mlsanityData to 7 Oct 2026

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

arXiv 2303.02219 ↗First posted 3 Mar 2023cs.LGcited by 13

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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.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 15 of its 39 references that are in the map. First posted on arXiv 3 Mar 2023.

Builds on

15 of 39 references.

References · 15

  1. 2016An overview of gradient descent optimization algorithmscited by 1,021
  2. 2015Automatic differentiation in machine learning: a surveycited by 846
  3. 2021Characterizing possible failure modes in physics-informed neural networkscited by 632
  4. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
  5. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  6. 2021Physics-informed neural networks with hard constraints for inverse designcited by 277
  7. 2020Physics-informed learning of governing equations from scarce datacited by 167
  8. 2018Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flowscited by 147
  9. 2017Non-convex Optimization for Machine Learningcited by 132
  10. 2021Multi-Objective Loss Balancing for Physics-Informed Deep Learningcited by 86
  11. 2021DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networkscited by 28
  12. 2020Approximation error analysis of some deep backward schemes for nonlinear PDEscited by 20
3 more
  1. 2020Non-convergence of stochastic gradient descent in the training of deep neural networkscited by 14
  2. 2021Training multi-objective/multi-task collocation physics-informed neural network with student/teachers transfer learningscited by 9
  3. 2019Deep backward schemes for high-dimensional nonlinear PDEscited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 4; 2025: 7; 2026: 2.

13 papers.

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  1. 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
  2. 2025Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunitiescited by 10
  3. 2026Muon with Spectral Guidance: Efficient Optimization for Scientific Machine Learningcited by 4
  4. 2024Quantifying Training Difficulty and Accelerating Convergence in Neural Network-Based PDE Solverscited by 3
  5. 2025PINNverse: Accurate parameter estimation in differential equations from noisy data with constrained physics-informed neural networkscited by 3
  6. 2025iPINNER: An Iterative Physics-Informed Neural Network with Ensemble Kalman Filtercited by 3
  7. 2025Morephy-Net: An Evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed Neural Operator Learning Networkscited by 3
  8. 2024Common pitfalls to avoid while using multiobjective optimization in machine learningcited by 2
  9. 2024Spectrally Informed Learning of Fluid Flowscited by 1
  10. 2025CPINN-ABPI: Physics-Informed Neural Networks for Accurate Power Estimation in MPSoCscited by 0
  11. 2025Dynamic Graph Neural Networks for Physiological Based Pharmacokinetic Modeling: A Novel Data Driven Approach to Drug Concentration Predictioncited by 0
  12. 2025PIP2 Net: Physics-informed Partition Penalty Deep Operator Networkcited by 0
1 more
  1. 2026fPINN-DeepONet: A Physics-Informed Operator Learning Framework for Multi-term Time-fractional Mixed Diffusion-wave Equationscited by 0