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PreprintCC BY-SA 4.0HAL

Revisiting Natural Gradient Descent for PINNs Using Adaptive Collocation Strategies

  • Chourouk El Hassanieh
  • Agustín Somacal
  • Mathilde Mougeot
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Abstract

Since their re-introduction in 2019, physics informed neural networks have evolved much beyond the vanilla PINN. From novel optimizers into adaptively sampling collocation points or loss re-weighting strategies, PINNs are showing promising results whether it is accuracy of the predicted solutions or accelerated computation time. In this paper, we focus on resampling strategies for selecting collocation points, tailored to Natural Gradient Descent optimization. Specifically, we propose two novel strategies: a repulsion strategy FBOAL-R which avoids samples to excessively cluster in small regions and a selfadaptive strategy FBOAL-SA for choosing the number of samples to be changed per iteration. These two strategies aim for more efficient domain coverage during training while maintaining a fixed collocation point cost.

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Cite

BibTeXRIS
BibTeX
@misc{hassanieh2026revisiting,
  title = {{Revisiting Natural Gradient Descent for PINNs Using Adaptive Collocation Strategies}},
  author = {Chourouk El Hassanieh and Agustín Somacal and Mathilde Mougeot},
  howpublished = {HAL},
  year = {2026},
  month = nov,
  url = {https://hal.science/hal-05853485v1},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Revisiting Natural Gradient Descent for PINNs Using Adaptive Collocation Strategies
AU  - Chourouk El Hassanieh
AU  - Agustín Somacal
AU  - Mathilde Mougeot
PY  - 2026
DA  - 2026/11/05
PB  - HAL
UR  - https://hal.science/hal-05853485v1
AB  - Since their re-introduction in 2019, physics informed neural networks have evolved much beyond the vanilla PINN. From novel optimizers into adaptively sampling collocation points or loss re-weighting strategies, PINNs are showing promising results whether it is accuracy of the predicted solutions or accelerated computation time. In this paper, we focus on resampling strategies for selecting collocation points, tailored to Natural Gradient Descent optimization. Specifically, we propose two novel strategies: a repulsion strategy FBOAL-R which avoids samples to excessively cluster in small regions and a selfadaptive strategy FBOAL-SA for choosing the number of samples to be changed per iteration. These two strategies aim for more efficient domain coverage during training while maintaining a fixed collocation point cost.
ER  -