mlsanityData to 7 Oct 2026

Machine Learning for semi linear PDEs

arXiv 1809.07609 ↗First posted 20 Sep 2018cs.LG math.AP stat.MLcited by 28

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Abstract (arXiv)

Recent machine learning algorithms dedicated to solving semi-linear PDEs are improved by using different neural network architectures and different parameterizations. These algorithms are compared to a new one that solves a fixed point problem by using deep learning techniques. This new algorithm appears to be competitive in terms of accuracy with the best existing algorithms.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). First posted on arXiv 20 Sep 2018.

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Citing papers per year: 2021: 3; 2022: 6; 2023: 9; 2024: 1; 2025: 5; 2026: 4.

28 papers.

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  1. 2023Tackling the Curse of Dimensionality with Physics-Informed Neural Networkscited by 78
  2. 2023Physics informed WNOcited by 26
  3. 2023Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networkscited by 23
  4. 2023Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEscited by 19
  5. 2022Mean-field neural networks: learning mappings on Wasserstein spacecited by 15
  6. 2022Convergence of a robust deep FBSDE method for stochastic controlcited by 11
  7. 2022Mean-field neural networks-based algorithms for McKean-Vlasov control problems *cited by 9
  8. 2023Deep learning numerical methods for high-dimensional fully nonlinear PIDEs and coupled FBSDEs with jumpscited by 6
  9. 2021Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEscited by 5
  10. 2022Computational Doob's h-transforms for Online Filtering of Discretely Observed Diffusionscited by 4
  11. 2024FBSJNN: A Theoretically Interpretable and Efficiently Deep Learning method for Solving Partial Integro-Differential Equationscited by 4
  12. 2022Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditionscited by 3
16 more
  1. 2023Simultaneous upper and lower bounds of American-style option prices with hedging via neural networkscited by 3
  2. 2023EPINN-NSE: Enhanced Physics-Informed Neural Networks for Solving Navier-Stokes Equationscited by 3
  3. 2025Integration Matters for Learning PDEs with Backward SDEscited by 3
  4. 2022A Deep Learning Approach for the solution of Probability Density Evolution of Stochastic Systemscited by 2
  5. 2023A Deep-Genetic Algorithm (Deep-GA) Approach for High-Dimensional Nonlinear Parabolic Partial Differential Equationscited by 2
  6. 2021Cell-average based neural network method for hyperbolic and parabolic partial differential equationscited by 1
  7. 2021A novel control method for solving high-dimensional Hamiltonian systems through deep neural networkscited by 1
  8. 2023Solution of FPK Equation for Stochastic Dynamics Subjected to Additive Gaussian Noise via Deep Learning Approachcited by 1
  9. 2025A deep solver for backward stochastic Volterra integral equationscited by 1
  10. 2025HEATNETs: Explainable Random Feature Neural Networks for High-Dimensional Parabolic PDEscited by 1
  11. 2025Error analysis for the deep Kolmogorov methodcited by 0
  12. 2025High-dimensional Bayesian filtering through deep density approximationcited by 0
  13. 2026KANHedge: Efficient Hedging of High-Dimensional Options Using Kolmogorov-Arnold Network-Based BSDE Solvercited by 0
  14. 2026INEUS: Iterative Neural Solver for High-Dimensional PIDEscited by 0
  15. 2026Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solverscited by 0
  16. 2026Deep numerical schemes for systems of Ergodic BSDEs with applications to regime-switching forward utilitiescited by 0