging for multi-scale continuous time Markov chains using parallel replica dynamics (2018) SIAM Multiscale Model. Simul. 16(1), 1--27
- D. Aristoff and L. Zhu. On the phase transition curve in a directed exponential random graph model (2018) Adv. Appl. Prob. 50(1), 272--301
- D. Aristoff and L. Zhu. Lattice gas models with long range interactions (2017) J. Math. Phys. 58(2), 023301
- D. Aristoff, S. Chill, and G. Simpson. Analysis of estimators for adaptive Kinetic Monte Carlo (2016) Comm. App. Math. and Comp. Sci. 11(2), 171--186
- D. Aristoff, J.M. Bello-Rivas, and R. Elber. A mathematical framework for exact milestoning (2016) SIAM Multiscale Model. Simul. 14(1), 301--322
- D. Aristoff. The parallel replica method for computing equilibrium averages of Markov chains (2015) Monte Carlo Methods Appl. 21(4), 255--273
- D. Aristoff, T. Lelièvre, C. Mayne, and I. Teo. Adaptive multilevel splitting in molecular dynamics simulations (2015) ESAIM: Proceedings and Surveys 48, 215--225
- D. Aristoff and L. Zhu. Asymptotic structure and singularities in constrained directed graphs (2015) Stoch. Proc. Appl. 125(11), 4154--4177
- D. Aristoff, T. Lelièvre, and G. Simpson. The parallel replica method for simulating long trajectories of Markov chains (2014) Appl. Math Res. Express 2014(2), 332--352
- D. Aristoff and T. Lelièvre. Mathematical analysis of temperature accelerated dynamics (2014) SIAM Multiscale Model. Simul. 12(1), 290--317
- D. Aristoff. Percolation of hard disks (2014) J. Appl. Prob. 51(1), 235--246
- D. Aristoff and C. Radin. Emergent structures in large networks (2013) J. Appl. Prob. 50, 883--888
- D. Aristoff and C. Radin. Rigidity in
Solids
(2011) J. Stat. Phys. 144, 1247--1255
*(with C. Radin)* - D. Aristoff and C. Radin. First order phase transition in a model of quasicrystals (2011) J. Phys. A: Math. Theor. 44, 255001
- D. Aristoff and C. Radin. Dilatancy transition in a granular model (2011) J. Stat. Phys. 143, 215--225
- D. Aristoff and C. Radin. First order phase transition of a long polymer chain (2011) J. Phys. A: Math. Theor. 44, 065004
- D. Aristoff and C. Radin. Random close packing in a granular model (2010) J. Math. Phys. 51, 113302
- D. Aristoff and C. Radin. Layering in crumpled sheets (2010) Europhys. Lett. 91, 56003
- D. Aristoff and C. Radin. Random loose packing in granular matter (2009) J. Stat. Phys. 135, 1--23

*invited presentations

- May 2021. Generalizing parallel replica dynamics: trajectory fragments, asynchronous computing, and PDMPs. SIAM conference on Mathematical Aspects of Materials Science (virtual)
- *May 2021. Unbiased importance sampling for non-equilibrium steady states. RESIM 2021 : 13th International Workshop on Rare-Event Simulation (virtual)
- *July 2019. Steady state importance sampling. ICIAM minisymposium on Advances in Monte Carlo Methods. Organizer. Valencia, Spain.
- *July 2019. Steady state importance sampling. ICIAM minisymposium on Advances in Monte Carlo Methods. Organizer. Valencia, Spain.
- *September 2018. Optimizing stratified steady-state resampling methods. CIRM conference on Advances in Computational Statistical Physics. Luminy, France.
- *July 2018. Optimization of weighted ensemble sampling. Scientific computing seminar. Ecole des Ponts ParisTech, Paris, France.
- *June 2018. Weighted ensemble: a new particle method for variance reduction. J-PSI working group of young researchers: statistical physics and interactions. INRIA, Paris, France.
- *April 2018. Coarse grained models for variance reduction in particle methods. IMA Working Group on Mathematical Modeling of Finite-temperature Coarse-graining. University of Minnesota, Minneapolis, MN.
- *March 2018. Piecewise deterministic Markov processes (PDMPs) for efficient sampling. Applied math seminar. University of Delaware, Newark, DE.
- *October 2017. Analysis and optimization of weighted ensemble sampling. IPAM: Complex High-Dimensional Energy Landscapes. UCLA, Los Angeles, CA.
- *November 2017. The Parallel Replica method for long time simulation of discrete and continuous time Markov chains. Minisymposium. Materials Research Society fall meeting and exhibit. Boston, MA.
- *August 2017. The parallel replica method for long time simulation of discrete and continuous time Markov chains. Seminar. Los Alamos National Laboratory Center for Nonlinear Studies, Los Alamos, NM.
- *June 2017. Markov chains, metastability and sampling. Colloquium. University of Denver, Denver, CO.
- *December 2017. Markov chains, metastability and sampling. Seminar. Center for Computational Mathematics, CU Denver, Denver, CO.
- *November 2016. Markov chains, metastability and sampling. Colloquium. University of Colorado Colorado Springs, Colorado Springs, CO.
- *October 2016. Structure of large graphs with constraints. Minisymposium. SIAM Central States Section. Little Rock, AR.
- *June 2016. Non equilibirum umbrella sampling and milestoning. Speaker and workshop participant. Journées Adaptive Multilevel Splitting évènements rares. Ecole des Ponts ParisTech, Paris, France.
- *April 2016. Sampling distributions of Markov chains. Colorado Nonlinear Day. University of Colorado Colorado Springs, Colorado Springs, CO.
- *April 2016. Sampling distributions of Markov chains. Colloquium. University of Colorado, Boulder, CO.
- *March 2016. Sampling distributions of Markov chains. Colloquium. Florida State University, Tallahassee, FL.
- *September 2015. Asymptotic structure in constrained graphs. Seminar. University of Colorado, Boulder, CO.
- *July 2015. Mathematical framework for exact milestoning. Speaker and workshop participant. BIRS conference on free-energy computations, Oaxaca, Mexico.
- May 2015. Workshop participant. IMA workshop on Graphical Models, Statistical Inference, and Algorithms. University of Minnesota, Minneapolis, MN.
- *April 2015. Mathematical framework for exact milestoning. Seminar. ICES, University of Texas, Austin, TX.
- *April 2015. Positive Temperature Models of Quasicrystals. Minisymposium. SIAM Central States Section, Missouri University of Science & Technology, Rolla, MO.
- *March 2015. The parallel replica method for Markov chains. SIAM sponsored workshop on dimension reduction, Penn State University, State College, PA.
- *February 2015. Phase transitions in models of quasicrystals. ICERM workshop on crystals, quasicrystals and random networks, Providence, RI.
- *July 2014. Mathematical Foundations of Temperature Accelerated Dynamics. AIMS Conference on Dynamical Systems. Madrid, Spain.
- *April 2014. The parallel replica method for Markov chains. Seminar. University of Delaware, Newark, DE.
- *March 2014. Mathematical analysis of temperature accelerated dynamics. Seminar. Drexel University, Philadelphia, PA.
- *December 2014. Emergent structures in large networks. Colloquium. Kansas State University. Manhattan, KS.
- *June 2013. Mathematical analysis of temperature accelerated dynamics. SIAM Conference on Mathematical Aspects of Materials. Philadelphia, PA.
- *March 2013. Mathematical analysis of temperature accelerated dynamics. Seminar. University of Texas, Austin, TX.
- October 2012. Workshop participant. IPAM conference on quantum and atomistic modeling of materials defects, Los Angeles, CA.

Teaching

- 2020 Fall DSCI 369: Linear algebra for data science
- 2020 Spring Math 317: Intro to real analysis
- 2019 Fall Math 545: Partial Diff Eq I
- 2019 Fall Math 517: Intro to real analysis
- 2019 Spring Math 332: Partial Diff Eq
- 2018 Fall Math 517: Intro to real analysis
- 2018 Spring Math 369: Linear algebra I
- 2018 Spring Math 676: Stochastic methods
- 2017 Spring Math 617: Measure theory
- 2016 Fall Math 369: Linear algebra I
- 2016 Fall Math 560: Linear algebra
- 2015 Fall Math 417: Advanced calculus I
- 2015 Fall Math 450: Numerical analysis I
- 2014 Fall Math 517: Intro to real analysis
- 2014 Fall Math 369: Linear algebra I

- I created Math 676, a graduate topics course on stochastic methods and applications.

Course notes are available on request. - I created course notes for Math 617, graduate measure theory.

The notes present ideas from a probabilistic perspective, starting from elementary knowledge of probability.

These 56-page notes are self-contained and include dozens of exercises. - I created a ``probability primer'' to bring prospective students
up to speed in basic ideas underlying my research.

The primer assumes no prior knowledge of probability or Monte Carlo methods.

This text is available on request.

- MS students advised: Peter Christman (MS 2018), Codie Lewis (MS 2019), Jeremy Buss (current)
- PhD students advised: Carter Lyons (current), Mats Johnson (current)

Service

- 2019-- Graduate Admissions Committee member, School of Advanced Materials Design
- 2019-- Graduate Committee member
- 2019-- Colloquium organizer
- 2019-2020 Hiring search committee member, Department of Statistics
- 2018-2019 Executive Committee member
- 2014-2018 Applied Math Seminar organizer

- SIAM conference on Mathematical Aspects of Materials Science (2016, 2021)
- Advanced Atomistic Algorithms in Materials Science, Materials Research Society Fall Meeting (2019, 2021)
- International Congress on Industrial and Applied Mathematics (2019)
- SIAM Conference on Analysis of Partial Differential Equations (2017)

- Annals of Applied Probability
- Journal de Mathematiques Pures et Appliquées
- SIAM Journal on Numerical Analysis

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