Research Highlights

Here we highlight a small number of Diamond research accomplishments, selected to showcase research that cuts across multiple research thrusts and sub-thrusts. Each of these highlights is an example of research that aligns with the objectives of the MMICCs program: to advance multifaceted, integrated mathematics that spans novel formulations, discretizations, algorithm development, data analysis techniques, uncertainty quantification methodologies, optimization techniques, machine learning, and other mathematical and statistical approaches; and to address mathematical problems with clear relevance and significant impact for scientific advances.

1. Prediction of fluid velocity distribution from pore structure in porous media (MIT, UT-Austin) 2. Stochastic inverse modeling and decision support using a measure-theoretic framework (CSU, UC Denver, UT-Austin, FSU, LANL) 3. Characterization of subsurface geologic heterogeneity: A new perspective using dimensionality reduction (LANL) 4. Representing uncertainty due to model inadequacy (UT-Austin, MIT, ORNL) 5. Electrochemical energy storage systems (ORNL, UT Austin) 6. Multifidelity uncertainty quantification (MIT, FSU, LANL) 7. Error estimation for reduced models (CSU, FSU) 8. Fast algorithms for highly oscillatory problems (Stanford) 9. Scalable joint parameter–model reduction for Bayesian inverse problems (MIT, UT Austin) 10. An extreme scale implicit solver for highly-heterogeneous PDEs (UT-Austin, NYU) 11. Adaptive model selection, validation, and uncertainty quantification in complex multi-scale systems (UT-Austin) 12. Large-scale algorithms for Bayesian inversion, with application to flow of the Antarctic ice sheet (UT-Austin, NYU, UC Merced) 13. Bayesian nonlinear optimal experimental design for systems governed by PDEs (UT Austin, MIT) DiaMonD publications, 2012–2016