BINN: A deep learning approach for computational mechanics problems based on boundary integral equations

We proposed the boundary-integral type neural networks (BINN) for boundary value problems in computational mechanics. The integral equations are employed to transfer all unknowns boundary, then approximated using and solved through a training process. loss function is chosen as residuals of equations. Regularization techniques adopted efficiently evaluate weakly singular Cauchy principal integrals Potential elastostatic mainly concerned this article demonstration. method has several outstanding advantages: First, dimensions original problem reduced by one, thus degrees freedom greatly reduced. Second, does not require any extra treatment introduce conditions, since they naturally considered Therefore, suitable complex geometries. Third, BINN on infinite or semi-infinite domains. Moreover, can easily handle heterogeneous with single network without domain decomposition.