PIPages
Labs

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

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.

Collaborative Research: Unified Neural Operator (UNO): Towards Trustworthy Operator Learning for Scientific Applications

NSF · Sep 2025 – Aug 2028

Fredholm Alternative Quadrature: A Novel Framework for Numerical Integration Over Geometrically Complex Domains

NSF · Jul 2023 – Jun 2027

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.

More about Boise State University

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