Extreme learning machines with Gaussian random field pretraining

Machine learning has become a powerful tool for solving differential equations, offering numerous advantages over traditional methods.However, the unsupervised training of physicsinformed neural networks (PINNs) can result in non-convex loss landscapes.Extreme learning machines (ELMs) address this by fixing internal weights and biases, requiring only the determination of output weights.Although ELMs offer benefits over PINNs, their reliance on randomized basis functions limits their expressiveness.To enhance expressiveness of the ELMs, we pretrain single-layer feedforward neural networks using Gaussian random fields, improving the quality of the basis functions.This method, termed PT-ELM, demonstrates that pretrained basis functions in ELMs yield accurate solutions for boundary layer problems with better convergence patterns.PT-ELM outperforms both traditional ELMs and the recently developed TransNet models.The PT-ELM approach can be adapted for solving data and physics driven problems to enhance predictive ability of the neural networks.