# Robust discovery of partial differential equations in complex situations

@article{Xu2021RobustDO, title={Robust discovery of partial differential equations in complex situations}, author={Hao Xu and Dongxiao Zhang}, journal={ArXiv}, year={2021}, volume={abs/2106.00008} }

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 performances of existing methods lack 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… Expand

#### 2 Citations

Sparsistent Model Discovery

- Computer Science, Mathematics
- ArXiv
- 2021

It is shown that the adaptive Lasso will have more chances of verifying the IRC than the Lasso and it is proposed to integrate it within a deep learning model discovery framework with stability selection and error control. Expand

Deep-Learning Discovers Macroscopic Governing Equations for Viscous Gravity Currents from Microscopic Simulation Data

- Physics, Computer Science
- ArXiv
- 2021

Deep-Learning Discovers Macroscopic Governing Equations for Viscous Gravity Currents from Microscopic Simulation Data and finds macroscopic rules for viscous gravity currents from microscopic simulation data. Expand

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