CEENs: Causality-enforced evolutional networks for solving time-dependent partial differential equations
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 in...
| Authors | Jeahan Jung, Heechang Kim, Hyomin Shin et al. |
|---|---|
| Primary category | cs.LG |
| Published | 3 October 2026 |
| Last updated at source | 3 October 2026 |
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