用神经网络自动学习优化中的分数阶参数，提升复杂问题求解能力
Applications of fractional calculus in learned optimization
- 训练神经网络预测分数阶梯度下降的阶数
- 在非线性与混沌问题中表现优于传统方法
- 适合需要自适应优化策略的研究者
分数阶梯度下降已被广泛研究，其通过引入分数阶导数扩展了传统梯度下降方法，提升了在复杂优化景观中导航的灵活性，并在处理非线性及混沌动力学问题时展现出优势。然而，分数阶参数的精细调优仍是未解难题。本文展示可通过训练神经网络有效预测梯度的分数阶，实现自适应优化。
原文摘要 · Abstract (English)
Fractional gradient descent has been studied extensively, with a focus on its ability to extend traditional gradient descent methods by incorporating fractional-order derivatives. This approach allows for more flexibility in navigating complex optimization landscapes and offers advantages in certain types of problems, particularly those involving non-linearities and chaotic dynamics. Yet, the challenge of fine-tuning the fractional order parameters remains unsolved. In this work, we demonstrate that it is possible to train a neural network to predict the order of the gradient effectively.
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