Varun Shankar
University of Utah, UT·Computer Science
Simulating fluid flows or the plasma inside fusion reactors with traditional numerical solvers can be extremely slow. Machine learning offers surrogates, fast stand-in models trained to mimic those solvers.
- Fields
Computer Science
Mathematics & Statistics
Engineering
- Topics
scientific machine learning
SciML
operator learning
- Grants
- 1 known grant, through Aug 2028
What they work on
- 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.
- Create scalable, adaptive training and inference algorithms that let UNO adjust to local solution features and handle high-dimensional data when data are plentiful.
- Prove universal approximation theorems and error estimates for UNO, and build theory to guide robust sampling, adaptivity and built-in uncertainty quantification.
- Apply UNO as a physics-preserving surrogate model for turbulent, multiscale and multiphysics fluid flow problems, including cases with little data.
More about the research
A promising approach is operator learning. Instead of learning one answer, it learns the rule that maps an input function, such as a starting condition, to an output function, such as the resulting flow. Many deep-learning versions, called neural operators, now exist. However, they lack a shared theory, their robustness is poorly understood, they are hard to interpret, and practitioners struggle to choose among them. That limits their use when the stakes are high.
Why it matters
Scientists and engineers who rely on costly simulations could gain faster, more trustworthy AI-based stand-ins with error guarantees and uncertainty estimates. That could help in modeling turbulent fluid flows and the magnetohydrodynamic systems, electrically conducting fluids in magnetic fields, that matter for fusion energy design. It would also make it easier to choose the right machine-learning method for each task.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Grady Wright
Boise State University, ID·Mathematics & Statistics
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.
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.
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.
The school
University of Utah: 58 labs on PI Pages, $789M a year on research, 366 research doctorates a year.
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