Stochastic differential and partial differential equations

• PDF methods for the analysis of SDEs and hyperbolic SPDEs.
• Formulation and analysis of stochastic models of power transmission networks accounting for fluctuations in load and generation, including the analysis of large deviations.
• Sparse regression-based methods for propagating uncertainty in stationary and dynamical systems with uncertainty.
• Scientific machine learning methods for uncertainty propagation and state estimation in SDEs and SPDEs.

Relevant publications

• Roth, J., Barajas-Solano, D. A., Stinis, P., Weare, J., & Anitescu, M. (2019). A Kinetic Monte Carlo Approach for Simulating Cascading Transmission Line Failure, arXiv preprint arXiv:1912.08081.
• 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., & Barajas-Solano, D. A. (2018). Persistent incomplete mixing in reactive flows, arXiv preprint arXiv:1803.06693.
• Yang, X., Barajas-Solano, D. A., Rosenthal, W. S., & Tartakovsky, A. M. (2017). PDF estimation for power grid systems via sparse regression, arXiv preprint arXiv:1708.08378.
• 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). Probabilistic density function method for nonlinear dynamical systems driven by colored noise, Phys. Rev. E, 93(5), 052121.
• Barajas-Solano, D. A., & Tartakovsky, D. M. (2016). Stochastic Collocation Methods for Nonlinear Parabolic Equations with Random Coefficients, SIAM/ASA J. Uncert. Quantif., 4(1), 475-494.
• Wang, P., Barajas-Solano, D. A., Constantinescu, E., Abhyankar, S., Ghosh, D., Smith, B. F., Huang, Z., & Tartakovsky, D. M. (2015). Probabilistic Density Function Method for Stochastic ODEs of Power Systems with Uncertain Power Input, SIAM/ASA J. Uncert. Quantif., 3(1), 873-896.
• 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.