- Softwares
- Posters
- Presentations
- Walsh Functions and Spaces
- 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
QMCPy
QMCPy is a Python package for Quasi-Monte Carlo which includes quasi-random (low discrepancy) sequence generators, automatic variable transforms, adaptive stopping criteria, and a suite of diverse use cases.
pip install qmcpy
QMCGenerators.jl
QMCGenerators.jl is a Julia package for quasi-random (low discrepancy) sequence generators. Lattice and digital sequences, including higher order versions, are supported along with a variety of randomization routines. This is a translation and enhancement of Dirk Nuyens’ Magic Point Shop.
] add QMCGenerators
FastGaussianProcesses.jl
FastGaussianProcesses.jl is a Julia package for fast construction of Gaussian processes regression models when one controls the design of experiments. Gradient information may also be quickly incorporated into the GP. A GP fit to $N$ sampling locations with $M$ derivative orders available would typically cost $\mathcal{O}(M^3N^3)$ to fit including kernel parameter optimization. Our fast algorithms cost only $\mathcal{O}(M^2 N \log N + M^3 N)$. Typically $M=1$ when only the function $f:[0,1]^s \to \mathbb{R}$ is evaluated. When the gradient is also evaluated we have $M = 1+s$. Incorporating second derivatives and beyond is support but limited.
] add FastGaussianProcesses
Posters
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
Walsh Functions and Spaces
2024 Illinois Institute of Technology, Computational Math and Stats Seminar and Multiscale 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 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 Conferene
- 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