mlsanityData to 7 Oct 2026

PINN Training using Biobjective Optimization: The Trade-off between Data Loss and Residual Loss

arXiv 2302.01810 ↗First posted 3 Feb 2023cs.LG cs.AI math.OCcited by 6

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Abstract (arXiv)

Physics informed neural networks (PINNs) have proven to be an efficient tool to represent problems for which measured data are available and for which the dynamics in the data are expected to follow some physical laws. In this paper, we suggest a multiobjective perspective on the training of PINNs by treating the data loss and the residual loss as two individual objective functions in a truly biobjective optimization approach. As a showcase example, we consider COVID-19 predictions in Germany and built an extended susceptibles-infected-recovered (SIR) model with additionally considered leaky-vaccinated and hospitalized populations (SVIHR model) to model the transition rates and to predict future infections. SIR-type models are expressed by systems of ordinary differential equations (ODEs). We investigate the suitability of the generated PINN for COVID-19 predictions and compare the resulting predicted curves with those obtained by applying the method of non-standard finite differences to the system of ODEs and initial data. The approach is applicable to various systems of ODEs that define dynamical regimes. Those regimes do not need to be SIR-type models, and the corresponding underlying data sets do not have to be associated with COVID-19.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 15 of its 46 references that are in the map. First posted on arXiv 3 Feb 2023.

Builds on

15 of 46 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. 2018Multi-Task Learning as Multi-Objective Optimizationcited by 809
  4. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
  5. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 329
  6. 2020Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanismcited by 231
  7. 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemscited by 220
  8. 2021Meta-learning PINN loss functionscited by 51
  9. 2019The stochastic multi-gradient algorithm for multi-objective optimization and its application to supervised machine learningcited by 45
  10. 2021Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networkscited by 43
  11. 2021Data vs. Physics: The Apparent Pareto Front of Physics-Informed Neural Networkscited by 26
  12. 2021Data-driven approaches for predicting spread of infectious diseases through DINNs: Disease Informed Neural Networkscited by 14
3 more
  1. 2020Efficient and Sparse Neural Networks by Pruning Weights in a Multiobjective Learning Approachcited by 2
  2. 2022Kalman-Bucy-Informed Neural Network for System Identificationcited by 2
  3. 2019A simple and efficient dichotomic search algorithm for multi-objective mixed integer linear programscited by 1

Built on by

Cited by year

Citing papers per year: 2023: 1; 2024: 2; 2025: 3.

6 papers.

  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. 2025PINNverse: Accurate parameter estimation in differential equations from noisy data with constrained physics-informed neural networkscited by 3
  4. 2024Common pitfalls to avoid while using multiobjective optimization in machine learningcited by 2
  5. 2025Identifying Memory Effects in Epidemics via a Fractional SEIRD Model and Physics-Informed Neural Networkscited by 2
  6. 2023Number Theoretic Accelerated Learning of Physics-Informed Neural Networkscited by 0