For projects with no linked papers, further details could be made available upon request.
High-d sampling and visualization in scientific computing: A library of high-dimensional test functions for optimization, uncertainty quantification, and numerical integration problems.
Model evaluation and uncertainty quantification for AI/ML: quantifying uncertainty in AI/ML predictive estimates, decomposing it into aleatoric and epistemic components, and consequently guiding active learning.
Vision: Quantifying uncertainty in object detection, segmentation, and image generation-captioning workflows.
Image classification: Accuracy/uncertainty impact of rotation and AWGN addition on NN classifiers, applied to MNIST/CIFAR.
1-d regression: estimating uncertainty bands with deep ensembles, Monte Carlo dropout, and conformal prediction over limited/noisy observations.
Time series classification: predicting class and estimating uncertainty with missing/incomplete time series.
Fourier and signal processing methods in biomedical and bioinfromatics applications: for feature extraction (e.g., period-3 in DNA), object localization (e.g., echos in ultrasound), and spectral analysis of high-d sampling techniques using Nd-FFT.
Voronoi Piecewise Surrogate (VPS) models: Leveraging the properties of Voronoi diagrams and Delaunaey graphs in global surrogate modeling problems for high-dimensional uncertainty quantification and adaptive sampling scenarios with a limited sample budget (e.g., multifidelity/costly/high-stakes numerical simulations).
Meshing and mesh tuning: creating (or tuning) 2d/3d meshes with guaranteed quality properties.
From computational methods to scientific computing and engineering applications
Extending mesh tuning methods, e.g., for non-obtuse triangulation [paper], to accurately model fiber reinforced polymers for elastic and failure simulations.
Machine Learning for collision detection and motion planning.