arXiv Machine Learning
Aug 14

Structure-preserving uncertainty quantification for GENERIC dynamics

arXiv:2608. 12624v1 Announce Type: new Abstract: Structure-preserving machine learning embeds physical structure directly into model architectures, yet uncertainty quantification (UQ) for such hard-constrained models remains limited because standard UQ methods may violate the encoded admissibility conditions, require architectural modifications, or impose substantial computational costs.

By Zequn He, Celia Reina
arXiv Machine Learning
Jun 11

Structure-Preserving Neural Surrogates with Tractable Uncertainty Quantification

arXiv:2606. 11650v1 Announce Type: new Abstract: Recent advances in scientific machine learning provide a means of near-real-time solution to partial differential equations (PDEs), but lack the theoretical underpinnings of conventional simulators that support contemporary verification and validation.

By Handi Zhang, Adrienne M. Propp, Brooks Kinch, Houman Owhadi, Nathaniel Trask
arXiv Machine Learning
4d ago

Hard Constraint Projection in a Physics Informed Neural Network (Burgers)

This paper extends the hard constraint projection (HCP) method to the nonlinear 1D Burgers' equation, integrating it into a physics‑informed neural network (PINN). By discretising the equation, constructing a constraint matrix, and adding an unlearnable projection layer, the HCP‑PINN enforces the governing PDE during training. Experiments show that the HCP‑PINN achieves higher accuracy—about an order of magnitude lower data error than a standard PINN—and better adherence to the PDE, while being less sensitive to the number and placement of collocation points.

By Miranda J S Horne, Peter K Jimack, Amirul Khan, He Wang