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

Keilung Choy; Wei Xie

stat.MLOct 7, 2026

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

Authors: Keilung Choy, Wei Xie

Organizations: Northeastern University

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.

Figures & tables

Figure 1: (A) An illustration of our developed multi-scale mechanistic foundation model with modular design characterizing iPSC cultures [ 33 ] including the modules. (B) Interoperability and in-context learning: Glucose and lactate trends predicted by our Bio-SoS model—trained solely on 2D monolayer data [ 26 ] —closely align with observations from 3D aggregate cultures [ 33 ] .

Figure 2: Schematic flowchart illustration of the proposed actor-simulator framework.

Figure 3: Schematic of the iPSC culture metabolisms and medium-exchange decision problem.

Figure 4: Comparison of calibration performance, measured by the relative parameter-estimation error $\left\|\frac{\widehat{\bm{\theta}}_{n}-\bm{\theta}^{\ast}}{\bm{\theta}^{\ast}}\right\|$ , for the three methods under 20-, 30-, and 40-parameter calibration settings. Solid curves denote means and shaded regions indicate pointwise 95% confidence intervals.

Figure 5: Comparison of policy optimization performance, measured by $J(\widehat{\pi}_{n};\mathcal{M}^{p})$ , for the three methods under 20-, 30-, and 40-parameter calibration settings. Solid curves show means across five training seeds; shaded regions denote pointwise 95% confidence intervals.

Figure 6: Comparison of calibration parameter estimation performance, i.e., $\left\|\frac{\widehat{\bm{\theta}}_{n}-\bm{\theta}^{\ast}}{\bm{\theta}^{\ast}}\right\|$ , obtained by the three candidate approaches in the 20-, 30-, and 40-unknown-parameter settings. Solid curves report the mean and shaded regions denote pointwise 95% confidence intervals.

Figure 7: Comparison of policy optimization performance in terms of $J(\widehat{\pi}_{n};\mathcal{M}^{p})$ obtained by the three candidate approaches in the 20-, 30-, and 40-unknown-parameter settings. Solid curves report the mean and shaded regions denote pointwise 95% confidence intervals.

Figure 8: Reference and calibrated inner–outer metabolic-flux contrasts at 24, 48, and 72 h for aggregate radii of 60, 120, 240, and 360 $\mu$ m. At the 15th iteration, the absolute error in the normalized contrast is below 0.05 for every displayed entry.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

20 parameters in all settings
$v_{max,HK}$	2.92	$v_{max,PGI}$	1.43	$v_{max,PFK/ALD}$	2.16
$v_{max,PGK}$	4.00	$v_{max,PK}$	3.98	$v_{max,fLDH}$	3.28
$v_{max,PyrT}$	0.17	$v_{max,fLacT}$	2.97	$v_{max,OP}$	0.01
$v_{max,NOP}$	0.02	$v_{max,PDH}$	0.22	$v_{max,CS}$	0.43
$v_{max,ME}$	0.51	$v_{max,fMDH}$	1.44	$v_{max,GlnT}$	1.81
$K_{m,NH4}$	0.17	$K_{m,ALA}$	0.20	$K_{m,GLC}$	1.46

Appendix

Table 1: Calibration parameters used in the monolayer and aggregate experiments.

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Digital twins of natural systems must remain aligned with physical systems that evolve over time, are only partially observed, and are typically modeled by mechanistic simulators whose parameters cannot be measured directly. In such settings, model adaptation is naturally posed as a simulation-based inference problem. However, sparse and indirect observations often fail to identify a unique and optimal calibration, leaving several simulator parameterizations compatible with the available evidence. This article presents a GFlowNet-based approach to model adaptation for digital twins of natural systems. We formulate adaptation as a generative modeling problem over complete simulator configurations, so that plausible parameterizations can be sampled with probability proportional to a reward derived from agreement between simulated and observed behavior. Using a controlled environment agriculture case study based on a mechanistic tomato model, we show that the learned policy recovers dominant regions of the adaptation landscape, retrieves strong calibration hypotheses, and preserves multiple plausible configurations under uncertainty.

Abstract

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