mlsanityData to 14 Oct 2026

A brief review of the Deep BSDE method for solving high-dimensional partial differential equations

arXiv 2505.17032 ↗First posted 7 May 2025math.NA cs.CE cs.LGcited by 5

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Abstract (arXiv)

High-dimensional partial differential equations (PDEs) pose significant challenges for numerical computation due to the curse of dimensionality, which limits the applicability of traditional mesh-based methods. Since 2017, the Deep BSDE method has introduced deep learning techniques that enable the effective solution of nonlinear PDEs in very high dimensions. This innovation has sparked considerable interest in using neural networks for high-dimensional PDEs, making it an active area of research. In this short review, we briefly sketch the Deep BSDE method, its subsequent developments, and future directions for the field.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 46 of its 81 references that are in the map. First posted on arXiv 7 May 2025.

Builds on

46 of 81 references.

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34 more
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 3.

5 papers.

  1. 2026Adjoint Matching through the Lens of the Stochastic Maximum Principle in Optimal Controlcited by 6
  2. 2025Finite-Agent Stochastic Differential Games on Large Graphs: II. Graph-Based Architecturescited by 1
  3. 2026Stochastic Control Methods for Optimizationcited by 1
  4. 2025High-dimensional Bayesian filtering through deep density approximationcited by 0
  5. 2026Unbiased and Second-Order-Free Training for High-Dimensional PDEscited by 0