Stochastic differential and partial differential equations for uncertainty quantification

I’m interested in employing stochastic differential and partial differential equations for modeling physical systems with uncertain drivers and/or parameters. Specific topics include:

• 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 study of large deviations.
• Scientific machine learning and sparse regression-based methods for uncertainty propagation and state estimation in SDEs and SPDEs.

Relevant publications

• Ma, T., Barajas-Solano, D. A., & Tartakovsky, A. M. (2025). Chance Constrained Load Frequency Control of Power Systems with Wind Resources, J. Frankl. Inst., 362(2), 107478.
• Roth, J., Barajas-Solano, D. A., Stinis, P., Weare, J., & Anitescu, M. (2021). A Kinetic Monte Carlo Approach for Simulating Cascading Transmission Line Failure, Multiscale Model. Simul., 19(1), 208–241.
• Tartakovsky, A. M., & Barajas-Solano, D. A. (2020). Explaining Persistent Incomplete Mixing in Multicomponent Reactive Transport with Eulerian Stochastic Model, Adv. Water Resour., 145, 103729.
• 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.
• 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.
• 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. (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.