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（AI）的进步正在推动自然科学发现的新范式。当前，AI已开始通过提升、加速并拓展我们对广泛时空尺度下自然现象的理解来推动自然科学的发展，由此催生了一个被称为“科学人工智能”（AI4Science）的新兴研究领域。作为一个新兴的研究范式，AI4Science的独特之处在于其庞大且高度跨学科的特性。因此，对这一领域进行统一且技术性的梳理是必要但具有挑战性的。本工作旨在对AI4Science的一个子领域——即面向量子、原子与连续体系的人工智能——提供技术层面的深入阐述。这些领域致力于从亚原子（波函数与电子密度）、原子（分子、蛋白质、材料及其相互作用）到宏观（流体、气候与地下系统）尺度理解物理世界，构成了AI4Science中一个重要的子领域。聚焦于这些领域的一个独特优势在于，它们在很大程度上共享一系列共同挑战，从而允许进行统一且基础性的探讨。一个关键共同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，尤其是对称性。我们对实现等变性以应对对称变换的技术进行了深入而直观的阐述。我们还讨论了其他常见的技术挑战，包括可解释性、分布外泛化能力、基于基础模型与大型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。我们力求全面且系统，并希望这一初步尝试能够激发更多社区的兴趣与努力，共同推动AI4Science的进一步发展。