# Conditional physics informed neural networks

arXiv: https://arxiv.org/abs/2104.02741 · HTML: https://mlsanity.com/paper/2104.02741/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 45 references that are in the map.
- First posted on arXiv 6 Apr 2021.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [Variational Physics-Informed Neural Networks For Solving Partial Differential Equations](https://mlsanity.com/paper/1912.00873/) (2019)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)
- [NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework](https://mlsanity.com/paper/2012.07938/) (2020)
- [PyDEns: a Python Framework for Solving Differential Equations with Neural Networks](https://mlsanity.com/paper/1909.11544/) (2019)
- [An unsupervised learning approach to solving heat equations on chip based on Auto Encoder and Image Gradient](https://mlsanity.com/paper/2007.09684/) (2020)

## Built on by (most cited first, 23 of 23)

- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [An Expert's Guide to Training Physics-informed Neural Networks](https://mlsanity.com/paper/2308.08468/) (2023)
- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks](https://mlsanity.com/paper/2402.00326/) (2024)
- [Can Physics-Informed Neural Networks beat the Finite Element Method?](https://mlsanity.com/paper/2302.04107/) (2023)
- [Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective](https://mlsanity.com/paper/2502.00604/) (2025)
- [Partial Differential Equations Meet Deep Neural Networks: A Survey](https://mlsanity.com/paper/2211.05567/) (2022)
- [Machine learning and domain decomposition methods -- a survey](https://mlsanity.com/paper/2312.14050/) (2023)
- [State-of-the-Art Review of Design of Experiments for Physics-Informed Deep Learning](https://mlsanity.com/paper/2202.06416/) (2022)
- [Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient](https://mlsanity.com/paper/2506.04375/) (2025)
- [Physics-informed ConvNet: Learning Physical Field from a Shallow Neural Network](https://mlsanity.com/paper/2201.10967/) (2022)
- [Error convergence and engineering-guided hyperparameter search of PINNs: towards optimized I-FENN performance](https://mlsanity.com/paper/2303.03918/) (2023)
- [AI for Scientific Discovery is a Social Problem](https://mlsanity.com/paper/2509.06580/) (2025)
- [Enforcing hidden physics in physics-informed neural networks](https://mlsanity.com/paper/2511.14348/) (2025)
- [Data-driven synchronization-avoiding algorithms in the explicit distributed structural analysis of soft tissue](https://mlsanity.com/paper/2207.02194/) (2022)
- [Towards Automated Knowledge Integration From Human-Interpretable Representations](https://mlsanity.com/paper/2402.16105/) (2024)
- [PACMANN: Point Adaptive Collocation Method for Artificial Neural Networks](https://mlsanity.com/paper/2411.19632/) (2024)
- [Predicting the spread of COVID-19 in Delhi, India using Deep Residual Recurrent Neural Networks](https://mlsanity.com/paper/2110.05477/) (2021)
- [Application of machine learning regression models to inverse eigenvalue problems](https://mlsanity.com/paper/2212.04279/) (2022)
- [Precipitation nowcasting of satellite data using physically-aligned neural networks](https://mlsanity.com/paper/2511.05471/) (2025)
- [Physics aware machine learning for micromagnetic energy minimization: recent algorithmic developments](https://mlsanity.com/paper/2409.12877/) (2024)
- [PINNs Algorithmic Framework for Simulation of Nonlinear Burgers' Type Models](https://mlsanity.com/paper/2506.12922/) (2025)
- [Physics-informed low-rank neural operators with application to parametric elliptic PDEs](https://mlsanity.com/paper/2509.07687/) (2025)

## Abstract (arXiv)

We introduce conditional PINNs (physics informed neural networks) for estimating the solution of classes of eigenvalue problems. The concept of PINNs is expanded to learn not only the solution of one particular differential equation but the solutions to a class of problems. We demonstrate this idea by estimating the coercive field of permanent magnets which depends on the width and strength of local defects. When the neural network incorporates the physics of magnetization reversal, training can be achieved in an unsupervised way. There is no need to generate labeled training data. The presented test cases have been rigorously studied in the past. Thus, a detailed and easy comparison with analytical solutions is made. We show that a single deep neural network can learn the solution of partial differential equations for an entire class of problems.