# Projects

## <*Under Construction*>

### Multivariate Functional Approximation MFA

We are investigating modeling discrete scientific data by a multivariate functional approximation (MFA) based on a tensor product of nonuniform B-spline (NURBS) functions. The model is an approximation that offers lossy compression combined with geometric and analytic properties making it useful for further analysis without translating back to the discrete form. NURBS are piecewise-continuous, differentiable, have local support, and are invariant to affine transformations. The NURBS model is efficiently represented by control data consisting of control points and knots.

### AICDI: Atomistically Informed Coherent Diffraction Imaging

This project is concerned with single crystal Bragg Coherent Diffractive Imaging (BCDI). Specifically, using machine learning algorithms to do atomistic model fitting of the data based on a training database derived from large scale molecular dynamics (MD) and statics (MS) simulations; for the purpose of classifying defects in a crystal without the need for phase retrieval.

### COHED: Coherence for High Energy Diffraction

A revolutionary capability of the APS upgrade will be the application of 3D strain-sensitive Bragg Coherent Diffractive Imaging (BCDI) of nanometer and micrometer crystalline volumes using highly penetrating X-ray energies. The main objective of this proposal is to investigate X-ray coherence at high energies (>=50 KeV) from both experimental and algorithmic perspectives.

### Learning to Solve Inverse Problems with Backpropagation

This research direction focuses on solving scientific inverse problems through fitting a physics-based model to measured data. The model parameters are learned in a similar manner to deep neural networks, utilizing the backpropagation method as implemented in Google TensorFlow package. This approach has advantages in terms of speed and accuracy compared to current state of the art algorithms, and demonstrates re-purposing the deep learning backpropagation algorithm to solve general inverse problems that are prevalent in experimental imaging.