Deep learning methods have been employed in gravitational-wave astronomy to accelerate the construction of surrogate waveforms for the inspiral of spin-aligned black hole binaries, among other applications. We face the challenge of modeling the residual error of an artificial neural network that models the coefficients of the surrogate waveform expansion (especially those of the phase of the waveform) which we demonstrate has sufficient structure to be learnable by a second network. Adding this second network, we were able to reduce the maximum mismatch for waveforms in a validation set by 13.4 times. We also explored several other ideas for improving the accuracy of the surrogate model, such as the exploitation of similarities between waveforms, the augmentation of the training set, the dissection of the input space, using dedicated networks per output coefficient and output augmentation. In several cases, small improvements can be observed, but the most significant improvement still comes from the addition of a second network that models the residual error. Since the residual error for more general surrogate waveform models (when e.g., eccentricity is included) may also have a specific structure, one can expect our method to be applicable to cases where the gain in accuracy could lead to significant gains in computational time.

翻译：深度学习方法已被用于引力波天文学中，以加速构建自旋对齐黑洞双星旋近过程的代理波形，以及其他应用。我们面临建模人工神经网络残差误差的挑战，该网络对代理波形展开系数（尤其是波形相位系数）进行建模，并证明该残差具有足够结构，可由第二个网络学习。通过添加第二个网络，我们将验证集波形最大失配降低了13.4倍。我们还探索了其他几种提高代理模型准确性的思路，例如利用波形间的相似性、扩充训练集、划分输入空间、为每个输出系数使用专用网络以及输出扩充。在若干情况下可观察到微小改进，但最显著的提升仍来自添加建模残差误差的第二个网络。由于更通用的代理波形模型（例如包含偏心率时）的残差误差也可能具有特定结构，因此可预期我们的方法适用于精度提升能带来显著计算时间收益的情形。