The increasing use of stochastic models for describing complex phenomena warrants surrogate models that capture the reference model characteristics at a fraction of the computational cost, foregoing potentially expensive Monte Carlo simulation. The predominant approach of fitting a large neural network and then pruning it to a reduced size has commonly neglected shortcomings. The produced surrogate models often will not capture the sensitivities and uncertainties inherent in the original model. In particular, (higher-order) derivative information of such surrogates could differ drastically. Given a large enough network, we expect this derivative information to match. However, the pruned model will almost certainly not share this behavior. In this paper, we propose to find surrogate models by using sensitivity information throughout the learning and pruning process. We build on work using Interval Adjoint Significance Analysis for pruning and combine it with the recent advancements in Sobolev Training to accurately model the original sensitivity information in the pruned neural network based surrogate model. We experimentally underpin the method on an example of pricing a multidimensional Basket option modelled through a stochastic differential equation with Brownian motion. The proposed method is, however, not limited to the domain of quantitative finance, which was chosen as a case study for intuitive interpretations of the sensitivities. It serves as a foundation for building further surrogate modelling techniques considering sensitivity information.

翻译：随着随机模型在描述复杂现象中的日益广泛应用，需要以较低计算成本捕捉参考模型特征的替代模型，以省去潜在昂贵的蒙特卡洛模拟。当前主流的先拟合大型神经网络再将其剪枝至较小规模的方法常忽视其缺陷：生成的替代模型往往无法保留原始模型固有的灵敏度和不确定性，尤其可能使（高阶）导数信息产生显著偏差。给定足够大的网络，我们期望导数信息能够匹配，但剪枝后的模型几乎必然无法保持这一特性。本文提出在学习和剪枝过程中利用灵敏度信息来构建替代模型。我们基于区间伴随显著性分析的剪枝工作，结合索伯列夫训练的最新进展，使基于剪枝神经网络的替代模型能准确建模原始灵敏度信息。通过布朗运动随机微分方程建模的多维篮子期权定价示例进行实验验证。该方法并不局限于定量金融领域（此处仅作为灵敏度直观解释的案例研究），可为后续考虑灵敏度信息的替代建模技术奠定基础。