In systems biology, complex mechanistic models are widely used to understand biological processes. Recently, multi-objective optimization has provided a useful framework for studying whether multiple biological objectives can be optimized simultaneously or whether improving one objective necessarily degrades another, i.e., whether an intrinsic trade-off exists. This question is characterized by the Pareto frontier. In this context, Pareto analysis can help biologists identify shared mechanisms across species by revealing which objectives can be jointly optimized and which cannot. However, computing the Pareto frontier is often computationally expensive. Existing approaches typically rely on brute-force exploration of the feasible region, which is inefficient and may still fail to recover the frontier under limited sampling budgets and the curse of high dimensionality. To address this challenge, we propose a physics-guided learning-based method for efficient and accurate Pareto frontier approximation from limited data. Rather than exhaustively searching the feasible space, our method directly optimizes inputs toward the frontier boundary, substantially reducing computational cost while improving frontier coverage. We apply our method to data-driven analysis of BMP signaling. The resulting Pareto structures are consistent with established biological findings, demonstrating the practical utility of our approach for biological process understanding.

Co-authors: Shenyu Lu, David Umulis, Xiaoqian Wang