Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next

Abstract Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. The study indicates that most research has focused on customizing the PINN through different activation functions, gradient optimization techniques, neural network structures, and loss function structures.

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• 1 PINNs are nowadays used to solve PDEs, fractional equations, integral-differential equations, and stochastic PDEs.
• 2 This novel methodology has arisen as a multi-task learning framework in which a NN must fit observed data while reducing a PDE residual.
• 3 This article provides a comprehensive review of the literature on PINNs: while the primary goal of the study was to characterize these networks and their related advantages and disadvantages.

This research advances how AI systems learn, reason, and solve problems — with direct implications for automation and scientific discovery.

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