Inductive program synthesis (PS) has recently begun to emerge as a useful new approach to automatically generate algorithms in quantum chemistry, as demonstrated in recent applications to the vibrational Schrödinger equation for simple model systems with one or two degrees-of-freedom. Here, we report a new physics-informed approach to inductive PS that is more conducive to the generation of discrete variable representation algorithms for real molecular systems. The new framework ensures separability of the kinetic and potential operators and does not require an exact solution to compare synthesized algorithmic predictions with. Algorithms with a tridiagonal matrix structure are generated via a variational-based stochastic optimization procedure. Crucially, through an extensive testing procedure, we demonstrate that variationally synthesized algorithms perform just as well as those generated using a target function. Assuming a direct product representation of normal coordinates, these algorithms are applied to three triatomic molecules. In total, we identify a set of seven PS algorithms that accurately reproduce the vibrational spectra of H2O, NO2, and SO2, as predicted by Colbert-Miller and sine-DVR algorithms.

中文翻译：

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使用物理信息程序合成探索分子振动光谱的新算法。


归纳程序合成 （PS） 最近开始成为一种有用的新方法，用于自动生成量子化学算法，正如最近在具有一个或两个自由度的简单模型系统的振动薛定谔方程中的应用所证明的那样。在这里，我们报告了一种新的物理学归纳 PS 方法，该方法更有利于为真实分子系统生成离散变量表示算法。新框架确保了动力学和潜在算子的可分离性，并且不需要精确的解来比较合成的算法预测。具有三对角矩阵结构的算法是通过基于变分的随机优化程序生成的。至关重要的是，通过广泛的测试程序，我们证明了变分合成算法的性能与使用 target 函数生成的算法一样好。假设法向坐标的直接乘积表示，这些算法应用于三个三原子分子。总的来说，我们确定了一组七种 PS 算法，这些算法可以准确再现 Colbert-Miller 和正弦 DVR 算法预测的 H2O、NO2 和 SO2 的振动光谱。