STL-based Optimization of Biomolecular Neural Networks for Regression and Control

Abstract: Biomolecular Neural Networks (BNNs), artificial neural networks with biologically synthesizable architectures, achieve universal function approximation capabilities beyond simple biological circuits. However, training BNNs remains challenging due to the lack of target data. To address this, we propose leveraging Signal Temporal Logic (STL) specifications to define training objectives for BNNs. We build on the quantitative semantics of STL, enabling gradient-based optimization of the BNN weights, and introduce a learning algorithm that enables BNNs to perform regression and control tasks in biological systems. Specifically, we investigate two regression problems in which we train BNNs to act as reporters of dysregulated states, and a feedback control problem in which we train the BNN in closed-loop with a chronic disease model, learning to reduce inflammation while avoiding adverse responses to external infections. Our numerical experiments demonstrate that STL-based learning can solve the investigated regression and control tasks efficiently.