Physics-informed distribution transformers via molecular dynamics and deep neural networks
Physics-informed distribution transformers via molecular dynamics and deep neural networks
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DOI：
10.1016/j.jcp.2022.111511
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发表时间：
2022-08-10
影响因子：
4.1
通讯作者：
Cai, Difeng
中科院分区：
文献类型：
--
作者：
Cai, Difeng
生成高均匀度的准随机点是许多领域的一项基本任务。现有的数论方法在[0，1]d中产生渐近意义上均匀分布的点，但对于给定的集合大小，可能不能产生良好的分布。将这些技术扩展到其他几何形状也是困难的，比如圆盘或流形。在本文中，我们提出了一种新的物理信息框架，将给定的点集转换为具有更好一致性的分布。我们将每个点建模为一个粒子，并为系统分配势能。在能量最小的情况下，可以相应地改善分布的均匀性。介绍了两种方案：一种是基于分子动力学的，另一种是基于深度神经网络的。新的物理信息框架作为一个黑盒转换器，能够改善给定的分布，并可以很容易地扩展到其他几何形状，如磁盘、球体、复杂流形等。提供了不同几何形状的各种实验，证明了新框架能够将分布不佳的输入转换为具有良好一致性的输入。(C)2022 Elsevier Inc.保留所有权利。
Generating quasirandom points with high uniformity is a fundamental task in many fields. Existing number-theoretic approaches produce evenly distributed points in [0, 1]d in asymptotic sense but may not yield a good distribution for a given set size. It is also difficult to extend those techniques to other geometries like a disk or a manifold. In this paper, we present a novel physics-informed framework to transform a given set of points into a distribution with better uniformity. We model each point as a particle and assign the system with a potential energy. Upon minimizing the energy, the uniformity of distribution can be improved correspondingly. Two kinds of schemes are introduced: one based on molecular dynamics and another based on deep neural networks. The new physics-informed framework serves as a black-box transformer that is able to improve given distributions and can be easily extended to other geometries such as disks, spheres, complex manifolds, etc. Various experiments with different geometries are provided to demonstrate that the new framework is able to transform poorly distributed input into one with superior uniformity. (c) 2022 Elsevier Inc. All rights reserved.