The summary of the study of sifan wang, yujun teng, and paris perdikaris, "understanding and mitigating gradient flow pathologies in physics-informed neural networks," is given below.
<h3>What was the study about?</h3>
Due to the consistent spread use of neural networks in a lot of scientific domains often tends to bring a lot of constraining them to satisfy some symmetries.
Therefore, the study seeks to know and examine a fundamental mode of failure of the methods that is related to numerical stiffness which can result in unbalanced back-propagated gradients in course of model training.
The study concluded a they did developed and provided a new insights into the area of training of constrained neural networks and constant improvement of the predictive accuracy of physics-informed neural networks using the factor of 50--100× in all of the range of problems in regards to computational physics.
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