# A physics-informed neural network framework for modeling obstacle-related equations

arXiv: https://arxiv.org/abs/2304.03552 · HTML: https://mlsanity.com/paper/2304.03552/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 56 references that are in the map.
- First posted on arXiv 7 Apr 2023.

## Builds on (most cited first, 12 of 12)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks](https://mlsanity.com/paper/2104.08426/) (2021)
- [Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacture](https://mlsanity.com/paper/2011.13511/) (2020)
- [Neural-net-induced Gaussian process regression for function approximation and PDE solution](https://mlsanity.com/paper/1806.11187/) (2018)

## Built on by (most cited first, 4 of 4)

- [WANCO: Weak Adversarial Networks for Constrained Optimization problems](https://mlsanity.com/paper/2407.03647/) (2024)
- [AsyReC: A Multimodal Graph-based Framework for Spatio-Temporal Asymmetric Dyadic Relationship Classification](https://mlsanity.com/paper/2504.05030/) (2025)
- [A Single-Loop Bilevel Deep Learning Method for Optimal Control of Obstacle Problems](https://mlsanity.com/paper/2601.04120/) (2026)
- [Fourier Neural Operators with Least-Squares Readout Refit for Learning Random Obstacle-to-Solution Maps](https://mlsanity.com/paper/2606.29436/) (2026)

## Abstract (arXiv)

Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g., TensorFlow or PyTorch. Physics-informed neural networks (PINNs) are an attractive tool for solving partial differential equations based on sparse and noisy data. Here extend PINNs to solve obstacle-related PDEs which present a great computational challenge because they necessitate numerical methods that can yield an accurate approximation of the solution that lies above a given obstacle. The performance of the proposed PINNs is demonstrated in multiple scenarios for linear and nonlinear PDEs subject to regular and irregular obstacles.