Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating, and enabling our understanding of natural phenomena at a wide range of spatial and temporal scales, giving rise to a new area of research known as AI for science (AI4Science). Being an emerging research paradigm, AI4Science is unique in that it is an enormous and highly interdisciplinary area. Thus, a unified and technical treatment of this field is needed yet challenging. This paper aims to provide a technically thorough account of a subarea of AI4Science; namely, AI for quantum, atomistic, and continuum systems. These areas aim at understanding the physical world from the subatomic (wavefunctions and electron density), atomic (molecules, proteins, materials, and interactions), to macro (fluids, climate, and subsurface) scales and form an important subarea of AI4Science. A unique advantage of focusing on these areas is that they largely share a common set of challenges, thereby allowing a unified and foundational treatment. A key common challenge is how to capture physics first principles, especially symmetries, in natural systems by deep learning methods. We provide an in-depth yet intuitive account of techniques to achieve equivariance to symmetry transformations. We also discuss other common technical challenges, including explainability, out-of-distribution generalization, knowledge transfer with foundation and large language models, and uncertainty quantification. To facilitate learning and education, we provide categorized lists of resources that we found to be useful. We strive to be thorough and unified and hope this initial effort may trigger more community interests and efforts to further advance AI4Science.

翻译：人工智能（AI）的进步正推动自然科学发现的新范式。如今，AI通过改进、加速并拓展我们对不同时空尺度自然现象的理解，已开始推动自然科学的发展，催生了被称为"AI for Science (AI4Science)"的新兴研究领域。作为新兴研究范式，AI4Science的独特之处在于其规模庞大且高度跨学科的特性。因此，对该领域进行统一且技术性的论述既必要又充满挑战。本文旨在对AI4Science的子领域——即量子、原子及连续介质系统中的AI应用——进行技术性的全面阐述。这些领域旨在理解从亚原子（波函数与电子密度）、原子（分子、蛋白质、材料及相互作用）到宏观（流体、气候及地下）尺度的物理世界，构成了AI4Science的重要分支。聚焦这些领域的独特优势在于，它们共享一组核心挑战，从而允许进行统一的基础性处理。其中一个关键共性挑战是如何通过深度学习方法捕获自然系统中的物理第一性原理，特别是对称性。我们深入且直观地阐述了实现对称变换等变性的技术。此外，我们还讨论了其他共性技术挑战，包括可解释性、分布外泛化、基于基础模型与大语言模型的知识迁移，以及不确定性量化。为促进学习与教育，我们提供了分类整理的实用资源列表。我们力求全面且统一，期望这一初步努力能激发更多社区的兴趣与投入，进一步推动AI4Science的发展。