Adjoint-Based Calibration and Optimal Control of Stochastic Multiscale Bioprocess Digital Twins

Abstract

We develop a bias-aware digital-twin calibration and control framework for multiscale bioprocess models within a biological systems-of-systems (Bio-SoS) paradigm. The digital twin is represented by a stochastic differential equation (SDE) model and calibrated from sparse, discrete observations using quasi-likelihood estimation and adjoint sensitivity analysis. SDE generator-based moment expansions characterize truncation-induced parameter bias, while forward-backward adjoints quantify how calibration uncertainty propagates to value functions and policy performance. The resulting parameter-error distribution supports both policy-directed adaptive experimental design and uncertainty-aware policy optimization through a second-order Gaussian-averaged objective. We characterize the asymptotic behavior of the resulting exploration criterion and derive a physical-system performance under the optimized policy. To implement these ideas, we develop an Actor-Simulator algorithm that jointly updates model parameters, selects informative experiments, and optimizes control policies. Numerical studies demonstrate improved calibration accuracy, sample efficiency, and control performance relative to state-of-the-art baselines.