Paul J. Atzberger | Research Group
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Publications

  1. SDYN-GANs: Adversarial Learning Methods for Multistep Generative Models for General Order Stochastic Dynamics, P. Stinis, C. Daskalakis, and P. J. Atzberger, Journal of Computational Physics, Vol. 519, 113442, (2024), [preprint] [arXiv] [full paper].

  2. Geometric Neural Operators (GNPs) for Data-Driven Deep Learning in Non-Euclidean Settings, B. Quackenbush and P. J. Atzberger, (accepted), (2024), [preprint] [arXiv] [full paper].

  3. Sparse L1-Autoencoders for Scientific Data Compression, M. Chung, R. Archibald, P. J. Atzberger, J. M. Solomon, (preprint), (2024), [preprint] [arXiv].

  4. Simulation of Stochastic Non-Equilibrium Thermal Effects of Particle Inclusions within Fluid Interfaces and Membranes, D. Jasuja and P. J. Atzberger, (2024), (preprint), [preprint] [arXiv].

  5. GD-VAEs: Geometric Dynamic Variational Autoencoders for Learning Nonlinear Dynamics and Dimension Reductions, R. Lopez and P. J. Atzberger, (preprint), (2022), [preprint] [graphical abstract] [arXiv] [software].

  6. MLMOD Package: Machine Learning Methods for Data-Driven Modeling in LAMMPS, P. J. Atzberger, Journal of Open Source Software (JOSS), 8(89), 5620, (2023), [preprint] [arXiv] [full paper] [software].

  7. Surface Fluctuating Hydrodynamics Methods for the Drift-Diffusion Dynamics of Particles and Microstructures within Curved Fluid Interfaces, D. Rower, M. Padidar, and P. J. Atzberger, Journal of Computational Physics, 455, (2022), [preprint] [arXiv] [graphical abstract] [full paper].

  8. Meshfree Methods on Manifolds for Hydrodynamic Flows on Curved Surfaces: A Generalized Moving Least-Squares (GMLS) Approach, B. J. Gross, N. Trask, P. Kuberry, and P. J. Atzberger, Journal of Computational Physics, Vol. 409, 15 May (2020), [preprint] [arXiv] [graphical abstract] [full paper].

  9. Coarse-Grained Methods for Heterogeneous Vesicles with Phase-Separated Domains: Elastic Mechanics of Shape Fluctuations, Plate Compression, and Channel Insertion, D.A. Rower, P.J. Atzberger, Mathematics and Computers in Simulation, Vol 209, 342-361, (2023), [preprint] [arXiv] [graphical abstract] [full paper].

  10. Protein Drift-Diffusion Dynamics and Phase Separation in Curved Cell Membranes and Dendritic Spines: Hybrid Discrete-Continuum Methods, P. Tran, T. Blanpied, P., and P. J. Atzberger, APS Phys. Rev. E, 106, 044402, (2022), [preprint] [arXiv] [full paper].

  11. Magnus Exponential Integrators for Stiff Time-Varying Stochastic Systems, D. Jasuja and P. J. Atzberger, (preprint), (2022), [preprint] [arXiv].

  12. Variational Autoencoders for Learning Nonlinear Dynamics of Physical Systems, R. Lopez, and P. J. Atzberger, AAAI-MLPS Proceedings (peer-reviewed), (2021), [preprint] [arXiv] [full paper] [graphical abstract].

  13. First-Passage Time Statistics on Surfaces of General Shape: Surface PDE Solvers using Generalized Moving Least Squares (GMLS), B. J. Gross, P. Kuberry, and P. J. Atzberger, 453 ,J. of Comp. Phys., (2022), [preprint] [arXiv] [full paper].

  14. GMLS-Nets: A Framework for Learning from Unstructured Data, N. Trask, R. G. Patel, B. J. Gross, and P. J. Atzberger, AAAI-MLPS Proceedings (peer-reviewed), (2020), [preprint] [arXiv] [full paper][software].

  15. GMLS-Nets: Scientific Machine Learning Methods for Unstructured Data, N. Trask, R. G. Patel, B. J. Gross, and P. J. Atzberger, NeurIPs 2019: Workshop on Machine Learning and the Physical Sciences, (peer-reviewed, four-page limit), (2019), [PDF] [full paper] [software].

  16. Stochastic Discontinuous Galerkin Methods (SDGM) Based on Fluctuation-Dissipation Balance, W. Pazner, N. Trask, P.J. Atzberger, 4, Results in Applied Mathematics, (2019) [preprint] [arXiv] [full paper].

  17. Bayesian Inference over the Stiefel Manifold via the Givens Representation, A. A. Pourzanjani, R. M. Jiang, B. Mitchell, P. J. Atzberger, L. R. Petzold, Bayesian Analysis, 16, 639 - 666, (2021) [preprint], [arXiv] [full paper].

  18. Topological Methods for Polymeric Materials: Characterizing the Relationship Between Polymer Entanglement and Viscoelasticity, E. Panagiotou, K. Millett, and P. J. Atzberger, Polymers, 11(3), 437 (2019) [preprint] [arXiv] [full paper] [graphical abstract].

  19. Importance of the Mathematical Foundations of Machine Learning Methods for Scientific and Engineering Applications, P. J. Atzberger, Paper accepted for presentation at SciML2018 Workshop, (two-page limit), US Department of Energy, January, (2018) [paper] [arXiv].

  20. Hydrodynamic Flows on Curved Surfaces: Spectral Numerical Methods for Radial Manifold Shapes, B. Gross and P.J. Atzberger, Journal of Computational Physics, Volume 371, pp 663-689, (2018) [preprint] [arXiv] [full paper] [graphical abstract].

  21. Spectral Numerical Exterior Calculus Methods for Differential Equations on Radial Manifolds, B. Gross and P.J. Atzberger, Journal of Scientific Computing, 76, pp 145–165, (2018) [preprint] [arXiv] [open share] [full paper] [graphical abstract].

  22. Electrostatics of Colloidal Particles Confined in Nanochannels: Role of Double-Layer Interactions and Ion-Ion Correlations, I.S. Sidhu , A.L. Frischknecht, P.J. Atzberger, ACS Omega 3 (9), 11340-11353, (2018) [preprint] [arXiv] [full paper] [graphical abstract].

  23. Fluctuating Hydrodynamic Methods for Fluid-Structure Interactions in Confined Channel Geometries, Y. Wang, H. Lei, P. Atzberger, Applied Mathematics and Mechanics (Springer), January, Volume 39, Issue 1, pp 125–152, (2018) [preprint] [full paper].

  24. Förster Resonance Energy Transfer: Role of Diffusion of Fluorophore Orientation and Separation in Observed Shifts of FRET Efficiency, B. Wallace, P.J. Atzberger, PLoS ONE 12(5): e0177122, (2017) [preprint] [full paper].

  25. Hydrodynamic Coupling of Particle Inclusions Embedded in Curved Lipid Bilayer Membranes, [featured on journal cover], J.K. Sigurdsson and P.J. Atzberger, 12, 6685-6707, Soft Matter, The Royal Society of Chemistry, (2016) [preprint] [arxiv] [full paper] [cover of journal] [graphical abstract].

  26. Fluctuating Hydrodynamics Methods for Dynamic Coarse-Grained Implicit-Solvent Simulations in LAMMPS, Y. Wang, J. K. Sigurdsson, and P.J. Atzberger, SIAM J. Sci. Comput. , 38(5), S62–S77, (2016) [preprint] [full paper] [software].

  27. Stochastic Reductions for Inertial Fluid-Structure Interactions Subject to Thermal Fluctuations, G. Tabak and P.J. Atzberger, SIAM J. Appl. Math., 75(4), 1884–1914, (2015) [preprint] [arXiv] [full paper].

  28. Simulation of Osmotic Swelling by the Stochastic Immersed Boundary Method, C.H. Wu, T.G. Fai, P.J. Atzberger, and C.S. Peskin, SIAM J. Sci. Comput., 37, (2015). [preprint] [full paper].

  29. Spatially Adaptive Stochastic Methods for Fluid-Structure Interactions Subject to Thermal Fluctuations in Domains with Complex Geometries,P. Plunkett, J. Hu, C. Siefert, P.J. Atzberger, Journal of Computational Physics, Vol. 277, 15 Nov. 2014, pg. 121--137, (2014) [preprint] [arXiv] [full paper].

  30. Shape matters in protein mobility within membranes, F. Quemeneur, J.K. Sigurdsson, M. Renner, P.J. Atzberger, P. Bassereau, and D. Lacoste, Proceedings of the National Academy of Sciences (PNAS), Vol. 11, No. 14, pg. 5083–5087, (2014), [PDF] [full paper].

  31. A First-Passage Kinetic Monte Carlo Method for Reaction-Drift-Diffusion Processes, A. Mauro, J. Shrake. J. Sigurdsson, P. Atzberger, S. Isaacson, J. Comp. Phys., Vol. 259, 15, pg. 536-567, (2014). [preprint arXiv] [full paper]

  32. Fluctuating Hydrodynamic Methods for Fluid-Structure Interactions in Confined Channel Geometries, Y. Wang, P. Atzberger, (technical report), [preprint].

  33. Simulation of Edge Facilitated Adsorption and Critical Concentration Induced Rupture of Vesicles at a Surface [featured on journal cover], P. Plunkett, B. Camley, K. Weirich, J. Israelachvili, P. Atzberger, 9, 8420-8427, Soft Matter, The Royal Society of Chemistry, (2013), [cover of journal] [full paper].

  34. Dynamic Implicit-Solvent Coarse-Grained Models of Lipid Bilayer Membranes : Fluctuating Hydrodynamics Thermostat, Y. Wang, J. K. Sigurdsson, E. Brandt, and P.J. Atzberger, Phys. Rev. E 88, 023301, (2013) [preprint] [full paper]

  35. Incorporating Shear into Stochastic Eulerian Lagrangian Methods for Rheological Studies of Complex Fluids and Soft Materials., P.J. Atzberger, Physica D, Vol. 265, pg. 57–70, (2013) [preprint] [arXiv] [full paper]

  36. Hybrid Continuum-Particle Method for Fluctuating Lipid Bilayer Membranes with Diffusing Protein Inclusions, J.K. Sigurdsson, F.L.H. Brown, and P.J. Atzberger, J. of Comp. Phys., Vol. 252, pg 65–85, (2013). [preprint] [full paper]

  37. Force Spectroscopy of Complex Biopolymers with Heterogeneous Elasticity, D. Valdman, B. Lopez, M. T. Valentine, and P.J. Atzberger, Soft Matter, The Royal Society of Chemistry, (2013). [preprint] [full paper]

  38. (Software) MANGO-SELM package for fluctuating hydrodynamics based simulations in LAMMPS. (2012). [software]

  39. Spectral Analysis Methods for the Robust Measurement of the Flexural Rigidity of Biopolymers, D. Valdman, P.J. Atzberger, D. Yu, and M. T. Valentine, Bio. Phys. J., Vol. 102, Iss. 5, pg. 1144-–1153, (2012). [preprint] [full paper]

  40. Influence of Target Concentration and Background Binding on In Vitro Selection of Affinity Reagents, J. Wang, J. F. Rudzinski, Q. H. Gonga, H.T. Soh, P.J. Atzberger, PLoS ONE 7(8), (2012), [preprint] [full paper]

  41. Stochastic Eulerian Lagrangian Methods for Fluid Structure Interactions with Thermal Fluctuations, P.J. Atzberger, J. of Comp. Phys., 230, pp. 2821--2837, (2011). [preprint] [arXiv] [full paper]

  42. Stochastic Reduction Method for Biological Chemical Kinetics using Time-Scale Separation, C.D. Pahlajani, M. Khammash, P.J. Atzberger, J. of Theor. Bio. Vol. 272, Iss. 1, 7 March, Pages 96-112, (2011). [preprint] [full paper]

  43. Experimental Study of the Separation Behavior of Nanoparticles in Micro- and Nano-Channels, M. Napoli, P.J. Atzberger, S. Pennathur, J. Microfluidics and Nanofluidics, Volume 10, Issue 1, Page 69, (2011). [preprint] [full paper]

  44. Spatially Adaptive Stochastic Numerical Methods for Intrinsic Fluctuations in Reaction-Diffusion Systems, P.J. Atzberger, J. Comp. Phys., Vol. 229, Iss. 9, 1 May, pp. 3474-3501, (2010). [preprint] [full paper]

  45. Simulation of Complex Fluids and Soft Materials using Stochastic Eulerian Lagrangian Methods with Shear Boundary Conditions, P.J. Atzberger, (2009), (technical report). [preprint arXiv] [preprint]

  46. Spatially Adaptive Stochastic Multigrid Methods for Fluid-Structure Systems with Thermal Fluctuations, P. J. Atzberger, (technical report), (2010). [technical report PDF] [arXiv]

  47. Hybrid Elastic and Discrete-Particle Approach to Biomembrane Dynamics with Application to the Mobility of Curved Integral Membrane Proteins, , A. Naji, P.J. Atzberger and F.L.H. Brown, Phys. Rev. Lett. 102, 138102, (2009). [preprint] [full paper]

  48. A Microfluidic Pumping Mechanism Driven by Non-equilibrium Osmotic Effects, P.J. Atzberger, S.A. Isaacson, and C.S. Peskin, Physica D: Nonlinear Phenomena, Vol. 238, Iss. 14, July, pp. 1168-1179, (2009),[preprint] [full paper]

  49. Micromagnetic Selection of Aptamers in Microfluidic Channels, X. Lou, J. Qian, X. Yi, L. Viel, A.E. Gerdon, E.T. Lagally, P.J. Atzberger, A.J. Heeger, and H.T. Soh, PNAS, Vol. 106 No. 9 pp. 2989-2994, (2009), [preprint] [full paper]

  50. Analysis of Selection Approaches for Aptamer Molecular Libraries, J. Rudzinski, T. Soh, P.J. Atzberger, Technical Report, (2009), [technical report PDF]

  51. On the Foundations of the Stochastic Immersed Boundary Method, P.R. Kramer, C.S. Peskin, and P.J. Atzberger, Comp. Meth. in Appl. Mech. and Eng., Vol. 197, Iss. 25-28, 15 April, pp. 2232-2249, (2008). [preprint] [full paper]

  52. Error Analysis of a Stochastic Immersed Boundary Method Incorporating Thermal Fluctuations, P.J. Atzberger and P.R. Kramer, Mathematics and Computers in Simulation, Vol. 79, Iss. 3, pg. 379 -- 408, (2008). [preprint] [full paper]

  53. A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales, P.J. Atzberger, P.R. Kramer, and C.S. Peskin, J. Comp. Phys., Vol. 224, Iss. 2, (2007). [preprint] [full paper]

  54. Stochastic Immersed Boundary Method Incorporating Thermal Fluctuations (brief introduction), P.J. Atzberger, P.R. Kramer, and C.S. Peskin, (proceedings of ICIAM 2007). [preprint] [full paper]

  55. Theoretical Framework for Microscopic Osmotic Phenomena, P.J. Atzberger and P.R. Kramer, APS Phys. Rev. E, 75, 1, (2007). [preprint] [full paper]

  56. A Note on the Correspondence of the Immersed Boundary Method with Thermal Fluctuations To Stokesian-Brownian Dynamics, P.J. Atzberger, Physica D, Vol. 226, Iss. 2, 15, pg. 144-150, (2007). [preprint] [full paper]

  57. Velocity Correlations of a Thermally Fluctuating Brownian Particle: A Novel Model of the Hydrodynamic Coupling, P.J. Atzberger, Phys. Lett. A, Vol. 351, Iss. 4-5, 6, March, pp. 225-230, (2006). [preprint] [full paper]

  58. A Brownian Dynamics Model of Kinesin in Three Dimensions Incorporating the Force-Extension Profile of the Coiled-Coil Cargo Tether, P.J. Atzberger and C.S. Peskin, Bull. Math. Biol., vol. 68, no. 1, pp. 131-160, (2006). [preprint] [full paper]

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*This material is based upon work supported by the National Science Foundation under Grant No. NSF DMS-0635535 and NSF CAREER DMS-0956210. Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).


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