# A Neural RDE-based model for solving path-dependent PDEs

arXiv: https://arxiv.org/abs/2306.01123 · HTML: https://mlsanity.com/paper/2306.01123/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 43 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 14 of 14)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Neural Rough Differential Equations for Long Time Series](https://mlsanity.com/paper/2009.08295/) (2020)
- [Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning](https://mlsanity.com/paper/2008.13333/) (2020)
- [Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations](https://mlsanity.com/paper/1804.07010/) (2018)
- [Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU](https://mlsanity.com/paper/2001.00706/) (2020)
- [The iisignature library: efficient calculation of iterated-integral signatures and log signatures](https://mlsanity.com/paper/1802.08252/) (2018)
- ["Hey, that's not an ODE": Faster ODE Adjoints via Seminorms](https://mlsanity.com/paper/2009.09457/) (2020)
- [Developing the Path Signature Methodology and its Application to Landmark-based Human Action Recognition](https://mlsanity.com/paper/1707.03993/) (2017)
- [Learning Spatial-Semantic Context with Fully Convolutional Recurrent Network for Online Handwritten Chinese Text Recognition](https://mlsanity.com/paper/1610.02616/) (2016)
- [Learning stochastic differential equations using RNN with log signature features](https://mlsanity.com/paper/1908.08286/) (2019)
- [Logsig-RNN: a novel network for robust and efficient skeleton-based action recognition](https://mlsanity.com/paper/2110.13008/) (2021)
- [PDGM: a Neural Network Approach to Solve Path-Dependent Partial Differential Equations](https://mlsanity.com/paper/2003.02035/) (2020)

## Built on by (most cited first, 2 of 2)

- [Rough Path Signatures: Learning Neural RDEs for Portfolio Optimization](https://mlsanity.com/paper/2510.10728/) (2025)
- [Branched Signature Kernel Solvers for ODEs with rough Single-Trajectory signals](https://mlsanity.com/paper/2605.25826/) (2026)

## Abstract (arXiv)

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.