Model inversion and data assimilation

I’m interested in combining observation data and physics models such as PDEs to estimate unknown parameters of these physics models and other quantities of interest of the system being considered. Problems and areas of particular interest include:

• Sparse, indirect, and noisy observations in problems with highly heterogeneous, spatiotemporally distributed parameters.
• Bayesian methods for high-dimensional model inversion, including variants of MCMC for high-dimensional problems, sparse and approximate Bayesian inference, and variational inference, among others.
• Bayesian methods for data assimilation and state estimation based on Gaussian Process regression.
• Application to model inversion and data assimilation for groundwater flow and reactive transport problems.

Relevant publications

• Tartakovsky, A. M., & Barajas-Solano, D. A. (2019). Physics-Informed Machine Learning with Conditional Karhunen-Loève Expansions, arXiv preprint arXiv:arXiv:1912.02248.
• 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.
• Ma, T., Huang, R., Barajas-Solano, D. A., Tipireddy, R., & Tartakovsky, A. M. (2019). Electric Load and Power Forecasting Using Ensemble Gaussian Process Regression, arXiv preprint arXiv:1910.03783.
• Tipireddy, R., Barajas-Solano, D. A., & Tartakovsky, A. M. (2019). Conditional Karhunen-Loève expansion for uncertainty quantification and active learning in partial differential equation models, arXiv preprint arXiv:1904.08069.
• 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.
• Barajas-Solano, D. A., & Tartakovsky, A. M. (2019). Approximate Bayesian model inversion for PDEs with heterogeneous and state-dependent coefficients, J. Comput. Phys., 395, 247-262.
• Yang, X., Barajas-Solano, D. A., Tartakovsky, G., & Tartakovsky, A. M. (2019). Physics-informed CoKriging: A Gaussian-process-regression-based multifidelity method for data-model convergence, J. Comput. Phys., 395, 410-431.
• 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.