An Ensemble-Proper Orthogonal Decomposition Method for the Nonstationary Navier-Stokes Equations. - Max D. Gunzburger; Nan Jiang 003; Michael Schneier (SIAM J. Numer. Anal., 2017)

Diagnostics for Eddy Viscosity Models of Turbulence Including Data-Driven/Neural Network Based Parameterizations. - William J. Layton; Michael Schneier (CoRR, 2019)

An Improved Discrete Least-Squares/Reduced-Basis Method for Parameterized Elliptic PDEs. - Max D. Gunzburger; Michael Schneier; Clayton G. Webster; Guannan Zhang (J. Sci. Comput., 2019)

An Evolve-Filter-Relax Stabilized Reduced Order Stochastic Collocation Method for the Time-Dependent Navier-Stokes Equations. - Max D. Gunzburger; Traian Iliescu; Muhammad Mohebujjaman; Michael Schneier (SIAM/ASA J. Uncertain. Quantification, 2019)

An embedded variable step IMEX scheme for the incompressible Navier-Stokes equations. - Victor P. DeCaria; Michael Schneier (CoRR, 2020)

An Artificial Compression Reduced Order Model. - Victor P. DeCaria; Traian Iliescu; William J. Layton; Michael McLaughlin; Michael Schneier (SIAM J. Numer. Anal., 2020)

Error Analysis of Supremizer Pressure Recovery for POD based Reduced-Order Models of the Time-Dependent Navier-Stokes Equations. - Kiera Kean; Michael Schneier (SIAM J. Numer. Anal., 2020)

On the Prandtl-Kolmogorov 1-equation model of turbulence. - Kiera Kean; William J. Layton; Michael Schneier (CoRR, 2021)

Clipping over dissipation in turbulence models. - Kiera Kean; William J. Layton; Michael Schneier (CoRR, 2021)

The Scott-Vogelius Method for Stokes Problem on Anisotropic Meshes. - Kiera Kean; Michael Neilan; Michael Schneier (CoRR, 2021)

On Optimal Pointwise in Time Error Bounds and Difference Quotients for the Proper Orthogonal Decomposition. - Birgul Koc; Samuele Rubino; Michael Schneier; John R. Singler; Traian Iliescu (SIAM J. Numer. Anal., 2021)

Latent Neural PDE Solver: a reduced-order modelling framework for partial differential equations. - Zijie Li; Saurabh Patil; Francis Ogoke; Dule Shu; Wilson Zhen; Michael Schneier; John R. Buchanan Jr.; Amir Barati Farimani (CoRR, 2024)

Text2PDE: Latent Diffusion Models for Accessible Physics Simulation. - Anthony Y. Zhou; Zijie Li; Michael Schneier; John R. Buchanan Jr.; Amir Barati Farimani (ICLR, 2025)

Latent neural PDE solver: A reduced-order modeling framework for partial differential equations. - Zijie Li; Saurabh Patil; Francis Ogoke; Dule Shu; Wilson Zhen; Michael Schneier; John R. Buchanan Jr.; Amir Barati Farimani (J. Comput. Phys., 2025)