Physics-informed Dynamics Representation Learning for Parametric PDEs

Honghui Wang, Yifan Pu, Shiji Song, Gao Huang

Keywords: physics-informed neural networks

Abstract:

While physics-informed neural networks have achieved remarkable progress in modeling dynamical systems governed by partial differential equations (PDEs), their ability to generalize across different scenarios remains restricted.
To address this limitation, we present PIDO, a novel physics-informed neural PDE solver that demonstrates robust generalization across various aspects of PDE configurations, including initial conditions, PDE coefficients, and training time horizons.
PIDO leverages the shared intrinsic structure inherent to dynamical systems with varying properties by
projecting the PDE solutions into a latent space via auto-decoding and subsequently learning the dynamics of these latent embeddings conditioned on the PDE coefficients.
However, the inherent optimization challenges associated with physics-informed loss present substantial obstacles to integrating such latent dynamics models.
To tackle this issue, we adopt a novel perspective by diagnosing these challenges within the latent space. This approach enables us to enhance both temporal extrapolation ability and training stability of PIDO via simple yet effective regularization techniques, ultimately leading to superior generalization performance compared to its data-driven counterpart.
The effectiveness of PIDO is validated on diverse benchmarks, including 1D combined equations and 2D Navier-Stokes equations. Moreover, we investigate the transferability of its learned representations to downstream tasks like long-term integration and inverse problems.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.

Reciprocal Reviewing: I understand the reciprocal reviewing requirement as described on https://iclr.cc/Conferences/2025/CallForPapers. If none of the authors are registered as a reviewer, it may result in a desk rejection at the discretion of the program chairs. To request an exception, please complete this form at https://forms.gle/Huojr6VjkFxiQsUp6.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 6115