Paul Cazeaux
Virginia Polytechnic Institute and State University, VA·Mathematics & Statistics
Many simulations in science and engineering track a huge number of interacting variables. Examples include electrons in quantum materials, turbulent plasma in fusion reactors, and medical scans that change over time.
- Fields
Mathematics & Statistics
Computer Science
Physics
- Topics
numerical linear algebra
randomized sketching
tensor networks
- Grants
- 1 known grant, through Jun 2029
What they work on
- Prove subspace embedding and distortion bounds for TTStack sketches, random projections built on tensor trains, and characterize trade-offs among sketch size, accuracy and block structure.
- Develop scalable randomized algorithms that work directly in tensor-train format, including sketch-and-compress routines, TT-GMRES and randomized Lanczos solvers, and streaming tensor-train approximation.
- Build theory for non-Hermitian eigenvalue solvers in tensor format to enable reliable ground-state calculations for transcorrelated quantum chemistry Hamiltonians, where standard variational methods fail.
- Validate the methods on quantum many-body physics, gyrokinetic plasma turbulence compression, dynamic medical imaging and multilayer moiré materials, released as open-source Julia software.
More about the research
With conventional methods, the memory and computing time needed grow exponentially as variables are added, so these problems quickly become impossible. This project builds mathematical tools that store such data in a compact, structured form. They then use carefully designed random projections, called randomized sketching, to get answers much faster while keeping the chance of failure near zero.
Why it matters
Faster and more reliable ways to handle high-dimensional data could speed up quantum chemistry calculations and the design of moiré quantum materials for electronics. They could enable fast digital twins of plasma turbulence in fusion reactors and quicker reconstruction of dynamic medical scans from limited data. The methods may also ease bottlenecks in large-scale AI training and inference that depend on tensor operations.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Vivak Patel
University of Wisconsin-Madison, WI·Mathematics & Statistics
Map a modular theory of randomized linear algebra algorithms onto composable computational kernels so that new, application-tailored randomized solvers can be assembled rapidly rather than coded from scratch.
Michal Derezinski
University of Michigan, MI·Computer Science·Early-career
Reformulate optimal matrix sketching, the construction of a small randomized approximation of input data, using black-box sampling methods, so that sketch and sub-sample outputs come with reliability guarantees suitable for software.
Fabian Faulstich
Rensselaer Polytechnic Institute, NY·Mathematics & Statistics·Early-career
Recast periodic coupled-cluster theory as a nonlinear Petrov–Galerkin method for a pseudo-differential operator on a high-dimensional torus, in order to derive sharp error estimates for electronic-structure simulations of crystalline materials.
The school
Virginia Polytechnic Institute and State University: 35 labs on PI Pages, $657M a year on research, 496 research doctorates a year.
More about Virginia Polytechnic Institute and State University
Reach out
A start for your email. Fill in the brackets.