# Stochastic projection based approach for gradient free physics informed learning

arXiv: https://arxiv.org/abs/2209.13724 · HTML: https://mlsanity.com/paper/2209.13724/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2022.

## Built on by (most cited first, 15 of 15)

- [Physics informed WNO](https://mlsanity.com/paper/2302.05925/) (2023)
- [Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation](https://mlsanity.com/paper/2302.05104/) (2023)
- [On the locality of local neural operator in learning fluid dynamics](https://mlsanity.com/paper/2312.09820/) (2023)
- [PhyPlan: Compositional and Adaptive Physical Task Reasoning with Physics-Informed Skill Networks for Robot Manipulators](https://mlsanity.com/paper/2402.15767/) (2024)
- [A physics-informed transformer neural operator for learning generalized solutions of initial boundary value problems](https://mlsanity.com/paper/2412.09009/) (2024)
- [Probabilistic machine learning based predictive and interpretable digital twin for dynamical systems](https://mlsanity.com/paper/2212.09240/) (2022)
- [DPA-WNO: A gray box model for a class of stochastic mechanics problem](https://mlsanity.com/paper/2309.15128/) (2023)
- [Waveformer for modelling dynamical systems](https://mlsanity.com/paper/2310.04990/) (2023)
- [An efficient wavelet-based physics-informed neural network for multiscale problems](https://mlsanity.com/paper/2409.11847/) (2024)
- [Harnessing physics-informed operators for high-dimensional reliability analysis problems](https://mlsanity.com/paper/2409.04708/) (2024)
- [Event-driven physics-informed operator learning for reliability analysis](https://mlsanity.com/paper/2511.06083/) (2025)
- [PhyPlan: Generalizable and Rapid Physical Task Planning with Physics Informed Skill Networks for Robot Manipulators](https://mlsanity.com/paper/2406.00001/) (2024)
- [Geometry adaptive waveformer for cardio-vascular modeling](https://mlsanity.com/paper/2503.17505/) (2025)
- [Stochastic Dimension Zeroth-Order Estimator: Stable and Memory-Efficient Training of PINNs](https://mlsanity.com/paper/2603.24002/) (2026)
- [Learning the Stellar Structure Equations via Self-supervised Physics-Informed Neural Networks](https://mlsanity.com/paper/2604.06255/) (2026)

## Abstract (arXiv)

We propose a stochastic projection-based gradient free physics-informed neural network. The proposed approach, referred to as the stochastic projection based physics informed neural network (SP-PINN), blends upscaled stochastic projection theory with the recently proposed physics-informed neural network. This results in a framework that is robust and can solve problems involving complex solution domain and discontinuities. SP-PINN is a gradient-free approach which addresses the computational bottleneck associated with automatic differentiation in conventional PINN. Efficacy of the proposed approach is illustrated by a number of examples involving regular domain, complex domain, complex response and phase field based fracture mechanics problems. Case studies by varying network architecture (activation function) and number of collocation points have also been presented.