Collaborative Research: Unified Neural Operator (UNO): Towards Trustworthy Operator Learning for Scientific Applications
DMS / CISE — Computational & Data-Enabled Science (CDS&E) · PI Varun Shankar; Co-PI Akil Narayan
Utah Digital Twin Lab · Kahlert School of Computing
Provably-accurate, scalable scientific machine learning
We build the models that digital twins run on: operator learners, structure-preserving networks, and high-order meshless solvers, for scientific discovery and engineering.
6active grants
5sponsors
6PhD students & postdocs
43papers & preprints
What we do
From numerics to digital twins
The Utah Digital Twin Lab (UDTL) develops provably-accurate, scalable scientific machine learning architectures that help create digital twins for scientific discovery and engineering. We work where scientific machine learning, scientific computing, high performance computing, and applied mathematics meet.
A useful digital twin has to be fast enough to query thousands of times, faithful to the physics it represents, and honest about its own error. We pursue all three, building on two decades of work on kernel and meshless methods.
01
Operator Learning & Surrogate Modeling
Fast, accurate surrogates that map inputs, geometries, and parameters directly to PDE solutions.
02Trustworthy, Property-Preserving SciML
Models that respect physics by construction, with guarantees on accuracy, stability, and correctness.
03Kernel & Meshless Numerical Methods
High-order RBF-FD and kernel methods for PDEs on irregular domains, surfaces, and moving manifolds.
04Digital Twins for Engineering & Biology
Coupling numerics, learning, and HPC for composites, fluids, robotics, and biomechanics.
Research areas
Where our work sits
- Scientific machine learning
- Numerical methods
- HPC & trustworthy systems
- Health & medicine
- Engineering
Scientific machine learning
- Operator learning
- Kernel neural operators
- Multiscale kernel frames
- Mixture-of-experts
- Gaussian processes
- PINNs & PANNs
- Property-preserving ML
- Surrogate modeling
Numerical methods
- RBF-FD
- Meshless methods
- PDEs on manifolds
- Moving domains
- Kernel approximation
- Multilevel solvers
- Node generation
- Stabilization
HPC & trustworthy systems
- High-performance computing
- GPU & multicore
- Compression-aware SciML
- Correct scientific software
- Blockchain compliance
Health & medicine
- Cancer detection
- Tacrolimus modeling
- Blood clotting & platelets
- Lymphatic pumping
Engineering
- Composites & fracture
- Continuum robotics
- Incompressible flows
- Nonlinear solvers
Lab director
Varun Shankar
Assistant Professor, Kahlert School of Computing, University of Utah. Varun works on scientific machine learning, kernel and meshless numerical methods, and high performance computing. He received his PhD in Computing from Utah and was a postdoc in Utah's Department of Mathematics.
Funding
All active grants →
Supported by
NSFDOEAFOSRAFRLSandia
AFOSR
PI
FA9550-25-1-0042
Property-preserving and multiscale operator learning for surrogate modeling
Laboratory Research Initiation Request (LRIR)
AFRL
PI
Numerical methods and scientific machine learning for composite materials and structures
Air Force Research Laboratory (subcontracts via UES and ARCTOS)
Recent work
All →-
The Frame Kernel Method for Multiscale Operator Learning
Branden Frieden, Ryan Whitehead, Keith Ballard, Robert M. Kirby, Varun Shankar
arXivIn review
-
A high-order, meshless, Lagrangian–Eulerian RBF-FD method for advection–diffusion–reaction on moving manifolds
Matthew Lowery, Grady B. Wright, Varun Shankar
arXivIn review
- Neural Operators for Design-Space Surrogate Modeling of Tendon-Actuated Continuum Robots Branden Frieden, James M Ferguson, Alan Kuntz, Varun Shankar IEEE International Conference on Robotics and Automation, ICRA, 2026
- Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning Matthew Lowery, John Turnage, Zachary Morrow, John D Jakeman, Akil Narayan, Shandian Zhe, Varun Shankar Transactions on Machine Learning Research, 2026
- Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation Madison Cooley, Shandian Zhe, Robert M Kirby, Varun Shankar SIAM Journal on Scientific Computing, 2026
-
Localized Operator Learning with Adaptive Partition-of-Unity Mixture-of-Expert Networks
Madison Cooley, Ramansh Sharma, Shandian Zhe, Robert M. Kirby, Varun Shankar
In review
News
- Sep 2026Varun gave an invited talk on multiscale kernel frames for operator learning at the Banff Workshop on Kernel Approximation and Gaussian Processes, and chaired its panel on kernel/GP software.
- Sep 2026Varun joined the editorial board of Nature Scientific Reports.
- May 2026New NSF/DOE CS2 award (with Ben Greenman and John Regehr): on-demand semantic analysis via program synthesis.
- 2026Kernel Neural Operators (KNOs) published in TMLR; PANNs published in SISC.
- 2026Neural-operator surrogates for tendon-actuated continuum robots at ICRA 2026 (with Alan Kuntz's group).
- Sep 2025New NSF award (PI): Unified Neural Operator (UNO) — towards trustworthy operator learning for scientific applications.
- 2025Congratulations to Dr. Madison Cooley on completing her PhD!