检索结果-内蒙古大学图书馆

Deuteration removes quantum dipolar defects from KDP crystals

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Yang, Bingjia Xie, Pinchen Car, Roberto Department of Chemistry Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Materials Institute Princeton University PrincetonNJ08544 United States

The structural, dielectric, and thermodynamic properties of the hydrogen-bonded ferroelectric crystal potassium dihydrogen phosphate (KH2PO4), KDP for short, differ significantly from those of DKDP (KD2PO4) [1, 2]. It is well established that deuteration affects the interplay of hydrogen-bond switches and heavy ion displacements that underlie the emergence of macroscopic polarization, but a detailed microscopic model is missing [3, 4]. Here we show that all-atom path integral molecular dynamics simulations can predict the isotope effects, revealing the microscopic mechanism that differentiates KDP and DKDP. Proton tunneling in the hydrogen bonds generates phosphate configurations that do not contribute to the polarization. These dipolar defects are always present in KDP, but disappear at low temperatures in DKDP, which behaves more classically. Quantum disorder confers residual entropy to ferroelectric KDP, explaining its lower spontaneous polarization and transition entropy relative to DKDP. Tunneling should also contribute to the anomalous heat capacity observed in KDP near absolute zero [5, 6]. The prominent role of quantum fluctuations in KDP is related to the unusual strength of the hydrogen bonds in this system and should be equally important in the other crystals of the KDP family, which exhibit similar isotope effects [7]. © 2024, CC BY.

关键词： Hydrogen bonds

Generalization and Memorization: The Bias Potential Model 2

学校读者我要写书评

暂无评论

Generalization and Memorization: The Bias Potential Model

2nd Mathematical and Scientific Machine Learning Conference, MSML 2021

作者： Yang, Hongkang Weinan, E. Program in Applied and Computational Mathematics Princeton University United States Department of Mathematics and PACM Princeton University United States

Models for learning probability distributions such as generative models and density estimators behave quite differently from models for learning functions. One example is found in the memorization phenomenon, namely the ultimate convergence to the empirical distribution, that occurs in generative adversarial networks (GANs). For this reason, the issue of generalization is more subtle than that for supervised learning. For the bias potential model, we show that dimension-independent generalization accuracy is achievable if early stopping is adopted, despite that in the long term, the model either memorizes the samples or diverges. © 2021 H. Yang & W. E.

关键词： Probability distributions

A Mathematical Framework for Learning Probability Distributions

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Yang, Hongkang Program in Applied and Computational Mathematics Princeton University United States

The modeling of probability distributions, specifically generative modeling and density estimation, has become an immensely popular subject in recent years by virtue of its outstanding performance on sophisticated data such as images and texts. Nevertheless, a theoretical understanding of its success is still incomplete. One mystery is the paradox between memorization and generalization: In theory, the model is trained to be exactly the same as the empirical distribution of the finite samples, whereas in practice, the trained model can generate new samples or estimate the likelihood of unseen samples. Likewise, the overwhelming diversity of distribution learning models calls for a unified perspective on this subject. This paper provides a mathematical framework such that all the well-known models can be derived based on simple principles. To demonstrate its efficacy, we present a survey of our results on the approximation error, training error and generalization error of these models, which can all be established based on this framework. In particular, the aforementioned paradox is resolved by proving that these models enjoy implicit regularization during training, so that the generalization error at early-stopping avoids the curse of dimensionality. Furthermore, we provide some new results on landscape analysis and the mode collapse *** Codes 68T07, 62G05, 60-08 Copyright © 2022, The Authors. All rights reserved.

关键词： Probability distributions

Thermal disorder and phonon softening in the ferroelectric phase transition of lead titanate

学校读者我要写书评

暂无评论

Physical Review B 2025年第9期111卷 094113-094113页

作者： Pinchen Xie Yixiao Chen Weinan E Roberto Car Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA AI for Science Institute Beijing China and Center for Machine Learning Research and School of Mathematical Sciences Peking University Beijing China

We report a molecular dynamics study of ab initio quality of the ferroelectric phase transition in crystalline PbTiO3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained on density functional theory data with modern machine learning techniques. Our simulations demonstrate that the transition has a strong order-disorder character, in agreement with diffraction experiments, and provide fresh insight into the approach to equilibrium across the phase transition. We find that the emergence and disappearance of the macroscopic polarization is driven by dipolar switching at the nanometer scale. We also computed the infrared optical absorption spectra in both the ferroelectric and the paraelectric phases, finding good agreement with the experimental Raman frequencies. Often, the almost ideal displacive character of the soft mode detected by Raman scattering in the paraelectric phase has been contrasted with the order-disorder character of the transition suggested by diffraction experiments. We settle this issue by showing that the soft mode coexists with a strong Debye relaxation associated with thermal disordering of the dipoles. The Debye relaxation feature is centered at zero frequency and appears near the transition temperature in both the ferroelectric and the paraelectric phases.

关键词： Ferroelectricity

Low-Rank Decomposition of Plasma Kinetic Distributions in the Collisional Transition Regime

学校读者我要写书评

暂无评论

Low-Rank Decomposition of Plasma Kinetic Distributions in th...

2022 IEEE International Conference on Plasma Science, ICOPS 2022

作者： Coughlin, J. Shumlak, U. Hu, J. University of Washington Applied Mathematics SeattleWA United States University of Washington Computational Plasma Dynamics Laboratory Aerospace and Energetics Research Program SeattleWA United States

ISBN: (纸本)9781665479257

The strength of collisional effects in a plasma can be summarized by the non-dimensional Knudsen number Kn. For very small values of Kn, plasma behavior is well-described by the 5N moment fluid model, including the Braginskii closure. When Kn is large, plasmas are best described by a fully kinetic model such as the Vlasov-Maxwell system. For intermediate values of the Knudsen number, i.e. 10-2 © 2022 IEEE.

关键词： Collisional plasmas

Fast alignment of heterogeneous images in sliced Wasserstein distance

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Shi, Yunpeng Singer, Amit Verbeke, Eric J. Department of Mathematics University of California at Davis DavisCA United States Department of Mathematics Princeton University PrincetonNJ United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States

Many applications of computer vision rely on the alignment of similar but non-identical images. We present a fast algorithm for aligning heterogeneous images based on optimal transport. Our approach combines the speed of fast Fourier methods with the robustness of sliced probability metrics and allows us to efficiently compute the alignment between two L × L images using the sliced 2-Wasserstein distance in O(L2 log L) operations. We show that our method is robust to translations, rotations and deformations in the images. Copyright © 2025, The Authors. All rights reserved.

关键词：

GPU-Accelerated Modified Bessel Function of the Second Kind for Gaussian Processes

学校读者我要写书评

暂无评论

GPU-Accelerated Modified Bessel Function of the Second Kind ...

ISC High Performance 2025 Research Paper Proceedings (40th International Conference)

作者： Zipei Geng Sameh Abdulah Ying Sun Hatem Ltaief David E. Keyes Marc G. Genton Statistics Program King Abdullah University of Science and Technology Thuwal Saudi Arabia Applied Mathematics and Computational Sciences (AMCS) Program King Abdullah University of Science and Technology Thuwal Saudi Arabia

ISBN: (数字)9783982633619

Modified Bessel functions of the second kind are widely used in physics, engineering, spatial statistics, and machine learning. Since contemporary scientific applications, including machine learning, rely on GPUs for acceleration, providing robust GPU-hosted implementations of special functions, such as the modified Bessel function, is crucial for performance. Existing implementations of the modified Bessel function of the second kind rely on CPUs and have limited coverage of the full range of values needed in some applications. In this work, we present a robust implementation of the modified Bessel function of the second kind on GPUs, eliminating the dependence on the CPU host. We cover a range of values commonly used in real applications, providing high accuracy compared to common libraries like the GNU Scientific Library (GSL) when referenced to Mathematica as the authority. Our GPU-accelerated approach also demonstrates a 2.68X performance improvement using a single A100 GPU compared to the GSL on 40-core Intel Cascade Lake CPUs. Our implementation is integrated into ExaGeoStat, the HPC framework for Gaussian process modeling, where the modified Bessel function of the second kind is required by the Matérn covariance function in generating covariance matrices. We accelerate the matrix generation process in ExaGeoStat by up to 12.62X with four A100 GPUs while maintaining almost the same accuracy for modeling and prediction operations using synthetic and real datasets.

关键词： Accuracy computational modeling Graphics processing units Gaussian processes Machine learning Libraries computational efficiency Covariance matrices Optimization Synthetic data

Revealing Actual Viscoelastic Relaxation Times in Capillary Breakup

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Hu, Nan Hwang, Jonghyun Ruangkriengsin, Tachin Stone, Howard A. Department of Mechanical and Aerospace Engineering Princeton University NJ08544 United States Program in Applied and Computational Mathematics Princeton University NJ08544 United States

We use experiments and theory to elucidate the size effect in capillary breakup rheometry, where pre-stretching in the visco-capillary stage causes the apparent relaxation time to be consistently smaller than the actual value. We propose a method accounting for both the experimental size and the finite extensibility of polymers to extract the actual relaxation time. A phase diagram characterizes the expected measurement variability and delineates scaling law conditions. The results refine capillary breakup rheometry for viscoelastic fluids and advance the understanding of breakup dynamics across scales. Copyright © 2025, The Authors. All rights reserved.

关键词： Relaxation time

Unified Variational Approach Description of Ground-State Phases of the Two-Dimensional Electron Gas

学校读者我要写书评

暂无评论

Physical Review Letters 2024年第26期133卷 266504-266504页

作者： Conor Smith Yixiao Chen (陈一潇) Ryan Levy Yubo Yang (杨煜波) Miguel A. Morales Shiwei Zhang Center for Computational Quantum Physics Flatiron Institute New York New York 10010 USA Department of Electrical and Computer Engineering University of New Mexico Albuquerque New Mexico 87131 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

The two-dimensional electron gas (2DEG) is a fundamental model, which is drawing increasing interest because of recent advances in experimental and theoretical studies of 2D materials. Current understanding of the ground state of the 2DEG relies on quantum Monte Carlo calculations, based on variational comparisons of different Ansätze for different phases. We use a single variational ansatz, a general backflow-type wave function using a message-passing neural quantum state architecture, for a unified description across the entire density range. The variational optimization consistently leads to lower ground-state energies than previous best results. Transition into a Wigner crystal (WC) phase occurs automatically at rs=37±1, a density lower than currently believed. Between the liquid and WC phases, the same ansatz and variational search strongly suggest the existence of intermediate states in a broad range of densities, with enhanced short-range nematic spin correlations.

关键词： Wave functions