Modeling groundwater flow and reactive transport

I’m interested in developing efficient uncertainty quantification and model inversion methods for groundwater flow and reactive transport problems, and in developing multiscale/multiresolution schemes for the numerical approximation of continuum-scale models of these phenomena. Specific areas of interest include:

• Probabilistic, data-driven models of heterogeneous parameter fields.
• PDF methods for stochastic upscaling and uncertainty quantification.
• Bayesian methods for model inversion, including MCMC variants for high-dimensional problems, approximate Bayesian inference, variational inference, and others.
• Scientific machine learning methods for state estimation and parameter estimation.
• Multiscale, multiresolution, and heterogeneous timestepping schemes for continuum-scale models of groundwater flow and transport.

Relevant publications

• Yang, L., Treichler, S., Kurth, T., Fischer, K., Barajas-Solano, D. A., Romero, J., Churavy, V., Tartakovsky, A. M., Houston, M., Prabhat, & Karniadakis, G. E. (2019). Highly-scalable, physics-informed GANs for learning solutions of stochastic PDEs, arXiv preprint arXiv:1910.13444.
• Tartakovsky, A. M., Perdikaris, P., Ortiz Marrero, C., Tartakovsky, G. D., & Barajas-Solano, D. A. (2018). Learning Parameters and Constitutive Relationships with Physics Informed Deep Neural Networks, arXiv preprint arXiv:1808.03398.
• Barajas-Solano, D. A., & Tartakovsky, A. M. (2018). Multivariate Gaussian Process Regression for Multiscale Data Assimilation and Uncertainty Reduction, arXiv preprint arXiv:1804.06490.
• Tartakovsky, A. M., & Barajas-Solano, D. A. (2018). Persistent incomplete mixing in reactive flows, arXiv preprint arXiv:1803.06693.
• Barajas-Solano, D. A., & Tartakovsky, A. M. (2018). Probability and Cumulative Density Function Methods for the Stochastic Advection-Reaction Equation, SIAM/ASA J. Uncert. Quantif., 6(1), 180-212.
• Barajas-Solano, D. A., & Tartakovsky, A. M. (2016). Hybrid Multiscale Finite Volume Method for Advection-Diffusion Equations Subject to Heterogeneous Reactive Boundary Conditions, Multiscale Model. Simul., 14(4), 1341-1376.
• Barajas-Solano, D. A., Wohlberg, B. E., Vesselinov, V. V., & Tartakovsky, D. M. (2014). Linear functional minimization for inverse modeling, Water Resour. Res., 51(6), 4516-4531.
• Barajas-Solano, D. A., & Tartakovsky, D. M. (2013). Computing green’s functions for flow in heterogeneous composite media, Int. J. Uncertain. Quantif., 3(1), 39-46.