论文标题
谐波（量子）神经网络
Harmonic (Quantum) Neural Networks
论文作者
论文摘要
谐波函数本质上很丰富，出现在麦克斯韦的限制情况下，纳维尔 - 斯托克斯方程，热和波方程。因此，从工业过程优化到机器人路径计划以及随机步行的第一次退出时间的计算，有许多谐波功能的应用。尽管它们无处不在和相关性，但在机器学习环境中，很少有尝试将谐波功能的归纳偏见纳入。在这项工作中，我们展示了表示神经网络中谐波功能的有效手段，并将这些结果扩展到量子神经网络以证明我们方法的一般性。我们对（量子）物理信息的神经网络进行基准测试，在那里我们表现出良好的表现。
Harmonic functions are abundant in nature, appearing in limiting cases of Maxwell's, Navier-Stokes equations, the heat and the wave equation. Consequently, there are many applications of harmonic functions from industrial process optimisation to robotic path planning and the calculation of first exit times of random walks. Despite their ubiquity and relevance, there have been few attempts to incorporate inductive biases towards harmonic functions in machine learning contexts. In this work, we demonstrate effective means of representing harmonic functions in neural networks and extend such results also to quantum neural networks to demonstrate the generality of our approach. We benchmark our approaches against (quantum) physics-informed neural networks, where we show favourable performance.
