A Neural RDE-based model for solving path-dependent PDEs
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Solving path dependent PDEs with LSTM networks and path signatures
Using a combination of recurrent neural networks and signature methods from the rough paths theory we design efficient algorithms for solving parametric families of path dependent partial differential equations (PPDEs) t…
Latent Neural Operator Pretraining for Solving Time-Dependent PDEs
Pretraining methods gain increasing attraction recently for solving PDEs with neural operators. It alleviates the data scarcity problem encountered by neural operator learning when solving single PDE via training on larg…
Operator learningDeep Signature FBSDE Algorithm
We propose a deep signature/log-signature FBSDE algorithm to solve forward-backward stochastic differential equations (FBSDEs) with state and path dependent features. By incorporating the deep signature/log-signature tra…
Low-Rank Adaptation of Evolutionary Deep Neural Networks for Efficient Learning of Time-Dependent PDEs
We study the Evolutionary Deep Neural Network (EDNN) framework for accelerating numerical solvers of time-dependent partial differential equations (PDEs). We introduce a Low-Rank Evolutionary Deep Neural Network (LR-EDNN…
Multiscale Neural Operators for Solving Time-Independent PDEs
Time-independent Partial Differential Equations (PDEs) on large meshes pose significant challenges for data-driven neural PDE solvers. We introduce a novel graph rewiring technique to tackle some of these challenges, suc…