mlsanityData to 14 Oct 2026

A deep branching solver for fully nonlinear partial differential equations

arXiv 2203.03234 ↗First posted 7 Mar 2022math.NA cs.LG cs.NAcited by 3

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Abstract (arXiv)

We present a multidimensional deep learning implementation of a stochastic branching algorithm for the numerical solution of fully nonlinear PDEs. This approach is designed to tackle functional nonlinearities involving gradient terms of any orders, by combining the use of neural networks with a Monte Carlo branching algorithm. In comparison with other deep learning PDE solvers, it also allows us to check the consistency of the learned neural network function. Numerical experiments presented show that this algorithm can outperform deep learning approaches based on backward stochastic differential equations or the Galerkin method, and provide solution estimates that are not obtained by those methods in fully nonlinear examples.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 10 of its 48 references that are in the map. First posted on arXiv 7 Mar 2022.

Builds on

10 of 48 references.

References · 10

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Citing papers per year: 2024: 2; 2025: 1.

3 papers.

  1. 2024Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEscited by 12
  2. 2025One model to solve them all: 2BSDE families via neural operatorscited by 4
  3. 2024Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in Lp-sensecited by 3