Introductory Notes on Learning$^2$
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The Flow has not summarised this story yet — read it at arXiv Machine Learning.
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.
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.
arXiv:2609.35884v1 Announce Type: new Abstract: Divergence-free vector fields are fundamental state variables in incompressible flows and many PDE systems. Redundant parameterizations, including Neur...
arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.
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.
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.