Modular-Sparsity Synchronization for PINNs Training

Introduction

This is the official repository for our ICASSP 2026 paper:

Modularity-Free Conflict-Averse Training for Generalized PINNs
Heejo Kong, Beomchul Park, Sung-Jin Kim, Seong-Whan Lee*
[Paper (IEEE)] [Poster] [BibTeX]

Usage

We implement ModSync using PyTorch-based PINN benchmarks, following the implementations of Dual-Cone-Gradient-Descent (DCGD) and ConFIG.

We evaluate ModSync on standard PINN benchmark equations, including:

• Burgers' equation
• Helmholtz equation
• Klein-Gordon equation

The current implementation supports multiple PINN optimizers:

• LRA [S. Wang et al., 2021]
• NTK [S. Wang et al., 2021]
• PCGrad [T. Yu et al., 2020]
• CAGrad [B. Liu et al., 2021]
• MultiAdam [J. Yao et al., 2023]
• DCGD [Y. Hwang and D. Lim, 2024]
• ConFIG [Q. Liu et al., 2025]

Training

Here is an example of training ModSync with the DCGD optimizer on Burgers' equation:

# Burgers' equation with DCGD + ModSync
CUDA_VISIBLE_DEVICES=0 bash run_burgers_ours.sh dcgd dcst

In the above command:

• dcgd denotes the conflict-averse optimizer.
• dcst denotes the ModSync-based structural optimization setting.
• CUDA_VISIBLE_DEVICES=0 specifies the GPU index.

To train ModSync on other benchmark equations or with different optimizers, use the following commands:

# Helmholtz equation with DCGD + ModSync
CUDA_VISIBLE_DEVICES=0 bash run_helmholtz_ours.sh dcgd dcst

# Burgers' equation with ConFIG + ModSync
CUDA_VISIBLE_DEVICES=0 bash run_burgers_ours.sh config dcst

# Klein-Gordon equation with DCGD + ModSync
CUDA_VISIBLE_DEVICES=0 bash run_klein_gordon_ours.sh dcgd dcst

You may change the first argument to select the optimizer, for example:

# Klein-Gordon equation with standard DCGD
CUDA_VISIBLE_DEVICES=0 bash run_klein_gordon_ours.sh.sh dcgd base

Evaluation

After training, the best checkpoints will be saved in ./results. Training logs, including optimization losses, are also reported during training. For PINN evaluation, please refer to:

python eval.py

or please see eval.py for detailed evaluation options.

Acknowledgments

We sincerely thank the authors of the following projects for releasing their code:

• DST (ICLR'20)
• RigL (ICML'20)
• DCGD (NeurIPS'24)
• ConFIG (ICLR'25)

Citation

@inproceedings{kong2026modularity,
  title={Modularity-Free Conflict-Averse Training for Generalized PINNs},
  author={Kong, Heejo and Park, Beomchul and Kim, Sung-Jin and Lee, Seong-Whan},
  booktitle={IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
  pages={6016--6020},
  year={2026},
  organization={IEEE}
}