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 work 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：人工智能的进步正在推动自然科学领域新范式的发展。当前，AI已开始通过改进、加速和促进我们对多时空尺度自然现象的理解来推动自然科学进步，从而催生了被称为"AI for Science (AI4Science)"的新兴研究领域。作为新兴研究范式，AI4Science具有规模庞大且高度跨学科的特殊性。因此，该领域亟需统一且技术性的系统阐述，但这极具挑战性。本文旨在对AI4Science的子领域——即量子、原子与连续介质系统中的AI应用——进行技术性全面论述。这些研究方向致力于理解从亚原子（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、气候与地下系统）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，它们共享大量共性挑战，从而能够实现统一的基础性研究。其中关键共性挑战是如何通过深度学习方法捕捉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手段，同时讨论了其他技术挑战，包括可解释性、分布外泛化、基于基础模型和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，我们分类整理了具有参考价值的资源列表。我们力求全面统一，期待这项开创性工作能激发更多学界同仁的共同推进AI4Science发展。