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- W3199123167 abstract "Data-driven discovery of partial differential equations (PDEs) has achieved considerable development in recent years. Several aspects of problems have been resolved by sparse regression-based and neural-network-based methods. However, the performance of existing methods lacks stability when dealing with complex situations, including sparse data with high noise, high-order derivatives, and shock waves, which bring obstacles to calculating derivatives accurately. Therefore, a robust PDE discovery framework, called the robust deep-learning genetic algorithm (R-DLGA), that incorporates the physics-informed neural network (PINN) is proposed in this paper. In the framework, preliminary results of potential terms provided by the DLGA are added into the loss function of the PINN as physical constraints to improve the accuracy of derivative calculation. It assists in optimizing the preliminary result and obtaining the ultimately discovered PDE by eliminating the error compensation terms. The stability and accuracy of the proposed R-DLGA in several complex situations are examined for proof and concept, and the results prove that the proposed framework can calculate derivatives accurately with the optimization of the PINN and possesses surprising robustness for complex situations, including sparse data with high noise, high-order derivatives, and shock waves." @default.
- W3199123167 created "2021-09-27" @default.
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- W3199123167 date "2021-09-21" @default.
- W3199123167 modified "2023-10-15" @default.
- W3199123167 title "Robust discovery of partial differential equations in complex situations" @default.
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- W3199123167 doi "https://doi.org/10.1103/physrevresearch.3.033270" @default.
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