# More Consistent Accuracy PINN via Alternating Easy-Hard Training

arXiv: https://arxiv.org/abs/2512.17607 · HTML: https://mlsanity.com/paper/2512.17607/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 43 references that are in the map.
- First posted on arXiv 19 Dec 2025.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [Automated Curriculum Learning for Neural Networks](https://mlsanity.com/paper/1704.03003/) (2017)
- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [Efficient training of physics-informed neural networks via importance sampling](https://mlsanity.com/paper/2104.12325/) (2021)
- [A Method for Representing Periodic Functions and Enforcing Exactly Periodic Boundary Conditions with Deep Neural Networks](https://mlsanity.com/paper/2007.07442/) (2020)
- [DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations](https://mlsanity.com/paper/2112.14038/) (2021)
- [Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness](https://mlsanity.com/paper/2305.17289/) (2023)
- [A Dual-Dimer Method for Training Physics-Constrained Neural Networks with Minimax Architecture](https://mlsanity.com/paper/2005.00615/) (2020)
- [PINNACLE: PINN Adaptive ColLocation and Experimental points selection](https://mlsanity.com/paper/2404.07662/) (2024)
- [A practical PINN framework for multi-scale problems with multi-magnitude loss terms](https://mlsanity.com/paper/2308.06672/) (2023)
- [Tackling the Curse of Dimensionality in Fractional and Tempered Fractional PDEs with Physics-Informed Neural Networks](https://mlsanity.com/paper/2406.11708/) (2024)
- [An Imbalanced Learning-based Sampling Method for Physics-informed Neural Networks](https://mlsanity.com/paper/2501.11222/) (2025)
- [Less Emphasis on Difficult Layer Regions: Curriculum Learning for Singularly Perturbed Convection-Diffusion-Reaction Problems](https://mlsanity.com/paper/2210.12685/) (2022)

## Abstract (arXiv)

Physics-informed neural networks (PINNs) have recently emerged as a prominent paradigm for solving partial differential equations (PDEs), yet their training strategies remain underexplored. While hard prioritization methods inspired by finite element methods are widely adopted, recent research suggests that easy prioritization can also be effective. Nevertheless, we find that both approaches exhibit notable trade-offs and inconsistent performance across PDE types. To address this issue, we develop a hybrid strategy that combines the strengths of hard and easy prioritization through an alternating training algorithm. On PDEs with steep gradients, nonlinearity, and high dimensionality, the proposed method achieves consistently high accuracy, with relative L2 errors mostly in the range of O(10^-5) to O(10^-6), significantly surpassing baseline methods. Moreover, it offers greater reliability across diverse problems, whereas compared approaches often suffer from variable accuracy depending on the PDE. This work provides new insights into designing hybrid training strategies to enhance the performance and robustness of PINNs.