Utah Digital Twin LabUDTL · University of Utah
Research

Four thrusts, one goal: digital twins you can trust

Our work runs from approximation theory and numerical analysis through learning architectures to deployed surrogates on HPC systems. Each thrust below lists its key ideas, representative papers, and the grants that fund it.

Operator Learning & Surrogate ModelingTrustworthy, Property-Preserving SciMLKernel & Meshless Numerical MethodsDigital Twins for Engineering & Biology
Thrust 01

Operator Learning & Surrogate Modeling

A digital twin must answer "what if?" questions far faster than a full simulation. We build neural and kernel operators that learn solution maps between function spaces from simulation and experimental data, and we design them to be memory-efficient, geometry-flexible, and multiscale.

$$\mathcal{G}^\dagger:\ \mathcal{U}\to\mathcal{V},\qquad \min_{\theta}\ \frac{1}{N}\sum_{i=1}^{N}\big\|\mathcal{G}_\theta(u_i)-\mathcal{G}^\dagger(u_i)\big\|_{\mathcal{V}}^2$$
  • Kernel Neural Operators (KNOs): replace dense integral kernels with compact, parametrized kernels and quadrature for scalable, geometry-flexible learning.
  • Multiscale kernel frames and partition-of-unity mixtures of experts that localize operators in space and scale.
  • Ensemble / MoE DeepONets, optimal weighted least squares, and deep Gaussian processes for functional maps with quantified uncertainty.
  • Applications to continuum robots, composite structures, and incompressible flows.
Thrust 02

Trustworthy, Property-Preserving SciML

Scientific users need more than low test error. We build architectures that preserve conservation laws and constraints exactly, that come with approximation guarantees, and that remain correct under compression, reduced precision, and real software stacks.

$$\nabla\!\cdot\mathbf{u}_\theta \equiv 0\ \text{ by construction},\qquad u_\theta(x)=\underbrace{\textstyle\sum_{|\alpha|\le \ell} c_\alpha\,P_\alpha(x)}_{\text{polynomial}} +\underbrace{\mathcal{N}_\theta(x)}_{\text{network}},\ \ \langle \mathcal{N}_\theta, P_\alpha\rangle\approx 0$$
  • Property-preserving operator learning for incompressible flows (divergence-free surrogates).
  • Polynomial-augmented networks (PANNs) with weak orthogonality constraints, HyResPINNs, and Fourier PINNs that balance expressiveness and trainability.
  • Certifiable, compression-aware SciML systems (NSF SHF) and correct scientific software via program synthesis (NSF/DOE CS2).
Thrust 03

Kernel & Meshless Numerical Methods

Our numerics roots are in radial basis function (RBF) and kernel methods. Meshless discretizations need only scattered nodes, which makes them a natural fit for complex and evolving geometry, and for coupling with learned models. We develop stable, high-order, scalable schemes and the node-generation and solver machinery around them.

$$\mathcal{L}u(\mathbf{x}_c)\;\approx\;\sum_{j=1}^{n} w_j\,u(\mathbf{x}_j),\qquad \begin{bmatrix} A & P\\ P^{\!\top} & 0\end{bmatrix} \begin{bmatrix}\mathbf{w}\\ \boldsymbol{\lambda}\end{bmatrix} =\begin{bmatrix}\mathcal{L}\phi(\|\mathbf{x}-\mathbf{x}_j\|)\big|_{\mathbf{x}_c}\\ \mathcal{L}P\big|_{\mathbf{x}_c}\end{bmatrix}$$
  • RBF-FD for advection–diffusion–reaction on manifolds, time-varying domains, and moving surfaces (Lagrangian–Eulerian).
  • Stabilization via hyperviscosity, overlapped RBF-FD, and semi-Lagrangian transport.
  • Meshfree multilevel solvers (MGM), robust node generation, and meshless isogeometric analysis on NURBS.
  • A unified framework for efficient kernel and polynomial interpolation.
Thrust 04

Digital Twins for Engineering & Biology

We partner with domain scientists and national labs to put these tools to work: process-to-performance modeling of textile composites and progressive fracture with the Air Force Research Laboratory, surrogate-driven design of continuum robots, and fluid–structure models of blood clotting and lymphatic pumping, all on modern parallel hardware.

  • Composites & fracture: CG-XFEM with hierarchical enrichments; nonlinear solvers for cohesive-zone models.
  • Robotics: neural-operator design-space surrogates for tendon-actuated continuum robots.
  • Biofluids: immersed-boundary simulation of platelets, whole blood, and lymphangion pumping.
  • HPC: fine-grained parallel immersed-boundary methods; HPC pipelines for textile composites.