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Computational Mathematician

Mid-Senior Level | Full-time
Information Technology/Computing | livermore, CA | 11/10/2021

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Company Description

Join us and make YOUR mark on the World!

Are you interested in joining some of the brightest talent in the world to strengthen the United States’ security? Come join Lawrence Livermore National Laboratory (LLNL) where our employees apply their expertise to create solutions for BIG ideas that make our world a better place.

We are looking for individuals that demonstrate an understanding of working in partnership with team peers, who engage, advocate, and contribute to building an inclusive culture, and provide expertise to solve challenging problems.

Job Description

We have an opening for a Computational Mathematician to perform research and development in the areas of numerical optimization, uncertainty quantification (UQ) and machine learning at extreme scale. You will join interdisciplinary teams that design and implement numerical algorithms for PDE constrained optimization and multiscale schemes for Markov Chain Monte Carlo simulation of multi-physics phenomena. Your work will advance state-of-the-art methods for scalable quantum optimal control, characterization of quantum systems, subsurface flow models, as well as various (non-PDE) network applications (such as power grid). This position is in the Center for Applied Scientific Computing (CASC) Division within the Computing Directorate.


In this role you will

  • Research new strategies and explore existing techniques for ODE-constrained optimization of control pulses applicable to scalable quantum hardware.
  • Research and develop methods for UQ simulations exploiting both highly accurate coarse (upscaled) finite element schemes (under development at LLNL) and machine learning algorithms.
  • Provide the supporting mathematical analysis of the underlying algorithms and implement them in a high-level programming language that utilizes existing and next-generation high performance computing (HPC) machines.
  • Implement GPU-based acceleration techniques for solving Schroedinger’s and Lindblad’s equations.
  • Develop prototype software utilizing high-performance computing to evaluate novel UQ.
  • Document complex research and development progress via technical reports, journal publications, and conference presentations.
  • Establish future research directions and contribute to group grant proposals, including proposal presentations and preparation of proposals.
  • Pursue independent (but complementary) research interests and interact with a broad spectrum of scientists internally and externally to define and carry out the research.
  • Perform other duties as assigned.


  • Ph.D. in Computational or Applied Mathematics, Numerical Analysis, Computational Physics, or a related field, or the equivalent combination of education and related experience.
  • Significant experience developing and implementing numerical methods for time-dependent wave propagation, numerical optimization, uncertainty quantification, machine learning, and Bayesian inference.
  • Research experience in one or more of the following areas: numerical PDEs, finite elements and multilevel solvers, Markov chain Monte Carlo.
  • Advanced knowledge of probability and statistics with application to UQ, constrained optimization (in particular where the constraints arise from differential equations), numerical analysis, numerical linear algebra, and numerical solution of differential equations.
  • Significant experience developing software a high-level language such as C/C++ or Python, or Julia in a Unix/Linux environment.
  • Ability to conduct high quality research and to develop implementations of sophisticated algorithms to evaluate the results.
  • Demonstrated publication record in peer-reviewed journals and/or conferences.
  • Advanced verbal and written communication skills to effectively collaborate in a team environment, present and explain technical information to technical as well non-technical audience, document work and write research papers.

Desired Qualifications

  • Experience implementing algorithms for distributed computers, multi-core CPUs or GPUs, or GPU-accelerated software, e.g., using Cuda or RAJA.
  • Knowledge of Bayesian approaches for parameter estimation.
  • Knowledge of quantum physics.

Additional Information

Why Lawrence Livermore National Laboratory?

  • Included in 2021 Best Places to Work by Glassdoor!
  • Work for a premier innovative national Laboratory
  • Comprehensive Benefits Package
  • Flexible schedules (*depending on project needs)
  • Collaborative, creative, inclusive, and fun team environment

Learn more about our company, selection process, position types and security clearances by visiting our Career site

COVID-19 Vaccination Mandate

LLNL demonstrates its commitment to public safety by requiring that all new Laboratory employees be immunized against COVID-19 unless granted an accommodation under applicable state or federal law. This requirement will apply to all new hires including those who will be working on site, as well as those who will be teleworking.

Pre-Employment Drug Test

External applicant(s) selected for this position will be required to pass a post-offer, pre-employment drug test.  This includes testing for use of marijuana as Federal Law applies to us as a Federal Contractor.

Equal Employment Opportunity

LLNL is an affirmative action and equal opportunity employer that values and hires a diverse workforce. All qualified applicants will receive consideration for employment without regard to race, color, religion, marital status, national origin, ancestry, sex, sexual orientation, gender identity, disability, medical condition, pregnancy, protected veteran status, age, citizenship, or any other characteristic protected by applicable laws.

LLNS is committed to offering reasonable accommodations during the application and recruiting processes due to a disability.  If you need assistance or an accommodation due to a disability, please submit a request via our online form

California Privacy Notice

The California Consumer Privacy Act (CCPA) grants privacy rights to all California residents. The law also entitles job applicants, employees, and non-employee workers to be notified of what personal information LLNL collects and for what purpose. The Employee Privacy Notice can be accessed here.

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