Recent advances in machine learning establish the ability of certain
neural-network architectures called neural operators to approximate maps
between function spaces. Motivated by a prospect of employing them in
fundamental physics, we examine applications to scattering processes in quantum
mechanics. We use an iterated variant of Fourier neural operators to learn the
physics of Schr\"odinger operators, which map from the space of initial wave
functions and potentials to the final wave functions. These deep operator
learning ideas are put to test in two concrete problems: a neural operator
predicting the time evolution of a wave packet scattering off a central
potential in $1+1$ dimensions, and the double-slit experiment in $2+1$
dimensions. At inference, neural operators can become orders of magnitude more
efficient compared to traditional finite-difference solvers.

最近，机器学习的最新发展提出了一种被称为神经算子的神经网络架构，能够近似函数空间之间的映射关系。我们以应用于基础物理学为目标，研究了它们在量子力学的散射过程中的应用。我们使用傅里叶神经算子的迭代变体来学习 Schrödinger 算子的物理性质，它将初始波函数和势能映射到最终波函数。这些深度算子学习的想法在两个具体问题中进行了测试：一个是在 $1+1$ 维度中预测波包散射在中心势场中的时间演化的神经算子，另一个是在 $2+1$ 维度中的双缝实验。在推断过程中，与传统的有限差分求解器相比，神经算子可以提高数个数量级的计算效率。