All of the past empirical models of the Earth’s bow shock shape were obtained by best-fitting some given surfaces to large collections of observed crossings. However, the issue of bow shock modelling can be addressed by means of artificial neural networks (ANN) as well. The ANN approach is powerful and flexible since an ANN can capture the hidden relation between the bow shock position and a set of given inputs and forecast its response on the basis of the inputs only.

In this paper we present a perceptron, a simple feedforward network, which computes the bow shock radial position, along a given direction, using as inputs: the two angular coordinates of that direction; the bow shock radial distance R_F79 provided by Formisano’s model (F79) (Formisano, 1979) and the upstream Alfvénic Mach’s number M_a.

The perceptron output can be regarded as a correction to the F79 representation of the bow shock shape. A statistical analysis, performed over a test data set of 944 bow shock crossings from several spacecraft, demonstrates that the ANN predictions are effectively more accurate than F79 ones. Indeed, the ANN mean value of the ratio between predicted and observed shock radial distance ${\bar{r}}_{ANN}$ is generally closer to the expected value μ_r ​= ​1 than the corresponding ${\bar{r}}_{F79}$. Such improvement on F79 is partly due to the addition of M_a to the model inputs. However, the statistical error ${\sigma }_{r_{ANN}}$ is practically the same as that from an identical network but with no M_a input line. In this regard, we discuss the possibility that an irreducible uncertainty in predictions originates from the bow shock motions related to the impacts of interplanetary discontinuities on the magnetosphere.

通过将一些给定的表面与大量观测到的交叉点最合适地拟合，可以获得过去所有的地球弓激波形状的经验模型。但是，弓形冲击建模的问题也可以通过人工神经网络（ANN）来解决。ANN方法强大而灵活，因为ANN可以捕获弓形冲击位置和一组给定输入之间的隐藏关系，并仅根据输入来预测其响应。

在本文中，我们提出了一个感知器，一个简单的前馈网络，该网络使用输入作为计算沿给定方向的船首冲击径向位置：该方向的两个角坐标；由Formisano模型（F79）（Formisano，1979）提供的船首冲击径向距离R _F79和上游AlfvénicMach的M _a。

感知器输出可以视为对弓形冲击形状的F79表示的校正。对来自多个航天器的944架弓首过境点的测试数据集进行的统计分析表明，ANN预测实际上比F79预测更准确。实际上，预测的和观察到的冲击径向距离之比的ANN平均值${\overline{\mathrm{[R}}}_{\mathrm{一种}ññ}$通常更接近预期值μ _{- [R}  = 1比相应的${\overline{\mathrm{[R}}}_{F79}$。F79的这种改进部分是由于在模型输入中添加了M _a。但是，统计错误${\sigma }_{{\mathrm{[R}}_{\mathrm{一种}ññ}}$实际上与来自相同网络_的输入线路相同，但输入线路没有M。在这方面，我们讨论了不可预测的不确定性源自与行星际不连续对磁层影响有关的弓激波运动的可能性。