Determining, understanding, and predicting the so-called structure-property
relation is an important task in many scientific disciplines, such as
chemistry, biology, meteorology, physics, engineering, and materials science.
Structure refers to the spatial distribution of, e.g., substances, material, or
matter in general, while property is a resulting characteristic that usually
depends in a non-trivial way on spatial details of the structure.
Traditionally, forward simulations models have been used for such tasks.
Recently, several machine learning algorithms have been applied in these
scientific fields to enhance and accelerate simulation models or as surrogate
models. In this work, we develop and investigate the applications of six
machine learning techniques based on two different datasets from the domain of
materials science: data from a two-dimensional Ising model for predicting the
formation of magnetic domains and data representing the evolution of dual-phase
microstructures from the Cahn-Hilliard model. We analyze the accuracy and
robustness of all models and elucidate the reasons for the differences in their
performances. The impact of including domain knowledge through tailored
features is studied, and general recommendations based on the availability and
quality of training data are derived from this.

通过研究两个不同数据集中的六种机器学习技术在材料科学领域的应用，本文分析了这些模型的准确性和稳健性，并阐明了它们性能差异的原因。研究还考察了包含领域知识的影响以及基于训练数据可用性和质量的一般建议。

高效材料科学模拟的代理模型：基于机器学习预测微观组织性质

Efficient Surrogate Models for Materials Science Simulations: Machine  Learning-based Prediction of Microstructure Properties

Understanding the relationship which integrable (solvable) models, all of
which possess very special symmetry properties, have with the generic
non-integrable models that are used to describe real experiments, which do not
have the symmetry properties, is one of the most fundamental open questions in
both statistical mechanics and quantum field theory. The importance of the
two-dimensional Ising model in a magnetic field is that it is the simplest
system where this relationship may be concretely studied. We here review the
advances made in this study, and concentrate on the magnetic susceptibility
which has revealed an unexpected natural boundary phenomenon. When this is
combined with the Fermionic representations of conformal characters, it is
suggested that the scaling theory, which smoothly connects the lattice with the
correlation length scale, may be incomplete for $H \neq 0$.

本文回顾了在研究具有特殊对称性的可积（可解决）模型与用于描述实际实验的无对称性的泛在非可积模型之间的关系中所取得的进展，并集中讨论了磁化率，在此基础上结合共形字符的费米表示，暗示了在 $H 
eq 0$ 时，用于将晶格与相关长度尺度相连接的比例理论可能是不完整的。

Ising 模型的重要性

The importance of the Ising model

The exact solution of the two-dimensional Ising model by Onsager in 1944
represents one of the landmarks in theoretical physics. On the occassion of the
fifty years of the exact solution, we give a historical review of this model.
After briefly discussing the exact solution by Onsager, we point out some of
the recent developments in this field. The exact solution by Onsager has
inspired several developments in various other fields. Some of these are also
briefly mentioned.

本篇论文对 Onsager 于 1944 年提出的二维 Ising 模型的精确解法进行历史回顾并简要介绍了该领域的一些最新发展。