Application of machine learning to condensed matter physics

机器学习已经被证明是我们这个时代最有影响力的发现之一。它在几乎每个科学领域都有广泛的应用，成为凝聚态材料重要性质的重要预测者。开发专门用于研究这些特性的机器学习算法将简化从极其大量的可能结构中寻找新的理想材料的研究。拟议的研究将开创一种跨学科的方法，利用新的机器学习技术和量子计算算法来研究凝聚态系统。这种结合将非常适合于深入了解这些材料的量子力学行为。凝聚态物理学是使用量子力学描述研究和建模固态材料。由于许多量子相互作用，找到这些描述的精确解是不可行的。已经有人尝试开发计算方法，可以接近这些新兴的属性，使新材料可以设计出理想的功能。神经网络似乎是分析这些系统的理想方法。它们在大搜索空间中高效搜索时非常有效，使其适用于凝聚态问题，这些问题具有广泛的可能材料结构。专门构建的凝聚态神经网络可以为凝聚态系统的物理学提供重要见解。拟议的研究旨在重新设计神经网络算法，其指导原则是删除当前公式中已经确定的隐含假设。这将增加网络的对称性，从而使其特别适用于具有许多类似对称性的凝聚态系统。这些重新设计似乎是广泛适用的，甚至在凝聚态应用领域之外;由此产生的研究应该是有影响力的，许多功能可以使用这种对称性原理进行大修。这个项目将包括对当前神经网络的许多方面进行新颖和大规模的大修，并在其许多应用中进行深远的改进。特别是，去除隐含假设并由此引入对称性的方法将对凝聚态物理和量子机器学习产生重大影响，量子机器学习的改进有助于凝聚态建模的进一步发展。以下是这项工作的预期成果总结：适用于凝聚态系统的具有对称性的新型高效神经网络函数。这些应该允许网络更有效地表示和操纵数据。改进对凝聚态系统属性的预测。通过指定所需特性来设计材料的潜力。洞察神经网络如何嵌入和操纵数据的本质。与量子机器学习和新的激活函数接口，更好地传达量子力学概率。递归神经网络模型的进一步进展，具有改进的存储器效率。这应该允许一个迭代的方法来模拟凝聚态系统。

Machine learning has already proven to be one of the most influential discoveries of our time. It has found widespread applications in almost every scientific field, becoming an essential predictor of important properties of condensed matter materials. Developing purpose-built machine learning algorithms for studying these properties would streamline research in the search for new desirable materials from the extremely vast number of possible constructions. The proposed research will pioneer an interdisciplinary approach, utilising both novel machine learning techniques and quantum computing algorithms to study condensed matter systems. This combination will be well-suited to yield insights into the quantum mechanical behavior of these materials.Condensed matter physics is the study and modeling of solid-state materials using quantum mechanical descriptions. Due to many quantum interactions, finding exact solutions to these descriptions is not feasible. There have been attempts to develop computational methods that can closely approximate these emergent properties so that new materials can be designed with desirable features. Neural networks appear to be an ideal method to analyze these systems. They are highly effective at efficiently searching through large search spaces, making them applicable to condensed matter problems, which feature a broad array of possible material constructions.Purpose-built condensed matter neural networks could provide significant insights into the physics of condensed matter systems. The proposed research aims to redesign neural network algorithms with the guiding principle of removing implicit assumptions already identified in the current formulations. This will increase the symmetry properties of networks, consequently making it particularly applicable to condensed matter systems that feature many analogous symmetries. These redesigns appear to be widely applicable, even outside the domain of condensed matter applications; the resulting research should be influential, with many functions that can be overhauled using this symmetry principle.This project will consist of a novel and large overhaul of many aspects of current neural networks, with far-reaching improvements across many of their applications. Particularly, the approach of removing implicit assumptions and consequently introducing symmetries will have a substantial impact in condensed matter physics and quantum machine learning, with improvements to quantum machine learning aiding further advances in condensed matter modeling.Below is a summary of the expected outcomes of this work:New highly efficient neural network functions exhibiting symmetries applicable to condensed matter systems. These should allow the network to represent and manipulate data more effectively.Improved predictions of the properties of condensed matter systems.Potential to design materials by specifying the desired characteristics.Insight into the nature of how neural networks embed and manipulate data.Interfaces with quantum machine learning and new activation functions that better convey quantum mechanical probabilities.Further advances in recurrent neural network models, with improved memory efficiency. This should allow for an iterative approach to modeling condensed matter systems.