Physics Informed Neural Networks (PINNs) are neural networks trained to solve a broad class of problems. PINNs is an application of deep learning and neural networks for solving partial differential equations (PDEs).This new technique offers several advantages, such as numerical simplicity compared to conventional schemes because it minimizes the residual of the equation at a predefined set of data known as collocation points.At these points, the predicted solution is obligated to satisfy the differential equation. In this paper we generalize the idea of PINNs for solving partial differential equations by introducing physics informed cellular neural networks (PICNNs). We shall present the predator-prey model and find its solutions by PICNNs. The advantages of the proposed new method are in the fastest algorithms and real time solutions.

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Physics Informed Neural Networks for Solving Predator-Prey Models

  • Angela Slavova,
  • Ventsislav Ignatov

摘要

Physics Informed Neural Networks (PINNs) are neural networks trained to solve a broad class of problems. PINNs is an application of deep learning and neural networks for solving partial differential equations (PDEs).This new technique offers several advantages, such as numerical simplicity compared to conventional schemes because it minimizes the residual of the equation at a predefined set of data known as collocation points.At these points, the predicted solution is obligated to satisfy the differential equation. In this paper we generalize the idea of PINNs for solving partial differential equations by introducing physics informed cellular neural networks (PICNNs). We shall present the predator-prey model and find its solutions by PICNNs. The advantages of the proposed new method are in the fastest algorithms and real time solutions.