# NSGA-PINN: A Multi-Objective Optimization Method for Physics-Informed Neural Network Training

arXiv: https://arxiv.org/abs/2303.02219 · HTML: https://mlsanity.com/paper/2303.02219/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 39 references that are in the map.
- First posted on arXiv 3 Mar 2023.

## Builds on (most cited first, 15 of 15)

- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [Non-convex Optimization for Machine Learning](https://mlsanity.com/paper/1712.07897/) (2017)
- [Multi-Objective Loss Balancing for Physics-Informed Deep Learning](https://mlsanity.com/paper/2110.09813/) (2021)
- [DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networks](https://mlsanity.com/paper/2109.04304/) (2021)
- [Approximation error analysis of some deep backward schemes for nonlinear PDEs](https://mlsanity.com/paper/2006.01496/) (2020)
- [Non-convergence of stochastic gradient descent in the training of deep neural networks](https://mlsanity.com/paper/2006.07075/) (2020)
- [Training multi-objective/multi-task collocation physics-informed neural network with student/teachers transfer learnings](https://mlsanity.com/paper/2107.11496/) (2021)
- [Deep backward schemes for high-dimensional nonlinear PDEs](https://mlsanity.com/paper/1902.01599/) (2019)

## Built on by (most cited first, 13 of 13)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunities](https://mlsanity.com/paper/2501.06572/) (2025)
- [Quantifying Training Difficulty and Accelerating Convergence in Neural Network-Based PDE Solvers](https://mlsanity.com/paper/2410.06308/) (2024)
- [PINNverse: Accurate parameter estimation in differential equations from noisy data with constrained physics-informed neural networks](https://mlsanity.com/paper/2504.05248/) (2025)
- [Muon with Spectral Guidance: Efficient Optimization for Scientific Machine Learning](https://mlsanity.com/paper/2602.16167/) (2026)
- [iPINNER: An Iterative Physics-Informed Neural Network with Ensemble Kalman Filter](https://mlsanity.com/paper/2506.00731/) (2025)
- [Morephy-Net: An Evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed Neural Operator Learning Networks](https://mlsanity.com/paper/2509.00663/) (2025)
- [Common pitfalls to avoid while using multiobjective optimization in machine learning](https://mlsanity.com/paper/2405.01480/) (2024)
- [Spectrally Informed Learning of Fluid Flows](https://mlsanity.com/paper/2408.14407/) (2024)
- [CPINN-ABPI: Physics-Informed Neural Networks for Accurate Power Estimation in MPSoCs](https://mlsanity.com/paper/2505.22469/) (2025)
- [Dynamic Graph Neural Networks for Physiological Based Pharmacokinetic Modeling: A Novel Data Driven Approach to Drug Concentration Prediction](https://mlsanity.com/paper/2510.22096/) (2025)
- [PIP2 Net: Physics-informed Partition Penalty Deep Operator Network](https://mlsanity.com/paper/2512.15086/) (2025)
- [fPINN-DeepONet: A Physics-Informed Operator Learning Framework for Multi-term Time-fractional Mixed Diffusion-wave Equations](https://mlsanity.com/paper/2605.16594/) (2026)

## Abstract (arXiv)

This paper presents NSGA-PINN, a multi-objective optimization framework for effective training of Physics-Informed Neural Networks (PINNs). The proposed framework uses the Non-dominated Sorting Genetic Algorithm (NSGA-II) to enable traditional stochastic gradient optimization algorithms (e.g., ADAM) to escape local minima effectively. Additionally, the NSGA-II algorithm enables satisfying the initial and boundary conditions encoded into the loss function during physics-informed training precisely. We demonstrate the effectiveness of our framework by applying NSGA-PINN to several ordinary and partial differential equation problems. In particular, we show that the proposed framework can handle challenging inverse problems with noisy data.