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Another training paradigm is associated with physics-informed machine learning. In particular, [[physics-informed neural networks]] (PINNs) use complete physics laws to fit neural networks to solutions of PDEs. Extensions of this paradigm to operator learning are broadly called physics-informed neural operators (PINO),<ref name="PINO">{{cite arXiv |last1=Li |first1=Zongyi | last2=Hongkai| first2=Zheng |last3=Kovachki |first3=Nikola | last4=Jin | first4=David | last5=Chen | first5= Haoxuan |last6=Liu |first6=Burigede | last7=Azizzadenesheli |first7=Kamyar |last8=Anima |first8=Anandkumar |title=Physics-Informed Neural Operator for Learning Partial Differential Equations |date=2021 |class=cs.LG |eprint=2111.03794 }}</ref> where loss functions can include full physics equations or partial physical laws. As opposed to standard PINNs, the PINO paradigm incorporates a data loss (as defined above) in addition to the physics loss <math>\mathcal{L}_{PDE}(a, \mathcal{G}_\theta (a))</math>. The physics loss <math>\mathcal{L}_{PDE}(a, \mathcal{G}_\theta (a))</math> quantifies how much the predicted solution of <math>\mathcal{G}_\theta (a)</math> violates the PDEs equation for the input <math>a</math>.
== See also ==
* [[Neural network (machine learning)|Neural network]]
* [[Physics-informed neural networks]]
* [[Neural field]]
== References ==
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