Multi-objective discovery of PDE systems using evolutionary approach
This work addresses a domain-specific problem for researchers in computational physics or applied mathematics by enabling more interpretable and applicable PDE system discovery, though it is incremental as it builds on existing evolutionary approaches.
The paper tackled the problem of discovering systems of partial differential equations (PDEs) from observational data, which is typically done in a single vector equation form that limits real-world applications, such as when external forcing forms are of interest. It introduced a multi-objective co-evolution algorithm that evolves individual equations and the system simultaneously, enabling the discovery of form-independent equations, and demonstrated this with the two-dimensional Navier-Stokes equation.
Usually, the systems of partial differential equations (PDEs) are discovered from observational data in the single vector equation form. However, this approach restricts the application to the real cases, where, for example, the form of the external forcing is of interest. In the paper, a multi-objective co-evolution algorithm is described. The single equations within the system and the system itself are evolved simultaneously to obtain the system. This approach allows discovering the systems with the form-independent equations. In contrast to the single vector equation, a component-wise system is more suitable for expert interpretation and, therefore, for applications. The example of the two-dimensional Navier-Stokes equation is considered.