The concept of the path-dependent partial differential equation (PPDE) was
first introduced in the context of path-dependent derivatives in financial
markets. Its semilinear form was later identified as a non-Markovian backward
stochastic differential equation (BSDE). Compared to the classical PDE, the
solution of a PPDE involves an infinite-dimensional spatial variable, making it
challenging to approximate, if not impossible. In this paper, we propose a
neural rough differential equation (NRDE)-based model to learn PPDEs, which
effectively encodes the path information through the log-signature feature
while capturing the fundamental dynamics. The proposed continuous-time model
for the PPDE solution offers the benefits of efficient memory usage and the
ability to scale with dimensionality. Several numerical experiments, provided
to validate the performance of the proposed model in comparison to the strong
baseline in the literature, are used to demonstrate its effectiveness.

本文提出了一种基于神经粗糙微分方程（NRDE）模型来学习路径相关部分微分方程（PPDE），该模型通过对数签名特征有效地编码路径信息并捕捉基本动态，在 PPDE 解的连续时间模型中提供了内存使用效率和处理维度扩展性的优点，并通过多个数值实验验证了其性能优越性。