The research of LEADS is divided into three thrust areas under overarching themes of foundation models and energy efficiency: functional analytic and probabilistic algorithms, geometric algorithms, and performance optimization. Each thrust is comprised of multiple tasks with a task lead assigned to each. 

Thrust 1: Functional Analytic and Probabilistic Algorithms

Thrust 1 develops core predictive SciML methods that underpin modeling needs across the project.

Task 1.1: Operator Networks

Task Lead: Eric C. Cyr, Sandia National Laboratories

Task 1.2: Hybrid Algorithms

Task Lead: Youngsoo Choi, Lawrence Livermore National Laboratory

Task 1.3: Generative AI

Task Lead: Guannan Zhang, Oak Ridge National Laboratory

Thrust 2: Geometric Algorithms

Thrust 2 complements Thrust 1 through topological, algebraic, and graph-based techniques that enable physics-informed structured representation learning, improving interpretability and robustness.

Task 2.1: Topology, Algebra, Geometry

Task Lead: Henry Kvinge, Pacific Northwest National Laboratory

Task 2.2: Graphs

Task Lead: Stephen Young, Pacific Northwest National Laboratory

Thrust 3: Performance Optimization

Thrust 3 leverages Thrusts 1 and 2 to enhance control and optimization, ensuring these algorithms operate reliably and efficiently at scale. 

Task 3.1: Control

Task Lead: Jan Drgona, Johns Hopkins University

Task 3.2: Optimization

Task Lead: Jerome Darbon, Brown University