A machine learning method is proposed for representing the elements of diabatic potential energy matrices (PEMs) with high fidelity. This is an extension of the so-called permutation invariant polynomial-neural network (PIP-NN) method for representing adiabatic potential energy surfaces. While for one-dimensional irreducible representations the diagonal elements of a diabatic PEM are invariant under exchange of identical nuclei in a molecular system, the off-diagonal elements require special symmetry consideration, particularly in the presence of a conical intersection. A multiplicative factor is introduced to take into consideration the particular symmetry properties while maintaining the PIP-NN framework. We demonstrate here that the extended PIP-NN approach is accurate in representing diabatic PEMs, as evidenced by small fitting errors and by the reproduction of absorption spectra and product branching ratios in both H₂O($\tilde{X}/\tilde{B}$) and NH₃($\tilde{X}/Ã$) non-adiabatic photodissociation.

中文翻译：

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置换不变多项式神经网络方法拟合势能面。IV。耦合的非绝热势能矩阵

提出了一种机器学习方法，以高保真度表示非绝热势能矩阵（PEM）的元素。这是用于表示绝热势能面的所谓置换不变多项式神经网络（PIP-NN）方法的扩展。尽管对于一维不可约表示，非绝热PEM的对角元素在分子系统中相同核的交换下是不变的，但非对角元素需要特殊的对称性考虑，尤其是在存在圆锥形相交的情况下。引入乘法因子以在保持PIP-NN框架的同时考虑特定的对称性。我们在此证明，扩展的PIP-NN方法可准确表示非绝热PEM，₂ O（$\tilde{X}/\widetilde{乙}$）和NH ₃（$\tilde{X}/\mathrm{一个}$）非绝热光解离。