Learning Biomolecular Models using Signal Temporal Logic

Abstract: Modeling dynamical biological systems is key for understanding, predicting, and controlling complex biological behaviors. Traditional methods for identifying governing equations, such as ordinary differential equations (ODEs), typically require extensive quantitative data, which is often scarce in biological systems due to experimental limitations. To address this challenge, we introduce an approach that determines biomolecular models from qualitative system behaviors expressed as Signal Temporal Logic (STL) statements, which are naturally suited to translate expert knowledge into computationally tractable specifications. Our method represents the biological network as a graph, where edges represent interactions between species, and uses a genetic algorithm to identify the graph. To infer the parameters of the ODEs modeling the interactions, we propose a gradient-based algorithm. On a numerical example, we evaluate two loss functions using STL robustness and analyze different initialization techniques to improve the convergence of the approach.