Research

My research develops reliable and effective methods at the intersection of artificial intelligence and computational mathematics. My goal is to transform predictive modeling of complex systems by combining AI with mathematical rigor. Integrating numerical analysis, scientific computing, and machine learning, my team tackles problems where conventional methods are prohibitively expensive and purely data-driven models unreliable. A defining feature of my program is its emphasis on methods that scale to real-world challenges, achieving orders-of-magnitude speedups and enabling industrial applications. Together, these advances expand what is computationally possible in fluid dynamics, energy and environmental systems, and finance.

Research keywords

Scientific Machine Learning; Reduced-Order Modeling; Multiscale Methods; High-Dimensional PDEs; Flow and Transport in Engineering, Environmental, and Biological Systems; Mathematical Finance

View publications

Funding

Active

• NSF DMS-2603912 · PI · US$199,000
  A Learning-Augmented Framework for Multi-Level Multiscale Modeling
  July 2026–June 2029
• NSF DMS-2608740 · PI · US$300,000
  Energy-Stable Neural Basis Methods for Multiscale Porous Media Flow
  June 2026–May 2029
• Gene Golub SIAM Summer School · Co-PI · US$183,640
  Nonlinear Solvers and Preconditioning Techniques for Multiphysics PDEs
  January–December 2027

Completed

• NSF DMS-2430460 · Co-PI · US$42,244
  CBMS Conference: Research at the Interface of Applied Mathematics and Machine Learning
  June 2025–May 2026