Simulations of reactive transport and precipitation with smoothed particle hydrodynamics. - Alexandre M. Tartakovsky; Paul Meakin; Timothy D. Scheibe; Rogene M. Eichler West (J. Comput. Phys., 2007)

Hybrid Simulations of Reaction-Diffusion Systems in Porous Media. - Alexandre M. Tartakovsky; Daniel M. Tartakovsky; Timothy D. Scheibe; Paul Meakin (SIAM J. Sci. Comput., 2008)

Lagrangian particle model for multiphase flows. - Alexandre M. Tartakovsky; Kim F. Ferris; Paul Meakin (Comput. Phys. Commun., 2009)

A novel method for modeling Neumann and Robin boundary conditions in smoothed particle hydrodynamics. - Emily M. Ryan; Alexandre M. Tartakovsky; Cristina H. Amon (Comput. Phys. Commun., 2010)

A Component-Based Framework for Smoothed Particle Hydrodynamics Simulations of Reactive Fluid Flow in Porous Media. - Bruce J. Palmer; Vidhya Gurumoorthi; Alexandre M. Tartakovsky; Timothy D. Scheibe (Int. J. High Perform. Comput. Appl., 2010)

Uncertainty quantification via random domain decomposition and probabilistic collocation on sparse grids. - Guang Lin 001; Alexandre M. Tartakovsky; Daniel M. Tartakovsky (J. Comput. Phys., 2010)

Numerical Studies of Three-dimensional Stochastic Darcy's Equation and Stochastic Advection-Diffusion-Dispersion Equation. - Guang Lin 001; Alexandre M. Tartakovsky (J. Sci. Comput., 2010)

Dimension reduction method for ODE fluid models. - Alexandre M. Tartakovsky; Alexander Panchenko; Kim F. Ferris (J. Comput. Phys., 2011)

Smoothed particle hydrodynamics non-Newtonian model for ice-sheet and ice-shelf dynamics. - Wenxiao Pan; Alexandre M. Tartakovsky; Joe J. Monaghan (J. Comput. Phys., 2013)

Exact PDF equations and closure approximations for advective-reactive transport. - Daniele Venturi 002; Daniel M. Tartakovsky; Alexandre M. Tartakovsky; George E. Karniadakis (J. Comput. Phys., 2013)

A Comparison of Closures for Stochastic Advection-Diffusion Equations. - K. D. Jarman Jr.; Alexandre M. Tartakovsky (SIAM/ASA J. Uncertain. Quantification, 2013)

CDF Solutions of Buckley-Leverett Equation with Uncertain Parameters. - Peng Wang 022; Daniel M. Tartakovsky; K. D. Jarman Jr.; Alexandre M. Tartakovsky (Multiscale Model. Simul., 2013)

Smoothed particle hydrodynamics continuous boundary force method for Navier-Stokes equations subject to a Robin boundary condition. - Wenxiao Pan; Jie Bao; Alexandre M. Tartakovsky (J. Comput. Phys., 2014)

Discrete Models of Fluids: Spatial Averaging, Closure, and Model Reduction. - Alexander Panchenko; Alexandre M. Tartakovsky; Kevin Cooper (SIAM J. Appl. Math., 2014)

Erratum: A Comparison of Closures for Stochastic Advection-Diffusion Equations. - K. D. Jarman Jr.; Alexandre M. Tartakovsky (SIAM/ASA J. Uncertain. Quantification, 2015)

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)

Pairwise Force Smoothed Particle Hydrodynamics model for multiphase flow: Surface tension and contact line dynamics. - Alexandre M. Tartakovsky; Alexander Panchenko (J. Comput. Phys., 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)

Solving differential equations with unknown constitutive relations as recurrent neural networks. - Tobias Hagge; Panos Stinis; Enoch Yeung; Alexandre M. Tartakovsky (CoRR, 2017)

Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics. - Wenxiao Pan; Kyungjoo Kim; Mauro Perego; Alexandre M. Tartakovsky; Michael L. Parks (J. Comput. Phys., 2017)

Basis adaptation and domain decomposition for steady-state partial differential equations with random coefficients. - Ramakrishna Tipireddy; Panos Stinis; Alexandre M. Tartakovsky (J. Comput. Phys., 2017)

Physics-Informed Kriging: A Physics-Informed Gaussian Process Regression Method for Data-Model Convergence. - Xiu Yang; Guzel Tartakovsky; Alexandre M. Tartakovsky (CoRR, 2018)

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)

Stochastic Basis Adaptation and Spatial Domain Decomposition for Partial Differential Equations with Random Coefficients. - Ramakrishna Tipireddy; Panos Stinis; Alexandre M. Tartakovsky (SIAM/ASA J. Uncertain. Quantification, 2018)

Sliced-Inverse-Regression-Aided Rotated Compressive Sensing Method for Uncertainty Quantification. - Xiu Yang; Weixuan Li; Alexandre M. Tartakovsky (SIAM/ASA J. Uncertain. Quantification, 2018)

Physics-informed Machine Learning Method for Forecasting and Uncertainty Quantification of Partially Observed and Unobserved States in Power Grids. - Alexandre M. Tartakovsky; Ramakrishna Tipireddy (HICSS, 2019)

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)

Engineering structural robustness in power grid networks susceptible to community desynchronization. - Daniel Dylewsky; Xiu Yang; Alexandre M. Tartakovsky; J. Nathan Kutz (Appl. Netw. Sci., 2019)

A comparative study of physics-informed neural network models for learning unknown dynamics and constitutive relations. - Ramakrishna Tipireddy; Paris Perdikaris; Panos Stinis; Alexandre M. Tartakovsky (CoRR, 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)

Enforcing constraints for interpolation and extrapolation in Generative Adversarial Networks. - Panos Stinis; Tobias Hagge; Alexandre M. Tartakovsky; Enoch Yeung (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)

CRNT4SBML: a Python package for the detection of bistability in biochemical reaction networks. - Brandon Reyes; Irene Otero-Muras; Michael T. Shuen; Alexandre M. Tartakovsky; Vladislav A. Petyuk (Bioinform., 2020)

Inverse Modeling of Viscoelasticity Materials using Physics Constrained Learning. - Kailai Xu; Alexandre M. Tartakovsky; Jeff Burghardt; Eric Darve (CoRR, 2020)

Learning Unknown Physics of non-Newtonian Fluids. - Brandon Reyes; Amanda A. Howard; Paris Perdikaris; Alexandre M. Tartakovsky (CoRR, 2020)

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)

An efficient epistemic uncertainty quantification algorithm for a class of stochastic models: A post-processing and domain decomposition framework. - Mahadevan Ganesh; Stuart C. Hawkins; Alexandre M. Tartakovsky; Ramakrishna Tipireddy (CoRR, 2020)

Learning Coarse-Grained Potentials for Binary Fluids. - Peiyuan Gao; Xiu Yang; Alexandre M. Tartakovsky (J. Chem. Inf. Model., 2020)

Non-local model for surface tension in fluid-fluid simulations. - Amanda A. Howard; Alexandre M. Tartakovsky (J. Comput. Phys., 2020)

Gaussian process regression and conditional polynomial chaos for parameter estimation. - Jing Li; Alexandre M. Tartakovsky (J. Comput. Phys., 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)

Time-dependent stochastic basis adaptation for uncertainty quantification. - Ramakrishna Tipireddy; Panos Stinis; Alexandre M. Tartakovsky (CoRR, 2021)

Physics-informed CoKriging model of a redox flow battery. - Amanda A. Howard; Alexandre M. Tartakovsky (CoRR, 2021)

Physics-constrained deep neural network method for estimating parameters in a redox flow battery. - QiZhi He; Panos Stinis; Alexandre M. Tartakovsky (CoRR, 2021)

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

A conservative level set method for N-phase flows with a free-energy-based surface tension model. - Amanda A. Howard; Alexandre M. Tartakovsky (J. Comput. Phys., 2021)

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

Physics Information Aided Kriging using Stochastic Simulation Models. - Xiu Yang; Guzel Tartakovsky; Alexandre M. Tartakovsky (SIAM J. Sci. Comput., 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)

Machine Learning in Heterogeneous Porous Materials. - Marta D'Elia; Hang Deng; Cedric G. Fraces; Krishna C. Garikipati; Lori Graham-Brady; Amanda A. Howard; George Em Karniadakis; Vahid Keshavarzzadeh; Robert M. Kirby; J. Nathan Kutz; Chunhui Li; Xing Liu; et al. (CoRR, 2022)

Enhanced physics-constrained deep neural networks for modeling vanadium redox flow battery. - QiZhi He; Yucheng Fu; Panos Stinis; Alexandre M. Tartakovsky (CoRR, 2022)

Physics-Informed Neural Network Method for Parabolic Differential Equations with Sharply Perturbed Initial Conditions. - Yifei Zong; QiZhi He; Alexandre M. Tartakovsky (CoRR, 2022)

Physics-informed Karhunen-Loéve and neural network approximations for solving inverse differential equation problems. - Jing Li; Alexandre M. Tartakovsky (J. Comput. Phys., 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)

Total Uncertainty Quantification in Inverse PDE Solutions Obtained with Reduced-Order Deep Learning Surrogate Models. - Yuanzhe Wang; 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)

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)

Physics-informed machine learning method with space-time Karhunen-Loève expansions for forward and inverse partial differential equations. - Alexandre M. Tartakovsky; Yifei Zong (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)

Mathematics of Digital Twins and Transfer Learning for PDE Models. - Yifei Zong; Alexandre M. Tartakovsky (CoRR, 2025)