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
The increasing deployment of Physics-Informed Neural Networks (PINNs) in scientific and engineering applications necessitates solutions for their current limitations, particularly regarding the conservation of physical laws.
Ensuring physical law conservation in AI models is crucial for their reliable and safe application in critical domains like scientific discovery, engineering design, and climate modeling, where errors can have significant consequences.
This novel projection method enhances the trustworthiness and accuracy of PINNs, expanding their applicability to complex real-world problems where physical consistency is non-negotiable.
- · AI researchers (physics-informed AI)
- · Engineering simulation software providers
- · Scientific computing platforms
- · Industries relying on complex simulations (e.g., aerospace, energy)
- · Traditional simulation methods (in some niche applications)
- · AI models lacking strong physical constraints
Increased adoption of PINNs in scientific and engineering fields due to enhanced reliability.
Faster and more accurate R&D cycles in areas like material science, drug discovery, and climate modeling.
Potential for entirely new discoveries or optimized designs that were previously unachievable with less physically-constrained AI or traditional methods.
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Read at arXiv cs.LG