Grady Wright
Boise State University, ID·Mathematics & Statistics
Computers solve hard math problems in science, such as predicting how fluids flow or adding up a quantity over an oddly shaped region. They do this with approximations.
- Fields
Mathematics & Statistics
Computer Science
Engineering
- Topics
numerical analysis
scientific machine learning
SciML
- Grants
- 2 known grants, through Aug 2028
What they work on
- Develop the Unified Neural Operator formalism, which splits neural operators into an input encoder, output basis functions and a projection operator, so that existing architectures fit one framework and new ones can be designed.
- Create scalable, adaptive training and inference algorithms that let UNO adapt to local solution features and handle high-dimensional data efficiently when data are plentiful.
- Prove universal approximation theorems and error estimates for UNO, and build in uncertainty quantification and physics preservation so the surrogates stay accurate for turbulent and multiphysics flows.
- Build Fredholm Alternative Quadrature, which computes integrals by discretizing Laplace operators with meshfree RBF-FD and solving an eigenvalue problem, so that it works on complicated domains and surfaces.
- Develop high-order RBF-FD discretizations, meshfree multilevel solvers and least-squares stabilization for FAQ formulas, and analyze their approximation properties.
More about the research
Those approximations have to be accurate, fast and trustworthy. The two projects here build new numerical methods for these tasks. One makes machine-learning stand-ins for physics simulations more reliable. The other gives a new way to compute integrals over complicated shapes and surfaces.
Why it matters
Engineers and scientists modeling fusion reactors, turbulent fluids and other complex systems need fast simulations they can trust. Certified, interpretable AI surrogates could cut computing costs while giving reliable error and uncertainty estimates. A meshfree way to integrate over irregular shapes and scattered data could help researchers compute totals, such as the amount of a hazardous chemical in a region, when the domain or the measurements are messy.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Varun Shankar
University of Utah, UT·Computer Science
Develop the Unified Neural Operator (UNO), which describes neural operators as an input encoder, output basis functions and a projection, and use it to cover existing methods and design new task-specific architectures.
Burak Aksoylu
Texas A&M University-San Antonio, TX·Mathematics & Statistics
Use machine learning to improve iterative local-to-nonlocal coupling, so that peridynamics models only the region where fracture occurs and cheaper local models handle the rest.
Yiran Wang
University of Alabama, AL·Mathematics & Statistics
Develop hybrid reduced order models in which neural networks add basis functions to precomputed multiscale ones, guided by stable Petrov-Galerkin formulations and residual-based error indicators.
The school
Boise State University: 10 labs on PI Pages, $58M a year on research, 64 research doctorates a year.
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