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

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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

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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

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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

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

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

2023 PyData Chicago

Unified Framework for Quasi-Monte Carlo Software

2023 Monte Carlo Methods and Applications

Other Presentations