Developing robust and predictive dynamical state-space models, such as ODEs, PDEs, and Boolean models, remains a key challenge in systems biology. These models often face difficulties due to limited data, leading to underdetermined model structures and an extensive parameter space. This presentation focuses on Physics-Informed Machine Learning, combining Mathematical Modeling and Machine Learning with fundamental physical principles. By incorporating concepts like the Variational Principle, Lagrangian, and Hamiltonian into computational algorithms, we aim to enhance the predictive capabilities for systems biology dynamics. This includes symmetry-induced velocity prediction from position data for non-conservative systems biology models. Through this integrative approach, which includes both modelling and simulation, we seek to improve our understanding of the complex dynamics in biological systems.
