![In a highly cyclic community (S3), vertices in each subgroup mostly connect directionally to vertices in the “next” adjacent subgroup. The new factorizations enable discovery of such phenomena.](/sites/default/files/styles/front_page_card/public/math-data-mining-llnl-project-card.png?itok=y2GlsH-n)
Math for Data Mining
Newly developed mathematical techniques reveal important tools for data mining analysis.
![simulation in the shape of a red cube](/sites/default/files/styles/front_page_card/public/phase-field-modeling-llnl-project-card.png?itok=ICUQPG8w)
Phase-Field Modeling
Based on a discretization and time-stepping algorithm, these equations include a local order parameter, a quaternion representation of local orientation, and species composition.
![closeup of molecular simulation](/sites/default/files/styles/front_page_card/public/first-principles-llnl-project-card.png?itok=hVPhZQXs)
First-Principles Molecular Dynamics
This scalable first-principles MD algorithm with O(N) complexity and controllable accuracy is capable of simulating systems that were previously impossible with such accuracy.
![Chandrika's portrait next to the SIAM logo on a blue geometric background](/sites/default/files/styles/front_page_card/public/2023-03/siam-kamath-comp-news.png?itok=76fbOUzm)
Chandrika Kamath honored as 2023 SIAM fellow
The prestigious fellow designation is a lifetime honorific title and honors SIAM members who have made outstanding contributions to fields served by the organization.
![blue and red lattice structure on the left where blue indicates the lattice component that needs to be removed; black lattice structure on the right showing the optimized red portion of the left image](/sites/default/files/styles/front_page_card/public/2023-03/cwrom-leaderboard.png?itok=9vFTY1yo)
Patent for reduced order modeling method boosts lattice design optimization
A new component-wise reduced order modeling method enables high-fidelity lattice design optimization.
Video: Meso and macroscale modeling 1 (IPAM at UCLA)
UCLA's Institute for Pure & Applied Mathematics hosted LLNL's Tzanio Kolev for a talk about high-order finite element methods.