LordNet: An Efficient Neural Network for Learning to Solve Parametric Partial Differential Equations without Simulated Data

arXiv:2206.09418v2 Announce Type: replace
Abstract: Neural operators, as a powerful approximation to the non-linear operators between infinite-dimensional function spaces, have proved to be promising in accelerating the solution of partial differential equations (PDE). However, it requires a large amount of simulated data, which can be costly to collect. This can be avoided by learning physics from the physics-constrained loss, which we refer to it as mean squared residual (MSR) loss constructed by the discretized PDE. We investigate the physical information …

abstract approximation arxiv cs.lg data differential function however linear network neural network non-linear operators parametric simulated data solution solve spaces type