Scientific machine learning

I’m interested in developing scientific machine-learning (SciML) methods for forward and inverse problems in computational physics, particularly problems involving heterogeneous spatio-temporal parametric variability, high-dimensional parameter representations, and parametric uncertainty. Specific areas of interest include:

• Data-driven surrogate modeling.
• Dimension reduction.
• Physics-informed SciML under uncertainty.
• Uncertainty quantification in SciML.

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.
• Venkatasubramanian, S., & Barajas-Solano, D. A. (2024). Variational Encoder-Decoders for Learning Latent Representations of Physical Systems, arXiv preprint arXiv:2412.05175.
• 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.
• 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.
• 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.