Model inversion and data assimilation

I’m interested in combining observation data and numerical models of complex physical systems to estimate unknown parameters, perform probabilistic predictions of quantities of interest, and quantify the uncertainty in these predictions. 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, likelihood-free inference, and variational inference, among others.
• Application to model inversion and data assimilation for groundwater flow and reactive transport problems.

Relevant publications

• Yeung, Y. H., Tipireddy, R., Barajas-Solano, D. A., & Tartakovsky, A. M. (2024). Conditional Karhunen-Loève Regression Model with Basis Adaptation for High-dimensional Problems: Uncertainty Quantification and Inverse Modeling, Comput. Methods Appl. Mech. Eng., 418(A), 116487.
• Sinha, S., Nandanoori, S. P., & Barajas-Solano, D. A. (2023). Online Real-time Learning of Dynamical Systems from Noisy Streaming Data, Sci. Rep., 13, 22564.
• Tartakovsky, A. M., Ma, T., Barajas-Solano, D. A., & Tipireddy, R. (2023). Physics-informed Gaussian Process Regression for States Estimation and Forecasting in Power Grids, Int. J. Forecasting, 39(2), 967–980.
• Ma, T., Huang, R., Barajas-Solano, D. A., Tipireddy, R., & Tartakovsky, A. M. (2022). Electric Load and Power Forecasting Using Ensemble Gaussian Process Regression, J. Mach. Learn. Mod. Comput., 3(2), 87–110.
• Yeung, Y. H., Barajas-Solano, D. A., & Tartakovsky, A. M. (2022). Physics-informed Machine Learning Method for Large-scale Data Assimilation Problems, Water Resour. Res., 58(5), e2021WR031023.
• Hirsh, S. M., Barajas-Solano, D. A., & Kutz, J. N. (2022). Sparsifying Priors for Bayesian Uncertainty Quantification in Model Discovery, Roy. Soc. Open. Sci., 9(2), 211823.
• Tartakovsky, A. M., Barajas-Solano, D. A., & He, Q. (2021). Physics-Informed Machine Learning with Conditional Karhunen-Loève Expansions, J. Comput. Phys., 426, 109904.
• Tipireddy, R., Barajas-Solano, D. A., & Tartakovsky, A. M. (2020). Conditional Karhunen-Loève expansion for uncertainty quantification and active learning in partial differential equation models, J. Comput. Phys., 418, 109604.
• Tartakovsky, A. M., Perdikaris, P., Ortiz Marrero, C., Tartakovsky, G. D., & Barajas-Solano, D. A. (2020). Physics-Informed Deep Neural Networks for Learning Parameters and Constitutive Relationships in Subsurface Flow Problems, Water Resour. Res., 56, e2019WR026731.
• He, Q., Barajas-Solano, D. A., Tartakovsky, G. D., & Tartakovsky, A. M. (2020). Physics-informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transport, Adv. Water Resour., 141, 103610.
• 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.
• Barajas-Solano, David A., Alexander, F. J., Anghel, M., & Tartakovsky, D. M. (2019). Efficient gHMC Reconstruction of Contaminant Release History, Front. Environ. Sci., 7.
• 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, 2019 IEEE/ACM Third Workshop on Deep Learning on Supercomputers (DLS), 1–11.
• 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., & Tartakovsky, A. M. (2018). Multivariate Gaussian Process Regression for Multiscale Data Assimilation and Uncertainty Reduction, arXiv preprint arXiv:1804.06490.
• 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.