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广泛应用，亟需以更低的计算成本捕捉参考模型特性的替代模型，从而省去潜在的高成本蒙特卡洛模拟。当前主流的做法是先训练大规模神经网络再进行剪枝压缩，但这一方法常忽略其固有缺陷：生成的替代模型往往无法保留原始模型固有的敏感性与不确定性。特别地，此类替代模型的（高阶）导数信息可能与原始模型存在显著差异。对于足够大的网络，我们预期导数信息能够匹配，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全过程中利用敏感性信息寻找替代模型的方法。该方法基于区间伴随显著性分析剪枝的研究，并结合索伯列夫训练的最新进展，使剪枝后的神经网络替代模型能够精确建模原始敏感性信息。我们以布朗运动驱动的随机微分方程定价多维篮子期权为例对该方法进行实验验证。所选案例虽出于敏感性直观解释的考量局限于定量金融领域，但所提方法并不局限于此——它可为构建考虑敏感性信息的替代建模技术奠定基础。