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Softwares

FastGPs

pip install fastgps

Gaussian process (GP) regression models typically require $\mathcal{O}(n^2)$ storage and $\mathcal{O}(n^3)$ computations. FastGPs implements GPs which requires only $\mathcal{O}(n)$ storage and $\mathcal{O}(n \log n)$ computations by pairing certain quasi-random sampling locations with matching kernels to yield structured Gram matrices. We support

  • GPU scaling,
  • batched inference,
  • robust hyperparameter optimization, and
  • multitask GPs.

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QMCPy

pip install qmcpy

QMCPy is a Python package for Quasi-Monte Carlo (QMC) which contains

  • quasi-random (low discrepancy) sequence generators and randomization routines, including
    • lattices with
      • extensible constructions
      • random shifts
    • digital nets (e.g. Sobol' points) with
      • extensible constructions
      • random digital shifts,
      • linear matrix scrambling,
      • nested uniform scrambling, and
      • higher order construction through digital interlacing.
  • adaptive error estimation and stopping criteria including
    • IID Monte Carlo algorithms
    • QMC which tracks the decay of Fourier/Walsh coefficients
    • QMC via Bayesian Cubature
    • QMC via multiple randomizations (replications)
    • growing support for multilevel Monte Carlo and Quasi-Monte Carlo
  • a suite of diverse use cases, and
  • automatic variable transforms.

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QMCGenerators.jl

] add QMCGenerators

QMCGenerators.jl is a Julia package which includes routines to generate and randomize quasi-random sequences used in Quasi-Monte Carlo. This supports the suite of low discrepancy sequence generators and randomization routines available in QMCPy, see the description above. This package is a translation and enhancement of Dirk Nuyens' Magic Point Shop.

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Presentations

Fast Multitask Gaussian Process Regression

2026 SIAM Conference on Uncertainty Quantification

Algorithms and Scientific Software for Quasi-Monte Carlo, Fast Gaussian Process Regression, and Scientific Machine Learning

Illinois Institute of Technology PhD Thesis Exam

Fast Bayesian Multilevel Quasi-Monte Carlo

2025 SIAM Conference on Analysis of Partial Differential Equations

Fast Gaussian Processes

2025 Conference on Monte Carlo Methods and Applications

Scientific Machine Learning for Exact Recovery of Nonlinear PDEs

2025 RIKEN-CCS

Scientific Machine Learning of Radiative Transfer Equations

2024 Illinois Institute of Technology, Department of Applied Mathematics, Computational Mathematics Seminar

Probabilistic Models for PDEs with Random Coefficients

2023 Los Alamos National Laboratory Student Lightening Talks

Adaptive Probability of Failure Estimation with Gaussian Processes

2023 SIAM Conference on Computational Science and Engineering

Other Presentations

Posters

Scientific Machine Learning for Exact Recovery of Nonlinear PDEs

2025 RIKEN-CCS

A Neural Surrogate Solver for Radiation Transfer

2024 NeurIPS Workshop on Data-Driven and Differentiable Simulations, Surrogates, and Solvers

Fast Gaussian Process Regression for Smooth Functions

2024 Illinois Institute of Technology Menger Day

Probabilistic Models for PDEs with Random Coefficients

2023 Los Alamos National Laboratory Student Symposium

Credible Intervals for Probability of Failure with Gaussian Processes

2022 Illinois Institute of Technology Welcome Week Student Research Poster Day

Robust Approximation of Sensitivity Indices in QMCPy

2022 Conference on Sensitivity Analysis of Model Output (SAMO)

QMCPy: Quasi-Monte Carlo Software in Python

2021 Chicago Area Undergraduate Research Symposium

Other Posters