CEENs: Causality-enforced evolutional networks for solving time-dependent partial differential equations
Abstract
Despite the growing popularity of physics-informed neural networks (PINNs), their applicability in the long-time integration of partial differential equations (PDEs) remains constrained. We argue that this problem stems from the lack of consideration of temporal causality in the original PINN formulation, resulting in a bias towards satisfying governing equations at later times before learning the initial condition and hence leading to erroneous solutions. To this end, we propose a novel method that seamlessly integrates temporal causality into the training process. Drawing inspiration from classical numerical methods where the temporal causality is reflected, we divide the time domain into nonoverlapping subintervals, assign a unique neural network to each subinterval, and construct a loss function founded on the integral form of PDEs within these subintervals. The proposed networks undergo sequential training, beginning with the initial time step. Our method demonstrates significant improvement in accuracy for long-time simulations of various PDE problems where the original PINN method fails while it requires less computational cost and memory compared to the PINN method. A parallelization algorithm is provided to further enhance the computational efficiency, showing a significant speedup for solving time-dependent PDEs.
Versions
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BibTeX
@misc{jung2026ceens,
title = {{CEENs: Causality-enforced evolutional networks for solving time-dependent partial differential equations}},
author = {Jeahan Jung and Heechang Kim and Hyomin Shin and Minseok Choi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04405},
eprint = {2610.04405},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04405},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - CEENs: Causality-enforced evolutional networks for solving time-dependent partial differential equations
AU - Jeahan Jung
AU - Heechang Kim
AU - Hyomin Shin
AU - Minseok Choi
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04405
UR - https://arxiv.org/abs/2610.04405
AB - Despite the growing popularity of physics-informed neural networks (PINNs), their applicability in the long-time integration of partial differential equations (PDEs) remains constrained. We argue that this problem stems from the lack of consideration of temporal causality in the original PINN formulation, resulting in a bias towards satisfying governing equations at later times before learning the initial condition and hence leading to erroneous solutions. To this end, we propose a novel method that seamlessly integrates temporal causality into the training process. Drawing inspiration from classical numerical methods where the temporal causality is reflected, we divide the time domain into nonoverlapping subintervals, assign a unique neural network to each subinterval, and construct a loss function founded on the integral form of PDEs within these subintervals. The proposed networks undergo sequential training, beginning with the initial time step. Our method demonstrates significant improvement in accuracy for long-time simulations of various PDE problems where the original PINN method fails while it requires less computational cost and memory compared to the PINN method. A parallelization algorithm is provided to further enhance the computational efficiency, showing a significant speedup for solving time-dependent PDEs.
ER -