Molecular Simulation is nowadays one of the most powerful tools for investigation of matter. Its results have led to fundamental discoveries with the effect of forging current technology and shaping its future beyond any expectation. From molecular docking^[1] to sophisticated materials,^[2] simulation can pilot the design of futuristic systems for the most advanced laboratories. However its physical models and numerical techniques need to be continuously upgraded in order to have a constructive interplay with rapidly evolving experimental techniques. Removing barriers between different length and time scales was the desired target at the beginning of the new millennium.^[3] The rationale behind this aim lies in the fact that molecular simulation is a quantitative tool that can satisfactorily determine both the microscopic origins of large scale properties and the influence of large scale behavior on the microscopic scale. Only knowledge of the interplay of scales can guide the accurate design of atomic or molecular systems with properties on demand. The program put forward in Ref. [3] has been implemented in many research centers all over the world, with relevant results in several fields of advanced research, from molecular biology,^[4] to materials science,^[5] to the design of novel “green” substances of high technological impact such as ionic liquids,^[6] to cite a few. Current molecular simulation routinely links different scales in space and time. Moreover the idea that the governing physical principles of simulated models should be framed, as much as possible, in a rigorous mathematical language is starting to become a standard procedure for many researchers, with the consequence that simulations are characterized by an increasing physical accuracy and reproducibility.^[7] Such conceptual progress is taking place in parallel to what can be considered a true technical revolution in the field, the contribution of artificial intelligence. Machine learning is not only increasing in a substantial manner the numerical efficiency of simulation algorithms but is also contributing to the refinement of atomic and molecular models where the currently available ones do not offer the desired accuracy.^[8] However, it should be kept in mind that machine learning approaches, while being more efficient than other numerical approaches, still need well defined physical models. In addition, there is a key question regarding the generalization properties of artificial neural networks, i.e. when and why machine learning algorithms can (or cannot) generalize from the training data. In my view the major challenge for the future consists in finding an optimal balance between the research that develops first principle models and the research that empowers the technical efficiency of machine learning. Finally, in a summary of the general state of art of the field, the progressing path of quantum computers towards performing molecular simulations in an efficient manner cannot be missed.^[9] It is not yet the revolution expected,^[10] but further progress in the next decade may indeed lead to a significant change of the way we are currently dealing with molecular simulations. Summarizing the concepts above, an ambitious and yet realistic program for the next decade would consist of developing simulation protocols where physical models across different length and time scales are systematically formalized in a rigorous mathematical language and are implemented in efficient numerical schemes according to the most advanced computational technologies.

Within the framework of the above overview, this themed issue of Advanced Theory and Simulations presents a collection of state‐of‐the‐art papers in the field. The papers cover a broad spectrum of subjects with the interplay of theoretical models, efficient numerical procedures and actual applications, distributed across a network of different disciplines such as physics, mathematics, chemistry and computer science. The common message of the papers reflects the principles of the ambitious program proposed above with the specific aim of promoting synergies between different subjects and disciplines. The hope is that this collection will represent a reference for newcomers and a concrete example to experienced scientists of a shared platform across subjects and disciplines that traditionally have been separated in the past.

如今，分子模拟是研究物质最强大的工具之一。其结果导致了基础发现，其结果是锻造当前技术并塑造其未来，这超出了任何预期。从分子对接^{[ 1 ]}到复杂的材料，^{[ 2 ]}仿真可以为最先进的实验室试行未来系统的设计。但是，它的物理模型和数值技术需要不断升级，以便与快速发展的实验技术产生建设性的相互作用。在新千年之初，消除在不同长度和时间尺度之间的障碍是期望的目标。^{[ 3 ]}此目标背后的基本原理是，分子模拟是一种定量工具，可以令人满意地确定大规模特性的微观起源以及大规模行为对微观尺度的影响。只有了解尺度的相互作用，才能指导具有所需特性的原子或分子系统的精确设计。参考文献中提出的程序。[ 3 ]已在世界各地的许多研究中心得到实施，在分子生物学^{[ 4 ]}到材料科学^{[ 5 ]}到新型高绿色“绿色”物质的设计等多个高级研究领域中均取得了相关成果。技术影响，例如离子液体，^{[6 ]}列举一些。当前的分子模拟通常将时空上不同的尺度联系起来。而且，应尽可能以严格的数学语言来构架模拟模型的控制物理原理的想法已开始成为许多研究人员的标准程序，其结果是，模拟的特点是物理精度和可重复性不断提高。^{[ 7 ]}这种概念上的进步与本领域真正的技术革命（人工智能的贡献）同时发生。机器学习不仅在很大程度上提高了仿真算法的数值效率，而且还有助于改进原子和分子模型，而当前无法使用这些模型来提供所需的精度。^{[ 8 ]}但是，应该记住，机器学习方法虽然比其他数值方法更有效，但仍需要定义明确的物理模型。此外，还有一个关于人工神经网络的泛化特性的关键问题，即何时以及为何机器学习算法可以（或不能）从训练数据中泛化。在我看来，未来的主要挑战在于在开发第一个原理模型的研究与赋予机器学习的技术效率的研究之间找到最佳的平衡。最后，在对本领域的一般技术现状的总结中，不能错过量子计算机向以有效方式执行分子模拟的发展路径。^{[ 9 ]}这并不是革命的预期^{[ 10 ]，}但是在下一个十年中的进一步发展确实可能导致我们目前处理分子模拟的方式发生重大变化。总结以上概念，下一个十年的雄心勃勃但又切合实际的程序将包括开发仿真协议，其中以严格的数学语言系统化形式化不同长度和时间范围的物理模型，并根据最先进的方法以有效的数值方案实施计算技术。

在以上概述的框架内，本主题是《高级理论与模拟》展示了该领域的最新论文。这些论文涵盖理论模型，有效的数值程序和实际应用之间的相互作用，涉及广泛的主题，分布在不同学科的网络中，例如物理，数学，化学和计算机科学。这些文件的共同信息反映了以上提出的雄心勃勃的计划的原则，其具体目的是促进不同学科和学科之间的协同增效。希望该馆藏将为新来者提供参考，并为经验丰富的科学家提供一个具体的例子，这些科学家将跨学科和学科的共享平台共享，这些学科和学科过去传统上是分开的。