SCOPA Lab

Integrating data with simulation to enable data-driven discovery in the applied sciences.

Overview

The Scientific Computing, Optimization, and Parallel Algorithms (SCOPA) lab is part of the Department of Mathematics at the University of Houston.

Our goal is the design of principled and scalable algorithms at the interface of machine learning, optimization, and scientific computing that integrate data with simulation to enable data-driven discovery in the applied sciences. We are interested in methods that combine the interpretability and predictive power of mechanistic models with the flexibility of learning, and in the numerical analysis that makes them trustworthy — stability, structure preservation, and a rigorous accounting of uncertainty. Our work is driven by applications in medical imaging and the life sciences, and much of it is released as open-source software for GPU and supercomputing platforms.

Research Areas

Scientific machine learning and data-driven modeling
Inverse problems and PDE-constrained optimization
Numerical optimization, including optimization for machine learning
Tensor methods, model reduction, and surrogate models
Uncertainty quantification and Bayesian inference
Nonlinear optimal control
Geometric methods and the analysis of shapes and manifold-valued data
Scalable, parallel, and GPU-accelerated algorithms

Research Themes

Integrating models with data

Much of our work concerns settings in which a mechanistic model — typically a system of differential equations — must be reconciled with observations. This leads to large-scale problems that are nonconvex, ill-posed, and expensive to solve. We are interested in formulations that respect the structure of the underlying problem, in fast solvers that make such problems tractable at realistic scale, and in Bayesian and randomized techniques that quantify the uncertainty of the resulting estimates.

Learning and numerics

Mechanistic models are interpretable and extrapolate beyond the data, but they are costly; learned models are fast and flexible, but can be opaque and unreliable outside the regime they were trained on. A growing part of our work combines the two in a principled way, through continuous-time and dynamical-systems formulations of learning, structure- and stability-preserving discretizations, optimization methods for training, and surrogate and operator-learning frameworks. The guiding question is how to bring the standards of numerical analysis — stability, convergence, well-posedness — to methods that learn from data.

Reduction and scale

Making these problems affordable is itself a mathematical question. Tensor-based reduced-order models and learned surrogates compress parametric models into forms cheap enough for many-query settings such as model calibration, uncertainty quantification, and digital twins. Complementing this, we design parallel and GPU-accelerated algorithms so that the resulting methods scale from a workstation to a supercomputer.

Geometry and applications

Many of the objects we work with — images, shapes, deformations, and covariance structures — do not live in flat vector spaces, and respecting their geometry is often what makes an algorithm both meaningful and efficient. These methods are driven by applications in medical imaging and the life sciences, including computational anatomy, biophysical modeling of disease progression, cardiology, and systems biology.

A more detailed description of our work is on the research page; our publications, talks, and posters and lab members are listed separately. Code is released at github.com/scopagroup.