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Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior

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arXiv 2023年

作者： Beckers, Thomas Seidman, Jacob Perdikaris, Paris Pappas, George J. Department of Electrical and Systems Engineering University of Pennsylvania PhiladelphiaPA19104 United States graduate program in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania PhiladelphiaPA19104 United States

Data-driven approaches achieve remarkable results for the modeling of complex dynamics based on collected data. However, these models often neglect basic physical principles which determine the behavior of any real-world system. This omission is unfavorable in two ways: The models are not as data-efficient as they could be by incorporating physical prior knowledge, and the model itself might not be physically correct. We propose Gaussian Process Port-Hamiltonian systems (GP-PHS) as a physics-informed Bayesian learning approach with uncertainty quantification. The Bayesian nature of GP-PHS uses collected data to form a distribution over all possible Hamiltonians instead of a single point estimate. Due to the underlying physics model, a GP-PHS generates passive systems with respect to designated inputs and outputs. Further, the proposed approach preserves the compositional nature of Port-Hamiltonian systems. © 2023, CC BY-NC-ND.

关键词： Hamiltonians

Unbiased Parameter Estimation for Bayesian Inverse Problems

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arXiv 2025年

作者： Chada, Neil K. Jasra, Ajay Maama, Mohamed Tempone, Raul Department of Mathematics City University of Hong Kong China School of Data Science The Chinese University of Hong Kong Shenzhen CN Shenzhen China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a solution of a differential equation and, even if exact solutions are available, an analytical intractability of the marginal likelihood and its associated gradient, which is used for parameter estimation. The focus of this article is to deliver unbiased estimates of the unknown parameters, that is, stochastic estimators that, in expectation, are equal to the maximizer of the marginal likelihood, and possess no numerical approximation error. Based upon the ideas of [4] we develop a new approach for unbiased parameter estimation for Bayesian inverse problems. We prove unbiasedness and establish numerically that the associated estimation procedure is faster than the current state-of-the-art methodology for this problem. We demonstrate the performance of our methodology on a range of problems which include a PDE and ODE. Copyright © 2025, The Authors. All rights reserved.

关键词： Markov processes

NOMAD: Nonlinear Manifold Decoders for Operator Learning

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arXiv 2022年

作者： Seidman, Jacob H. Kissas, Georgios Perdikaris, Paris Pappas, George J. Graduate Program in Applied Mathematics and Computational Science University of Pennsylvania United States Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania United States Department of Electrical and Systems Engineering University of Pennsylvania United States

Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps (operators) between infinite dimensional function spaces, these models are able to learn discretization invariant representations of target functions. A common approach is to represent such target functions as linear combinations of basis elements learned from data. However, there are simple scenarios where, even though the target functions form a low dimensional submanifold, a very large number of basis elements is needed for an accurate linear representation. Here we present NOMAD, a novel operator learning framework with a nonlinear decoder map capable of learning finite dimensional representations of nonlinear submanifolds in function spaces. We show this method is able to accurately learn low dimensional representations of solution manifolds to partial differential equations while outperforming linear models of larger size. Additionally, we compare to state-of-the-art operator learning methods on a complex fluid dynamics benchmark and achieve competitive performance with a significantly smaller model size and training cost. © 2022, CC BY-NC-SA.

关键词： Benchmarking

Unbiased Approximations for Stationary Distributions of McKean-Vlasov SDEs

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arXiv 2024年

作者： Awadelkarim, Elsiddig Chada, Neil K. Jasra, Ajay Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Mathematics City University of Hong Kong Hong Kong School of Data Science The Chinese University of Hong Kong Shenzhen Shenzhen China

We consider the development of unbiased estimators, to approximate the stationary distribution of Mckean-Vlasov stochastic differential equations (MVSDEs). These are an important class of processes, which frequently appear in applications such as mathematical finance, biology and opinion dynamics. Typically the stationary distribution is unknown and indeed one cannot simulate such processes exactly. As a result one commonly requires a time-discretization scheme which results in a discretization bias and a bias from not being able to simulate the associated stationary distribution. To overcome this bias, we present a new unbiased estimator taking motivation from the literature on unbiased Monte Carlo. We prove the unbiasedness of our estimator, under assumptions. In order to prove this we require developing ergodicity results of various discrete time processes, through an appropriate discretization scheme, towards the invariant measure. Numerous numerical experiments are provided, on a range of MVSDEs, to demonstrate the effectiveness of our unbiased estimator. Such examples include the Currie-Weiss model, a 3D neuroscience model and a parameter estimation problem. © 2024, CC BY-NC-SA.

关键词： Stochastic systems

Global and Local Reduced Models for Interacting, Heterogeneous Agents

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Global and Local Reduced Models for Interacting, Heterogeneo...

2021 AIChE Annual Meeting

作者： Thiem, Thomas N. Kemeth, Felix P. Bertalan, Tom Laing, Carlo R. Kevrekidis, Ioannis G. Department of Chemical and Biological Engineering Princeton University United States Department of Chemical and Biomolecular Engineering Whiting School of Engineering Johns Hopkins University United States Department of Mechanical Engineering Massachusetts Institute of Technology United States School of Natural and Computational Sciences Massey University New Zealand Department of Applied Mathematics and Statistics Johns Hopkins University United States

ISBN: (纸本)9781713852834

Large collections of coupled, heterogeneous agents can manifest complex dynamical behavior presenting difficulties for simulation and analysis. However, if the collective dynamics lie on a low-dimensional manifold then the original agent-based model may be approximated with a simplified surrogate model on and near the low-dimensional space where the dynamics live. Analytically identifying such simplified models can be challenging or impossible, but here we present a data-driven coarse-graining methodology for discovering such reduced models. We consider two types of reduced models: globally-based models which use global information and predict dynamics using information from the whole ensemble, and locally-based models that use local information, that is, information from just a subset of agents close (close in heterogeneity space, not physical space) to an agent, to predict the dynamics of an agent. For both approaches we are able to learn laws governing the behavior of the reduced system on the low-dimensional manifold directly from time series of states from the agent-based system. These laws take the form of either a system of ordinary differential equations (ODEs), for the globally-based approach, or a partial differential equation (PDE) in the locally-based case. For each technique we employ a specialized artificial neural network integrator that has been templated on an Euler time stepper (i.e. a ResNet) to learn the laws of the reduced model. As part of our methodology, we utilize the proper orthogonal decomposition (POD) to identify the low-dimensional space of the dynamics. Our globally-based technique uses the resulting POD basis to define a set of coordinates for the agent states in this space, and then seeks to learn the time evolution of these coordinates as a system of ODEs. For the locally-based technique, we propose a methodology for learning a partial differential equation representation of the agents;the PDE law depends on the state variables and

关键词： Dynamics

Velocity-gauge Real-time Time-dependent Density Functional Tight-binding for Large-scale Condensed Matter Systems

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arXiv 2023年

作者： Xu, Qiang Del Ben, Mauro Okyay, Mahmut Sait Choi, Min Ibrahim, Khaled Z. Wong, Bryan M. Materials Science & Engineering Program Department of Chemistry Department of Physics & Astronomy University of California-Riverside RiversideCA92521 United States Applied Mathematics & Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States

We present a new velocity-gauge real-time, time-dependent density functional tight-binding (VG-rtTDDFTB) implementation in the open-source DFTB+ software package (https://***) for probing electronic excitations in large, condensed matter systems. Our VG-rtTDDFTB approach enables real-time electron dynamics simulations of large, periodic, condensed matter systems containing thousands of atoms with a favorable computational scaling as a function of system size. We provide computational details and benchmark calculations to demonstrate its accuracy and computational parallelizability on a variety of large material systems. As a representative example, we calculate laser-induced electron dynamics in a 512-atom amorphous silicon supercell to highlight the large periodic systems that can be examined with our implementation. Taken together, our VG-rtTDDFTB approach enables new electron dynamics simulations of complex systems that require large periodic supercells, such as crystal defects, complex surfaces, nanowires, and amorphous materials. Copyright © 2023, The Authors. All rights reserved.

关键词： Gages

Diverse Manifestations of Electron-Phonon Coupling in a Kagome Superconductor

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Physical Review Letters 2025年第10期134卷 106401-106401页

作者： Jing-Yang You Chih-En Hsu Mauro Del Ben Zhenglu Li Mork Family Department of Chemical Engineering and Materials Science University of Southern California Los Angeles California 90089 USA Department of Physics National University of Singapore 2 Science Drive 3 Singapore 117551 Singapore Department of Physics Tamkang University Tamsui New Taipei 251301 Taiwan Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA

Recent angle-resolved photoemission spectroscopy (ARPES) experiments on the kagome metal CsV3Sb5 revealed distinct multimodal dispersion kinks and nodeless superconducting gaps across multiple electron bands. The prominent photoemission kinks suggest a definitive coupling between electrons and certain collective modes, yet the precise nature of this interaction and its connection to superconductivity remain to be established. Here, employing the state-of-the-art ab initio many-body perturbation theory computation, we present direct evidence that electron-phonon (e-ph) coupling induces the multimodal photoemission kinks in CsV3Sb5, and profoundly, drives the nodeless s-wave superconductivity, showcasing the diverse manifestations of the e-ph coupling. Our calculations well capture the experimentally measured kinks and their fine structures, and reveal that vibrations from different atomic species dictate the multimodal behavior. Results from anisotropic GW-Eliashberg equations predict a phonon-mediated superconductivity with nodeless s-wave gaps, in excellent agreement with various ARPES and scanning tunneling spectroscopy measurements. Despite the universal origin of the e-ph coupling, the contributions of several characteristic phonon vibrations vary in different phenomena, highlighting a versatile role of e-ph coupling in shaping the low-energy excitations of kagome metals.

关键词： Shear waves

Imaging atomic-scale chemistry from fused multi-modal electron microscopy

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npj computational Materials 2022年第1期8卷 164-171页

作者： Jonathan Schwartz Zichao Wendy Di Yi Jiang Alyssa J.Fielitz Don-Hyung Ha Sanjaya D.Perera Ismail El Baggari Richard D.Robinson Jeffrey A.Fessler Colin Ophus Steve Rozeveld Robert Hovden Department of Materials Science and Engineering University of MichiganAnn ArborMIUSA Mathematics and Computer Science Division Argonne National LaboratoryLemontILUSA Advanced Photon Source Facility Argonne National LaboratoryLemontILUSA Dow Chemical Co. MidlandMIUSA Department of Material Science and Engineering Cornell UniversityIthacaNew YorkUSA School of Integrative Engineering Chung-Ang UniversitySeoulRepublic of Korea Department of Physics Cornell UniversityIthacaNYUSA The Rowland Institute at Harvard CambridgeMAUSA Department of Electrical Engineering and Computer Science University of MichiganAnn ArborMIUSA National Center for Electron Microscopy Lawrence Berkeley National LaboratoryMolecular FoundryBerkeleyCAUSA Applied Physics Program University of MIchiganAnn ArborMIUnited States

Efforts to map atomic-scale chemistry at low doses with minimal noise using electron microscopes are fundamentally limited by inelastic ***,fused multi-modal electron microscopy offers high signal-to-noise ratio(SNR)recovery of material chemistry at nano-and atomic-resolution by coupling correlated information encoded within both elastic scattering(high-angle annular dark-field(HAADF))and inelastic spectroscopic signals(electron energy loss(EELS)or energy-dispersive x-ray(EDX)).By linking these simultaneously acquired signals,or modalities,the chemical distribution within nanomaterials can be imaged at significantly lower doses with existing detector *** many cases,the dose requirements can be reduced by over one order of *** high SNR recovery of chemistry is tested against simulated and experimental atomic resolution data of heterogeneous nanomaterials.

关键词： materials chemistry fused

Transient rod-climbing in an Oldroyd-B fluid

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arXiv 2025年

作者： Ruangkriengsin, Tachin Brandão, Rodolfo Wu, Katie Hwang, Jonghyun Boyko, Evgeniy Stone, Howard A. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States School of Mathematics University of Bristol Fry Building Woodland Road BristolBS8 1UG United Kingdom Department of Mechanical and Aerospace Engineering Princeton University PrincetonNJ08544 United States Faculty of Mechanical Engineering Technion – Israel Institute of Technology Haifa3200003 Israel

The Weissenberg effect, or rod-climbing phenomenon, occurs in non-Newtonian fluids where the fluid interface ascends along a rotating rod. Despite its prominence, theoretical insights into this phenomenon remain limited. In earlier work, Joseph & Fosdick (Arch. Rat. Mech. Anal., vol. 49, 1973, pp. 321–380) employed domain perturbation methods for second-order fluids to determine the equilibrium interface height by expanding solutions based on the rotation speed. In this work, we investigate the time-dependent interface height through asymptotic analysis with dimensionless variables and equations using the Oldroyd-B model. We begin by neglecting surface tension and inertia to focus on the interaction between gravity and viscoelasticity. In the small-deformation scenario, the governing equations indicate the presence of a boundary layer in time, where the interface rises rapidly over a short time scale before gradually approaching a steady state. By employing a stretched time variable, we derive the transient velocity field and corresponding interface profile on this short time scale and recover the steady-state profile on a longer time scale. Subsequently, we reintroduce small but finite inertial effects to investigate their interplay with viscoelasticity and propose a criterion for determining the conditions under which rod-climbing occurs. © 2025, CC BY.

关键词： Non Newtonian liquids