# Machine Learning for semi linear PDEs

arXiv: https://arxiv.org/abs/1809.07609 · HTML: https://mlsanity.com/paper/1809.07609/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Sep 2018.

## Built on by (most cited first, 28 of 28)

- [Tackling the Curse of Dimensionality with Physics-Informed Neural Networks](https://mlsanity.com/paper/2307.12306/) (2023)
- [Physics informed WNO](https://mlsanity.com/paper/2302.05925/) (2023)
- [Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks](https://mlsanity.com/paper/2312.14499/) (2023)
- [Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs](https://mlsanity.com/paper/2311.15283/) (2023)
- [Mean-field neural networks: learning mappings on Wasserstein space](https://mlsanity.com/paper/2210.15179/) (2022)
- [Convergence of a robust deep FBSDE method for stochastic control](https://mlsanity.com/paper/2201.06854/) (2022)
- [Mean-field neural networks-based algorithms for McKean-Vlasov control problems *](https://mlsanity.com/paper/2212.11518/) (2022)
- [Deep learning numerical methods for high-dimensional fully nonlinear PIDEs and coupled FBSDEs with jumps](https://mlsanity.com/paper/2301.12895/) (2023)
- [Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs](https://mlsanity.com/paper/2105.03336/) (2021)
- [Computational Doob's h-transforms for Online Filtering of Discretely Observed Diffusions](https://mlsanity.com/paper/2206.03369/) (2022)
- [FBSJNN: A Theoretically Interpretable and Efficiently Deep Learning method for Solving Partial Integro-Differential Equations](https://mlsanity.com/paper/2412.11010/) (2024)
- [Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions](https://mlsanity.com/paper/2205.03672/) (2022)
- [Simultaneous upper and lower bounds of American-style option prices with hedging via neural networks](https://mlsanity.com/paper/2302.12439/) (2023)
- [EPINN-NSE: Enhanced Physics-Informed Neural Networks for Solving Navier-Stokes Equations](https://mlsanity.com/paper/2304.03689/) (2023)
- [Integration Matters for Learning PDEs with Backward SDEs](https://mlsanity.com/paper/2505.01078/) (2025)
- [A Deep Learning Approach for the solution of Probability Density Evolution of Stochastic Systems](https://mlsanity.com/paper/2207.01907/) (2022)
- [A Deep-Genetic Algorithm (Deep-GA) Approach for High-Dimensional Nonlinear Parabolic Partial Differential Equations](https://mlsanity.com/paper/2311.11558/) (2023)
- [Cell-average based neural network method for hyperbolic and parabolic partial differential equations](https://mlsanity.com/paper/2107.00813/) (2021)
- [A novel control method for solving high-dimensional Hamiltonian systems through deep neural networks](https://mlsanity.com/paper/2111.02636/) (2021)
- [Solution of FPK Equation for Stochastic Dynamics Subjected to Additive Gaussian Noise via Deep Learning Approach](https://mlsanity.com/paper/2311.04511/) (2023)
- [A deep solver for backward stochastic Volterra integral equations](https://mlsanity.com/paper/2505.18297/) (2025)
- [HEATNETs: Explainable Random Feature Neural Networks for High-Dimensional Parabolic PDEs](https://mlsanity.com/paper/2511.00886/) (2025)
- [Error analysis for the deep Kolmogorov method](https://mlsanity.com/paper/2508.17167/) (2025)
- [High-dimensional Bayesian filtering through deep density approximation](https://mlsanity.com/paper/2511.07261/) (2025)
- [KANHedge: Efficient Hedging of High-Dimensional Options Using Kolmogorov-Arnold Network-Based BSDE Solver](https://mlsanity.com/paper/2601.11097/) (2026)
- [INEUS: Iterative Neural Solver for High-Dimensional PIDEs](https://mlsanity.com/paper/2605.06281/) (2026)
- [Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solvers](https://mlsanity.com/paper/2606.22150/) (2026)
- [Deep numerical schemes for systems of Ergodic BSDEs with applications to regime-switching forward utilities](https://mlsanity.com/paper/2606.24271/) (2026)

## 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.