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Computational modelling has been playing an important role in designing and optimizing many engineering systems. Despite great achievements using numerical discretization techniques of partial differential equations (PDEs) arised in computational simulation, incorporating noisy data into existing algorithms is not straightforward, generating finite-element mesh remains complex, solving high-dimensional problems is still challenging. Physics-informed neural networks (PINNs) have emerged as a promising alternative, but the low rate of convergence has been considered as the main weakness of this approach. In this paper we develop and implement the Sobolev-training for physics-informed neural networks with the aim to obtain a more accurate machine learning (ML) procedure for static analysis of simple engineering structures such as rods and beams. It turns out that with a simple modification of the loss function we are able to obtain a much better learning algorithm with high precision for these static problems.

physic-informed neural networks, sobolev training, static analysis.