Zobrazeno 1 - 10
of 84
pro vyhledávání: '"Atzberger, P. J."'
Autor:
Jasuja, Dev, Atzberger, Paul J.
We formulate theoretical modeling approaches and develop practical computational simulation methods for investigating the non-equilibrium statistical mechanics of fluid interfaces with passive and active immersed particles. Our approaches capture phe
Externí odkaz:
http://arxiv.org/abs/2410.01165
We introduce Geometric Neural Operators (GNPs) for accounting for geometric contributions in data-driven deep learning of operators. We show how GNPs can be used (i) to estimate geometric properties, such as the metric and curvatures, (ii) to approxi
Externí odkaz:
http://arxiv.org/abs/2404.10843
We introduce adversarial learning methods for data-driven generative modeling of the dynamics of $n^{th}$-order stochastic systems. Our approach builds on Generative Adversarial Networks (GANs) with generative model classes based on stable $m$-step s
Externí odkaz:
http://arxiv.org/abs/2302.03663
Autor:
Atzberger, Paul J.
Publikováno v:
Physica D, Vol. 265, (2013)
We develop computational methods that incorporate shear into fluctuating hydrodynamics methods. We are motivated by the rheological responses of complex fluids and soft materials. Our approach is based on continuum stochastic hydrodynamic equations t
Externí odkaz:
http://arxiv.org/abs/2212.10651
Autor:
Jasuja, Dev, Atzberger, P. J.
We introduce exponential numerical integration methods for stiff stochastic dynamical systems of the form $d\mathbf{z}_t = L(t)\mathbf{z}_tdt + \mathbf{f}(t)dt + Q(t)d\mathbf{W}_t$. We consider the setting of time-varying operators $L(t), Q(t)$ where
Externí odkaz:
http://arxiv.org/abs/2212.08978
Autor:
Lopez, Ryan, Atzberger, Paul J.
We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. We develop approaches for learning nonlinear state space models of the dynamics for gene
Externí odkaz:
http://arxiv.org/abs/2206.05183
Publikováno v:
APS Phys. Rev. E, 106, 044402, (2022)
We develop methods for investigating protein drift-diffusion dynamics in heterogeneous cell membranes and the roles played by geometry, diffusion, chemical kinetics, and phase separation. Our hybrid stochastic numerical methods combine discrete parti
Externí odkaz:
http://arxiv.org/abs/2110.00725
Autor:
Atzberger, Paul J.
MLMOD is a software package for incorporating machine learning approaches and models into simulations of microscale mechanics and molecular dynamics in LAMMPS. Recent machine learning approaches provide promising data-driven approaches for learning r
Externí odkaz:
http://arxiv.org/abs/2107.14362
Publikováno v:
Journal of Comp. Phys.,453, (2022)
We develop numerical methods for computing statistics of stochastic processes on surfaces of general shape with drift-diffusion dynamics $d\mathbf{X}_t = a(\mathbf{X}_t)dt + \mathbf{b}(\mathbf{X}_t)d\mathbf{W}_t$. We formulate descriptions of Brownia
Externí odkaz:
http://arxiv.org/abs/2102.02421
Autor:
Lopez, Ryan, Atzberger, Paul J.
We develop data-driven methods for incorporating physical information for priors to learn parsimonious representations of nonlinear systems arising from parameterized PDEs and mechanics. Our approach is based on Variational Autoencoders (VAEs) for le
Externí odkaz:
http://arxiv.org/abs/2012.03448