Probabilistic Density Function Method for Stochastic ODEs of Power Systems with Uncertain Power Input. - Peng Wang 022; David A. Barajas-Solano; Emil M. Constantinescu; Shrirang Abhyankar; Debojyoti Ghosh; Barry F. Smith; Zhenyu Huang 001; Alexandre M. Tartakovsky (SIAM/ASA J. Uncertain. Quantification, 2015)

Stochastic Collocation Methods for Nonlinear Parabolic Equations with Random Coefficients. - David A. Barajas-Solano; Daniel M. Tartakovsky (SIAM/ASA J. Uncertain. Quantification, 2016)

Hybrid Multiscale Finite Volume Method for Advection-Diffusion Equations Subject to Heterogeneous Reactive Boundary Conditions. - David A. Barajas-Solano; Alexandre M. Tartakovsky (Multiscale Model. Simul., 2016)

Probability and Cumulative Density Function Methods for the Stochastic Advection-Reaction Equation. - David A. Barajas-Solano; Alexandre M. Tartakovsky (SIAM/ASA J. Uncertain. Quantification, 2018)

Highly-Ccalable, Physics-Informed GANs for Learning Solutions of Stochastic PDEs. - Liu Yang; Prabhat; George E. Karniadakis; Sean Treichler; Thorsten Kurth; Keno Fischer; David A. Barajas-Solano; Joshua Romero; Valentin Churavy; Alexandre M. Tartakovsky; Michael Houston (DLS@SC, 2019)

Electric Load and Power Forecasting Using Ensemble Gaussian Process Regression. - Tong Ma; Renke Huang; David A. Barajas-Solano; Ramakrishna Tipireddy; Alexandre M. Tartakovsky (CoRR, 2019)

Highly-scalable, physics-informed GANs for learning solutions of stochastic PDEs. - Liu Yang; Sean Treichler; Thorsten Kurth; Keno Fischer; David A. Barajas-Solano; Joshua Romero; Valentin Churavy; Alexandre M. Tartakovsky; Michael Houston; Prabhat; George E. Karniadakis (CoRR, 2019)

Physics-Informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transport. - QiZhi He; David Barajas-Solano; Guzel Tartakovsky; Alexandre M. Tartakovsky (CoRR, 2019)

Approximate Bayesian model inversion for PDEs with heterogeneous and state-dependent coefficients. - David A. Barajas-Solano; Alexandre M. Tartakovsky (J. Comput. Phys., 2019)

Physics-informed CoKriging: A Gaussian-process-regression-based multifidelity method for data-model convergence. - Xiu Yang; David A. Barajas-Solano; Guzel Tartakovsky; Alexandre M. Tartakovsky (J. Comput. Phys., 2019)

Dynamic mode decomposition for forecasting and analysis of power grid load data. - Daniel Dylewsky; David Barajas-Solano; Tong Ma; Alexandre M. Tartakovsky; J. Nathan Kutz (CoRR, 2020)

Physics-Informed Gaussian Process Regression for Probabilistic States Estimation and Forecasting in Power Grids. - Tong Ma; David Alonso Barajas-Solano; Ramakrishna Tipireddy; Alexandre M. Tartakovsky (CoRR, 2020)

Conditional Karhunen-Loève expansion for uncertainty quantification and active learning in partial differential equation models. - Ramakrishna Tipireddy; David A. Barajas-Solano; Alexandre M. Tartakovsky (J. Comput. Phys., 2020)

Physics-Informed Machine Learning Method for Large-Scale Data Assimilation Problems. - Yu-Hong Yeung; David A. Barajas-Solano; Alexandre M. Tartakovsky (CoRR, 2021)

Physics-informed machine learning with conditional Karhunen-Loève expansions. - Alexandre M. Tartakovsky; David A. Barajas-Solano; QiZhi He (J. Comput. Phys., 2021)

A Kinetic Monte Carlo Approach for Simulating Cascading Transmission Line Failure. - Jacob Roth; David A. Barajas-Solano; Panos Stinis; Jonathan Weare; Mihai Anitescu (Multiscale Model. Simul., 2021)

Stochastically Forced Ensemble Dynamic Mode Decomposition for Forecasting and Analysis of Near-Periodic Systems. - Daniel Dylewsky; David Barajas-Solano; Tong Ma; Alexandre M. Tartakovsky; J. Nathan Kutz (IEEE Access, 2022)

Online Real-time Learning of Dynamical Systems from Noisy Streaming Data. - Subhrajit Sinha; Sai Pushpak Nandanoori; David Barajas-Solano (CoRR, 2022)

Conditional Korhunen-Loéve regression model with Basis Adaptation for high-dimensional problems: uncertainty quantification and inverse modeling. - Yu-Hong Yeung; Ramakrishna Tipireddy; David A. Barajas-Solano; Alexandre M. Tartakovsky (CoRR, 2023)

Randomized Physics-Informed Neural Networks for Bayesian Data Assimilation. - Yifei Zong; David Barajas-Solano; Alexandre M. Tartakovsky (CoRR, 2024)

Solving High-dimensional Inverse Problems Using Amortized Likelihood-free Inference with Noisy and Incomplete Data. - Jice Zeng; Yuanzhe Wang; Alexandre M. Tartakovsky; David Barajas-Solano (CoRR, 2024)

Variational Encoder-Decoders for Learning Latent Representations of Physical Systems. - Subashree Venkatasubramanian; David A. Barajas-Solano (CoRR, 2024)

Gaussian process regression and conditional Karhunen-Loève models for data assimilation in inverse problems. - Yu-Hong Yeung; David A. Barajas-Solano; Alexandre M. Tartakovsky (J. Comput. Phys., 2024)

Randomized physics-informed machine learning for uncertainty quantification in high-dimensional inverse problems. - Yifei Zong; David Barajas-Solano; Alexandre M. Tartakovsky (J. Comput. Phys., 2024)

Chance constrained load frequency control of power systems with wind resources. - Tong Ma; David Alonso Barajas-Solano; Alexandre M. Tartakovsky (J. Frankl. Inst., 2025)