Fabian Faulstich
Rensselaer Polytechnic Institute, NY·Mathematics & Statistics·Early-career
Quantum materials are substances whose useful behavior — superconductivity, unusual magnetism, efficient catalysis — comes from the way their electrons push on one another rather than from the simple properties of individual atoms. Predicting that behavior on a computer is far cheaper than making and measuring new materials, so good simulations let experimentalists spend their effort on the most promising candidates.
- Fields
Mathematics & Statistics
Physics
Materials Science
- Topics
quantum materials
coupled-cluster theory
electronic structure
- Grants
- 1 known grant, through Jul 2031
What they work on
- 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.
- Exploit multiscale and low-rank compression techniques within that framework to reduce the computational complexity that currently limits wavefunction-based simulation of extended periodic systems.
- Study the coupled-cluster equations as low-degree polynomial systems using algebraic geometry, to characterize their solution structure and identify the physically relevant state when multiple competing phases coexist.
- Use machine learning and randomized numerical linear algebra to accelerate and stabilize coupled-cluster solvers by learning high-quality initial guesses, low-dimensional solution structure, and tensor-compression strategies.
More about the research
The catch is that the fast, widely used simulation tools rely on approximations that break down exactly where things get interesting: in materials whose electrons are strongly correlated, meaning each electron's motion depends heavily on all the others. This project builds mathematical foundations and algorithms to make high-accuracy, wavefunction-based simulation practical for crystals, where the atomic pattern repeats periodically.
Why it matters
Simulations that stay reliable for strongly interacting electrons would let researchers screen candidate materials for energy-efficient electronics, sustainable catalysis, precision sensing, and quantum information technologies before committing to costly experiments, and would come with error estimates telling users how much to trust a prediction. The mathematical tools developed — error analysis, polynomial-system methods, and compression strategies — could also apply to other high-dimensional scientific computing problems.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Anna Ma
University of California-Irvine, CA·Mathematics & Statistics
Analyze the sample complexity of low-rank tensor completion, meaning how many observed entries are needed to recover a multi-dimensional dataset with simple underlying structure.
Longxiu Huang
Michigan State University, MI·Mathematics & Statistics
Develop mode-wise sampling methods that analyze large tensors (multidimensional data arrays) by working with small slices along each dimension, and prove that this sampling reliably captures the full data.
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.
The school
Rensselaer Polytechnic Institute: 5 labs on PI Pages, $140M a year on research, 113 research doctorates a year.
Reach out
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