Physics Informed Machine Learning in Multi Agent Systems: A modular PINN design to solve systems of ordinary differential equations

Sammanfattning

In the area of Physics-Informed Machine Learning, there have been several efforts to combine data-driven modeling with physical and mathematical methods. One emerging technique that does this is Physics-Informed Neural Networks (PINNs). PINNs have been widely studied in recent years to find data driven models that can capture physical and mathematical phenomena described in differential equations. Standard PINNs are useful in some cases, however, they do come with some negative properties, such as not always converging to a valid solution for certain problems. To extend the possibilities of modeling systems of ordinary differential equations, this thesis examines a modular architectural PINN design and compares how it performs compared to a standard PINN. To examine the modular architecture, three problems are studied: 1) a four-agent consensus problem, 2) a two-species standard Lotka-Volterra problem and 3) a generalized Lotka-Volterra problem with 3 species. The findings suggest that the performance of a modular PINN compared to the standard PINN is dependent on the problem at hand. Yet the thesis shows that it is possible to use a modular PINN and that it has the potential to perform well.