SUNDIALS is a SUite of Nonlinear and DIfferential/ALgebraic equation Solvers for initial value problems for ordinary differential equation systems, sensitivity analysis capabilities, additive Runge-Kutta methods, differential-algebraic equation systems, nonlinear algebraic systems, and more.

# Topic: *Computational Math*

Multiphysics simulation codes must perform at scale on present and future massively parallel supercomputers, be adaptable and extendable, be sustainable across multiple generations of hardware, and work on general 2D and 3D domains. To this end, the Multiphysics on Advanced Platforms Project incorporates multiple software packages into one integrated code.

The Vidya project is a portfolio of research efforts to advance research in physics-informed ML, improve employment of ML with sparse data, invest in validated and explainable ML, explore learning hardware systems in HPC systems, create an advanced ML-tailored data environment, improve simulation workflows, and build ML expertise across the complex.

Highlights include power grid challenges, performance analysis, complex boundary conditions, and a novel multiscale modeling approach.

libROM is a library designed to facilitate Proper Orthogonal Decomposition (POD) based Reduced Order Modeling (ROM).

The MFEM software library provides high-order mathematical algorithms for large-scale scientific simulations. An October workshop brought together MFEM’s global user and developer community for the first time.

The open-source MFEM library enables application scientists to quickly prototype parallel physics application codes based on PDEs discretized with high-order finite elements.

An LLNL mathematician and collaborators have developed a machine learning–based technique capable of automatically deriving a mathematical model for the motion of binary black holes from raw gravitational wave data.

In a project with U.S. Steel, LLNL computational physicists built models of the hot-rolling process to run on LLNL’s HPC platforms. The models track the steel from reheat-furnace dropout through the subsequent steps of rolling, cooling on the runout table, coiling and, finally, post-rolling cooling.

As Computing’s fifth Fernbach Fellow, postdoctoral researcher Steven Roberts will develop, analyze, and implement new time integration methods.

LLNL held its first-ever Machine Learning for Industry Forum (ML4I) on August 10–12. Co-hosted by the Lab’s High-Performance Computing Innovation Center and Data Science Institute, the virtual event brought together more than 500 attendees from the Department of Energy (DOE) complex, commercial companies, professional societies, and academia.

The Enabling Technologies for High-Order Simulations (ETHOS) project performs research of fundamental mathematical technologies for next-generation high-order simulations algorithms.

The 2021 Conference on Computer Vision and Pattern Recognition, the premier conference of its kind, will feature two papers co-authored by an LLNL researcher targeted at improving the understanding of robust machine learning models.

New research debuting at ICLR 2021 demonstrates a learning-by-compressing approach to deep learning that outperforms traditional methods without sacrificing accuracy.

The latest issue of LLNL's *Science & Technology Review* magazine showcases Computing in the cover story alongside a commentary by Bruce Hendrickson.

Highlights include scalable deep learning, high-order finite elements, data race detection, and reduced order models.

The hypre team's latest work gives scientists the ability to efficiently utilize modern GPU-based extreme scale parallel supercomputers to address many scientific problems.

SIAM announced its 2021 Class of Fellows, including LLNL computational mathematician Rob Falgout. Falgout is best known for his development of multigrid methods and for hypre, one of the world’s most popular parallel multigrid codes.

Our researchers will be well represented at the virtual SIAM Conference on Computational Science and Engineering (CSE21) on March 1–5. SIAM is the Society for Industrial and Applied Mathematics with an international community of more than 14,500 individual members.

An LLNL team has developed a “Learn-by-Calibrating” method for creating powerful scientific emulators that could be used as proxies for far more computationally intensive simulators.

Three papers address feature importance estimation under distribution shifts, attribute-guided adversarial training, and uncertainty matching in graph neural networks.

Proxy apps serve as specific targets for testing and simulation without the time, effort, and expertise that porting or changing most production codes would require.

The Association for Women in Mathematics has named computational scientist Carol Woodward as a 2021 fellow, recognizing her commitment to supporting and advancing women in the mathematical sciences.

The SAMRAI library is the code base in CASC for exploring application, numerical, parallel computing, and software issues associated with structured adaptive mesh refinement.

This summer, the Computing Scholar Program welcomed 160 undergraduate and graduate students into virtual internships. The Lab’s open-source community was already primed for student participation.