mlsanityData to 7 Oct 2026

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

arXiv 2304.03552 ↗First posted 7 Apr 2023cs.LG cs.IT cs.NAcited by 4

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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.

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

Builds on

12 of 56 references.

References · 12

  1. 2017Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networkscited by 4,861
  2. 2016Neural Architecture Search with Reinforcement Learningcited by 1,489
  3. 2015Automatic differentiation in machine learning: a surveycited by 846
  4. 2017Solving high-dimensional partial differential equations using deep learningcited by 549
  5. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
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  7. 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 292
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  9. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 261
  10. 2021Exact imposition of boundary conditions with distance functions in physics-informed deep neural networkscited by 135
  11. 2020Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacturecited by 48
  12. 2018Neural-net-induced Gaussian process regression for function approximation and PDE solutioncited by 22

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 1; 2026: 2.

4 papers.

  1. 2024WANCO: Weak Adversarial Networks for Constrained Optimization problemscited by 3
  2. 2025AsyReC: A Multimodal Graph-based Framework for Spatio-Temporal Asymmetric Dyadic Relationship Classificationcited by 2
  3. 2026A Single-Loop Bilevel Deep Learning Method for Optimal Control of Obstacle Problemscited by 0
  4. 2026Fourier Neural Operators with Least-Squares Readout Refit for Learning Random Obstacle-to-Solution Mapscited by 0