# PDGM: a Neural Network Approach to Solve Path-Dependent Partial Differential Equations

arXiv: https://arxiv.org/abs/2003.02035 · HTML: https://mlsanity.com/paper/2003.02035/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2020.

## Built on by (most cited first, 4 of 4)

- [Deep Signature FBSDE Algorithm](https://mlsanity.com/paper/2108.10504/) (2021)
- [A deep learning approach to the probabilistic numerical solution of path-dependent partial differential equations](https://mlsanity.com/paper/2209.15010/) (2022)
- [A Neural RDE-based model for solving path-dependent PDEs](https://mlsanity.com/paper/2306.01123/) (2023)
- [A Deep Learning-Based Method for Fully Coupled Non-Markovian FBSDEs with Applications](https://mlsanity.com/paper/2511.08735/) (2025)

## Abstract (arXiv)

In this paper, we propose a novel numerical method for Path-Dependent Partial Differential Equations (PPDEs). These equations firstly appeared in the seminal work of Dupire [2009], where the functional Ito calculus was developed to deal with path-dependent financial derivatives contracts. More specificaly, we generalize the Deep Galerking Method (DGM) of Sirignano and Spiliopoulos [2018] to deal with these equations. The method, which we call Path-Dependent DGM (PDGM), consists of using a combination of feed-forward and Long Short-Term Memory architectures to model the solution of the PPDE. We then analyze several numerical examples, many from the Financial Mathematics literature, that show the capabilities of the method under very different situations.