Guaranteeing Conservation of Integrals with Projection in Physics-Informed Neural Networks

arXiv:2511.09048v2 Announce Type: replace Abstract: We propose a novel projection method that guarantees the conservation of integral quantities in Physics-Informed Neural Networks (PINNs). While the soft constraint that PINNs use to enforce the structure of partial differential equations (PDEs) enables necessary flexibility during training, it also permits the discovered solution to violate physical laws. To address this, we introduce a projection method that guarantees the conservation of the linear and quadratic integrals, both separately and jointly. We derived the projection formulae by s

Source: arXiv cs.LG — read the full report at the original publisher.

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