A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales. - Paul J. Atzberger; Peter R. Kramer; Charles S. Peskin (J. Comput. Phys., 2007)

Error analysis of a stochastic immersed boundary method incorporating thermal fluctuations. - Paul J. Atzberger; Peter R. Kramer (Math. Comput. Simul., 2008)

Spatially adaptive stochastic numerical methods for intrinsic fluctuations in reaction-diffusion systems. - Paul J. Atzberger (J. Comput. Phys., 2010)

Stochastic Eulerian Lagrangian methods for fluid-structure interactions with thermal fluctuations. - Paul J. Atzberger (J. Comput. Phys., 2011)

Hybrid continuum-particle method for fluctuating lipid bilayer membranes with diffusing protein inclusions. - Jon Karl Sigurdsson; Frank L. H. Brown; Paul J. Atzberger (J. Comput. Phys., 2013)

A First-Passage Kinetic Monte Carlo method for reaction-drift-diffusion processes. - Ava J. Mauro; Jon Karl Sigurdsson; Justin Shrake; Paul J. Atzberger; Samuel A. Isaacson (J. Comput. Phys., 2014)

Spatially adaptive stochastic methods for fluid-structure interactions subject to thermal fluctuations in domains with complex geometries. - Pat Plunkett; Jonathan J. Hu; Christopher M. Siefert; Paul J. Atzberger (J. Comput. Phys., 2014)

Stochastic Reductions for Inertial Fluid-Structure Interactions Subject to Thermal Fluctuations. - Gil Tabak; Paul J. Atzberger (SIAM J. Appl. Math., 2015)

Simulation of Osmotic Swelling by the Stochastic Immersed Boundary Method. - Chen-Hung Wu; Thomas G. Fai; Paul J. Atzberger; Charles S. Peskin (SIAM J. Sci. Comput., 2015)

Fluctuating Hydrodynamics Methods for Dynamic Coarse-Grained Implicit-Solvent Simulations in LAMMPS. - Y. Wang; Jon Karl Sigurdsson; Paul J. Atzberger (SIAM J. Sci. Comput., 2016)

Importance of the Mathematical Foundations of Machine Learning Methods for Scientific and Engineering Applications. - Paul J. Atzberger (CoRR, 2018)

Hydrodynamic flows on curved surfaces: Spectral numerical methods for radial manifold shapes. - Ben J. Gross; Paul J. Atzberger (J. Comput. Phys., 2018)

Spectral Numerical Exterior Calculus Methods for Differential Equations on Radial Manifolds. - Ben J. Gross; Paul J. Atzberger (J. Sci. Comput., 2018)

GMLS-Nets: A framework for learning from unstructured data. - Nathaniel Trask; Ravi G. Patel; Ben J. Gross; Paul J. Atzberger (CoRR, 2019)

GMLS-Nets: A Machine Learning Framework for Unstructured Data. - Nathaniel Trask; Ravi G. Patel; Paul J. Atzberger; Ben J. Gross (AAAI Spring Symposium: MLPS, 2020)

Variational Autoencoders for Learning Nonlinear Dynamics of Physical Systems. - Ryan Lopez; Paul J. Atzberger (CoRR, 2020)

Meshfree methods on manifolds for hydrodynamic flows on curved surfaces: A Generalized Moving Least-Squares (GMLS) approach. - Ben J. Gross; Nathaniel Trask; Paul Kuberry; Paul J. Atzberger (J. Comput. Phys., 2020)

Variational Autoencoders for Learning Nonlinear Dynamics of PDEs and Reductions. - Ryan Lopez; Paul J. Atzberger (AAAI Spring Symposium: MLPS, 2021)

MLMOD Package: Machine Learning Methods for Data-Driven Modeling in LAMMPS. - Paul J. Atzberger (CoRR, 2021)

Drift-Diffusion Dynamics and Phase Separation in Curved Cell Membranes and Dendritic Spines: Hybrid Discrete-Continuum Methods. - Patrick D. Tran; Thomas A. Blanpied; Paul J. Atzberger (CoRR, 2021)

Magnus Exponential Integrators for Stiff Time-Varying Stochastic Systems. - Dev Jasuja; Paul J. Atzberger (CoRR, 2022)

Incorporating Shear into Stochastic Eulerian Lagrangian Methods for Rheological Studies of Complex Fluids and Soft Materials. - Paul J. Atzberger (CoRR, 2022)

First-passage time statistics on surfaces of general shape: Surface PDE solvers using Generalized Moving Least Squares (GMLS). - Ben J. Gross; Paul Kuberry; Paul J. Atzberger (J. Comput. Phys., 2022)

Surface fluctuating hydrodynamics methods for the drift-diffusion dynamics of particles and microstructures within curved fluid interfaces. - David A. Rower; Misha Padidar; Paul J. Atzberger (J. Comput. Phys., 2022)

SDYN-GANs: Adversarial Learning Methods for Multistep Generative Models for General Order Stochastic Dynamics. - Panos Stinis; Constantinos Daskalakis; Paul J. Atzberger (CoRR, 2023)

Coarse-grained methods for heterogeneous vesicles with phase-separated domains: Elastic mechanics of shape fluctuations, plate compression, and channel insertion. - David A. Rower; Paul J. Atzberger (Math. Comput. Simul., 2023)

MLMOD: Machine Learning Methods for Data-Driven Modeling in LAMMPS. - Paul J. Atzberger (J. Open Source Softw., 2023)

Geometric Neural Operators (GNPs) for Data-Driven Deep Learning of Non-Euclidean Operators. - Blaine Quackenbush; Paul J. Atzberger (CoRR, 2024)

Sparse L1-Autoencoders for Scientific Data Compression. - Matthias Chung; Rick Archibald; Paul J. Atzberger; Jack Michael Solomon (CoRR, 2024)

SDYN-GANs: Adversarial learning methods for multistep generative models for general order stochastic dynamics. - Panos Stinis; C. Daskalakis; Paul J. Atzberger (J. Comput. Phys., 2024)

Geometric neural operators (gnps) for data-driven deep learning in non-euclidean settings. - Blaine Quackenbush; Paul J. Atzberger (Mach. Learn. Sci. Technol., 2024)

GD-VAEs: Geometric dynamic variational autoencoders for learning nonlinear dynamics and dimension reductions. - Ryan Lopez; Paul J. Atzberger (J. Comput. Phys., 2025)

Transferable Foundation Models for Geometric Tasks on Point Cloud Representations: Geometric Neural Operators. - Blaine Quackenbush; Paul J. Atzberger (CoRR, 2025)