TRIPODS+X:RES: Collaborative Research: Creating Inference from Machine Learned and Science Based Generative Models

在许多科学学科中，计算模拟被用来增强我们对复杂系统的物理过程的理解。在所有这样的模拟中，都需要简化以使问题易于处理，从而限制了可以解决的问题的范围。通常，基于主导物理的包含许多相互作用的组件的大系统的计算模拟需要复杂且耗时的计算。该项目将应用基于系统物理的几何变换的深度学习神经网络(NN)，以高效的方式准确地逼近基于物理的传统计算模拟。神经网络模型所赋予的更高的效率将有助于提出目前在计算上难以处理的科学问题。虽然拟议的工作将集中于使用这种方法来发现新的应变诱导的极相和相位竞争，并理解宇宙中的大尺度结构，但这项工作中发展的概念可以应用于其他科学学科的计算模拟。拟议的工作将集中于基础数据科学方法的发展和这些方法的应用，以原则性和高效的方式增强基于科学的计算代价高昂的模型，从而使改进的数据驱动的科学推理成为可能。这项工作将特别强调神经网络模型的设计，通过物理上有意义的领域体系结构，可以在最小的信息损失下逼近N体和高度关联的现象。这项工作将开发工具来指导发现和实验合成新的应变诱导的极性相和相竞争，这些相显示出增强的机电响应；它将扩大我们的模拟能力和对宇宙中大尺度结构的理解。最终，这项工作将提供领域特定的进展，以及其他领域的框架，以利用数据驱动模型来增强计算密集型、高度相关的N-Body问题，这些模型尊重问题的物理性质并导致计算效率的提高。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

In many scientific disciplines computational simulations are used to enhance our understanding of physical processes of complex systems. In all such simulations simplifications are required to make the problem tractable, limiting the scope of the questions that can be addressed. Generally, computational simulations of large systems with many interacting components, based on the governing physics, requires complex and time consuming computations. This project will apply deep learning neural networks (NN) with geometric transformations based on the physics of the system to accurately approximate traditional physics-based computational simulations in a highly efficient manner. The increased efficiency imparted by the NN model will facilitate the asking of scientific questions which are currently computationally intractable. While the proposed work will focus on using this method to discover new strain-induced polar phases and phase competition, and to understand the large-scale structure in the universe, the concepts developed in this work can be applied to computational simulations in other scientific disciplines.The proposed work will focus on the development of foundational data science methods and the application of these methods to augment computationally-expensive science-based generative models in a way that is principled and efficient, thereby enabling improved data-driven scientific inference. The work will place specific emphasis on the design of neural network models, which through physically-significant domain architectures can approximate N-body and highly-correlated phenomena with minimal loss of information. The work will develop tools to guide the discovery and experimental synthesis of new strain-induced polar phases and phase competition, which exhibit enhanced electromechanical responses; and it will expand our simulation capabilities and understanding of the large-scale structure in the universe. Ultimately, this work will provide both domain specific advances, as well as a framework for other domain areas to augment computationally intensive, highly-correlated, N-body problems with data-driven models, which respect the physics of the problem and lead to increased computational efficiency.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.