CL-PINN

This repository contains the lightweight research-code release for Continual-Learning Physics-Informed Neural Networks for Parameterized Partial Differential Equations.

CL-PINN treats parameterized PDE training as a sequence of parameter tasks. It combines active parameter selection, parameter-wise loss balancing, sparse experience replay, and an optional parameter subnetwork. The repository also contains the controlled external-baseline implementations used in the revised study.

Methods

Paper name	Implementation name	Main mechanism
UNI	uniform	Fixed approximately uniform parameter set
FIX	fixed	Fixed user-specified parameter set
AG	active_greedy	Greedy selection from the parameter grid
AC	active_cl	Bayesian parameter selection and dynamic task weighting
ACR	active_cl_replay	AC with fixed-capacity sparse replay
ACR2-arch	active_cl_replay_regularize	ACR with the two-branch ParamFNN architecture

The optional Adam parameter-branch decay and L-BFGS parameter-branch freezing controls are configured independently. ACR2-finetune denotes a downstream single-parameter residual-head adaptation procedure and is not part of the base ACR2-arch training run.

Repository layout

cl_pinn/                  CL-PINN source, experiment entry points, and tests
deepxde/                  Read-only DeepXDE snapshot used by this release
external_baselines/       Controlled baseline implementations
results/                  Small aggregate tables only
docs/                     Data and reproducibility notes
tools/                    Environment validation helpers

This is intentionally a lightweight code release. Raw checkpoints, training logs, per-run arrays, full reference datasets, paper-revision files, and local archives are not included. See docs/DATA.md and docs/REPRODUCIBILITY.md.

Installation

Python 3.10 is recommended. Install the PyTorch build appropriate for your CUDA or CPU environment first, then install this project:

python -m venv .venv
source .venv/bin/activate
python -m pip install --upgrade pip
python -m pip install -e ".[test,bayesian]"
export DDE_BACKEND=pytorch

Validation

Run the unit tests:

export DDE_BACKEND=pytorch
python -m pytest -q cl_pinn/tests

Validate the numerical environment on a CPU-only machine:

python tools/test_pinn_environment.py --allow-cpu

Omit --allow-cpu for the full CUDA validation used on the experiment server.

Running experiments

The safe command-line runner exposes a minimal Burgers smoke configuration:

cl-pinn-run \
  --case burgers \
  --method active_cl_replay \
  --seed 0 \
  --output-dir runs/smoke/burgers_acr_seed0 \
  --smoke

Reference data must be placed as described in docs/DATA.md. Full paper configurations are exposed through cl_pinn/experiments/reproduce_legacy.py; review the requested case, method, budget, and output directory before launching a long run. New runs refuse to overwrite a non-empty output directory.

Reproducibility scope

The formal study used random seeds [0, 1, 2], FP32, and an Adam-to-L-BFGS training schedule. Bayesian selection, sparse replay, ParamFNN architecture, branch decay, branch freezing, and single-parameter fine-tuning are represented by separate configuration controls. Aggregate result tables included here are for traceability; they do not replace the raw per-run artifacts.

The vendored DeepXDE revision is recorded in deepxde/VENDORED_VERSION.json. External comparisons are described in external_baselines/README.md.

DeepXDE attribution

This project builds on and vendors a read-only snapshot of DeepXDE. When using this repository, please also cite:

Lu, L., Meng, X., Mao, Z., and Karniadakis, G. E. (2021). DeepXDE: A deep learning library for solving differential equations. SIAM Review, 63(1), 208--228. https://doi.org/10.1137/19M1274067

License

No project-level open-source license is asserted in this release; absent a separate license, all rights remain with the authors. The vendored DeepXDE source remains under LGPL-2.1; see deepxde/LICENSE and deepxde/VENDORED_VERSION.json.

Cite this Article

@misc{chen2026continuallearningphysicsinformedneuralnetworks,
      title={Continual-Learning Physics-Informed Neural Networks for Parameterized Partial Differential Equations}, 
      author={Xujia Chen and Xinyue Hu and Letian Chen and Yi Liu and Wenhui Fan},
      year={2026},
      eprint={2608.04778},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2608.04778}, 
}