Główne pojęcia
A robust framework that seamlessly integrates symbolic mathematics and automatic equation embedding to discover open-form partial differential equations from limited and noisy data.
Streszczenie
The proposed R-DISCOVER framework consists of two primary procedures: discovering and embedding.
Discovering Process:
- The framework utilizes a RL-guided hybrid PDE generator to efficiently generate diverse open-form PDE expressions represented as binary tree structures.
- A neural network-based predictive model is built to fit the system response and serve as a reward evaluator for the generated PDE expressions.
- The RL agent is updated using the risk-seeking policy gradient method with the better-fitting PDE expressions.
- A parameter-free model selection method is proposed to determine the initially identified PDE by balancing data fitness and coefficient stability.
Embedding Process:
- The initially identified PDE is automatically incorporated as a physical constraint into the neural network-based predictive model by traversing the PDE tree.
- The predictive model is then optimized with the discovered PDE constraint and the observed data, enhancing the robustness to noise.
The alternating updates of the discovering and embedding processes enable the framework to uncover accurate governing equations from nonlinear dynamic systems with limited and highly noisy data, outperforming other physics-informed neural network-based discovery methods.
Statystyki
The relative error of the coefficients between the uncovered and true equations can be as low as 5%.
The true positive rate, which measures the accuracy of the identified equation form, can reach 1, indicating the correct equation form has been successfully retrieved.
Cytaty
"The proposed framework seamlessly integrates symbolic mathematics and automatic equation embedding to robustly discover open-form partial differential equations from nonlinear systems."
"The RL-guided hybrid PDE generator can efficiently generate diverse open-form PDE expressions, while the automatic embedding of discovered equations enhances the robustness to noise."
"The alternating updates of discovering and embedding processes enable the framework to uncover accurate governing equations from limited and highly noisy data."