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自动微分是利用计算机自动化求导的技术, 最近几十年因为它在机器学习研究中的应用而被很多人了解. 如今越来越多的科学工作者意识到, 高效、自动化的求导可以为很多科学问题的求解提供新的思路, 其中自动微分在物理模拟中的应用尤为重要, 而且具有挑战性. 物理系统的可微分模拟可以帮助解决混沌理论、电磁学、地震学、海洋学等领域中的很多重要问题, 但又因为其对计算时间和空间的苛刻要求而对自动微分技术本身提出了挑战. 本文回顾了将自动微分技术运用到物理模拟中的几种方法, 并横向对比它们在计算时间、空间和精度方面的优势和劣势. 这些自动微分技术包括伴随状态法, 前向自动微分, 后向自动微分, 以及可逆计算自动微分.Automatic differentiation is a technology to differentiate a computer program automatically. It is known to many people for its use in machine learning in recent decades. Nowadays, researchers are becoming increasingly aware of its importance in scientific computing, especially in the physics simulation. Differentiating physics simulation can help us solve many important issues in chaos theory, electromagnetism, seismic and oceanographic. Meanwhile, it is also challenging because these applications often require a lot of computing time and space. This paper will review several automatic differentiation strategies for physics simulation, and compare their pros and cons. These methods include adjoint state methods, forward mode automatic differentiation, reverse mode automatic differentiation, and reversible programming automatic differentiation.
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Keywords:
- automatic differentiation /
- scientific computing /
- reversible programming /
- optimal checkpointing /
- physics simulation








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