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A new training paradigm referred to as “gradient boosting” (GB) has been developed to significantly enhance the performance of physics informed neural networks (PINNs) when simulating multi-scale and singular perturbation problems. This approach is based on the idea of employing a sequence of neural networks to solve problems presenting great challenges for traditional PINNs. Numerical experiments have demonstrated the effectiveness of this algorithm through various benchmarks, including comparisons with finite element methods and PINNs.
