# Impact of Loss Weight and Model Complexity on Physics-Informed Neural Networks for Computational Fluid Dynamics

arXiv: https://arxiv.org/abs/2509.21393 · HTML: https://mlsanity.com/paper/2509.21393/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 44 references that are in the map.
- First posted on arXiv 24 Sep 2025.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [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)
- [On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks](https://mlsanity.com/paper/2012.10047/) (2020)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)
- [PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs](https://mlsanity.com/paper/2106.14103/) (2021)
- [CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method](https://mlsanity.com/paper/2110.15832/) (2021)
- [Deep Learning of Vortex Induced Vibrations](https://mlsanity.com/paper/1808.08952/) (2018)
- [Learning in Sinusoidal Spaces with Physics-Informed Neural Networks](https://mlsanity.com/paper/2109.09338/) (2021)
- [A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applications](https://mlsanity.com/paper/2010.02011/) (2020)
- [Variational Autoencoders for Learning Nonlinear Dynamics of Physical Systems](https://mlsanity.com/paper/2012.03448/) (2020)
- [Fully Connected Deep Structured Networks](https://mlsanity.com/paper/1503.02351/) (2015)
- [Poisson CNN: Convolutional neural networks for the solution of the Poisson equation on a Cartesian mesh](https://mlsanity.com/paper/1910.08613/) (2019)

## Built on by (most cited first, 2 of 2)

- [High-Fidelity Modeling of Stochastic Chemical Dynamics on Complex Manifolds: A Multi-Scale SIREN-PINN Framework for the Curvature-Perturbed Ginzburg-Landau Equation](https://mlsanity.com/paper/2601.08104/) (2026)
- [Critical evaluation of PINN for FWD inverse analysis and differentiable FEM as an alternative](https://mlsanity.com/paper/2606.03210/) (2026)

## Abstract (arXiv)

Physics Informed Neural Networks offer a mesh free framework for solving PDEs but are highly sensitive to loss weight selection. We propose two dimensional analysis based weighting schemes, one based on quantifiable terms, and another also incorporating unquantifiable terms for more balanced training. Benchmarks on heat conduction, convection diffusion, and lid driven cavity flows show that the second scheme consistently improves stability and accuracy over equal weighting. Notably, in high Peclet number convection diffusion, where traditional solvers fail, PINNs with our scheme achieve stable, accurate predictions, highlighting their robustness and generalizability in CFD problems.