- Softwares
- Posters
- A Neural Surrogate Solver for Radiation Transfer
- Fast Gaussian Process Regression for Smooth Functions
- Probabilistic Models for PDEs with Random Coefficients
- Credible Intervals for Probability of Failure with Gaussian Processes
- Robust Approximation of Sensitivity Indices in QMCPy
- QMCPy: Quasi-Monte Carlo Software in Python
- Other Posters
- Presentations
- Quasi-Monte Carlo and Fast Multi-Task Gaussian Process Regression
- Scientific Machine Learning of Radiative Transfer Equations
- Fast Gaussian Process Regression with Derivative Information using Lattice and Digital Sequences
- Probabilistic Models for PDEs with Random Coefficients
- Adaptive Probability of Failure Estimation with Gaussian Processes
- Monte Carlo with QMCPy for Vector Functions of Integrals
- Unified Framework for Quasi-Monte Carlo Software
- Other Presentations
Softwares
FastGPs
pip install fastgps
Gaussian process regression (GPR) models typically require $\mathcal{O}(n^2)$ storage and $\mathcal{O}(n^3)$ computations. FastGPs implements GPR 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
- multi-task GPR.
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.
- lattices with
- 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.
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.
Posters
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
-
QMCPy: A Quasi-Monte Carlo Software in Python 3. @ 2021 SIAM Conference on Computational Science and Engineering
-
Multi-threaded/-processed Requests to Cloud Services for Intelligent Address Standardization @ 2019 SIAM Conference on Computational Science and Engineering
Presentations
Quasi-Monte Carlo and Fast Multi-Task Gaussian Process Regression
2025 Caltech Lunch Group Seminar
Scientific Machine Learning of Radiative Transfer Equations
2024 Illinois Institute of Technology, Department of Applied Mathematics, Computational Mathematics Seminar
Fast Gaussian Process Regression with Derivative Information using Lattice and Digital Sequences
2024 Illinois Institute of Technology PhD Comprehensive Exam
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
Monte Carlo with QMCPy for Vector Functions of Integrals
Unified Framework for Quasi-Monte Carlo Software
2023 Monte Carlo Methods and Applications
Other Presentations
- Fast Gaussian Process Regression for Smooth Functions using Lattice and Digital Sequences with Matching Kernels @ 2024 Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing Conference
- Walsh Functions and Spaces @ 2024 Illinois Institute of Technology, Department of Applied Mathematics, Computational Mathematics and Multiscale Seminar
- Fast Physics Informed Kernel Methods for Nonlinear PDEs with Unknown Coefficients @ 2024 SampSci Conference
- Fast Gaussian Process Regression with Derivative Information @ 2024 SIAM Conference on Uncertainty Quantification and 2024 Midwest Numerical Analysis Day
- QMCPy Client for UM-Bridge @ 2022 UM-Bridge Workshop
- Quasi-Monte Carlo for Functions of Multi-Dimensional Integrals @ 2022 Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing Conference
- QMCPy, A Quasi-Monte Carlo Framework @ 2021 Midwest Numerical Analysis Day
- Building QMCPy’s Quasi-Monte Carlo Framework. @ 2021 International Conference on Monte Carlo Methods and Applications
- QMCPy Quasi-Monte Carlo Software @ 2021 SIAM Great Lakes Section Meeting
- (Quasi)-Monte Carlo Importance Sampling with QMCPy. @ 2021 Illinois Institute of Technology, Department of Applied Mathematics, Computational Mathematics Seminar
- QMCPy: A Quasi-Monte Carlo Software in Python 3 @ 2020 Chicago Area SIAM Student Conference
- QMCPy: A Quasi-Monte Carlo Software in Python 3. @ 2020 PyData Chicago