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RAPTOR-GEN: RApid PosTeriOR GENerator for Bayesian Learning in Biomanufacturing

Wandi Xu, Wei Xie

TL;DR

RAPTOR-GEN presents a mechanism-informed Bayesian framework for biomanufacturing that combines a multi-scale probabilistic knowledge graph (pKG) with stochastic differential equations to model SRN-based Bio-SoS dynamics. It introduces a Bayesian Updating pKG-LNA metamodel to achieve tractable likelihoods from sparse, heterogeneous data and a Langevin-diffusion–based LD-LNA sampler to efficiently explore the posterior with finite-sample guarantees. The method yields provable error bounds, including a nonasymptotic $d_{ ext{W}_1}$ bound and asymptotic Bernstein–von Mises consistency, and it is implemented via a one-stage or two-stage RAPTOR-GEN algorithm for fast, robust posterior sampling. Empirical studies on enzyme kinetics and a prokaryotic autoregulation network demonstrate accurate latent-state and parameter recovery with superior efficiency and stability compared to traditional LD-based MCMC and ABC approaches. The framework is positioned to accelerate digital twin development in biomanufacturing and offers adaptable extensions to other Bio-SoS domains and decision-guided control tasks.

Abstract

Biopharmaceutical manufacturing is vital to public health but lacks the agility for rapid, on-demand production of biotherapeutics due to the complexity and variability of bioprocesses. To overcome this, we introduce RApid PosTeriOR GENerator (RAPTOR-GEN), a mechanism-informed Bayesian learning framework designed to accelerate intelligent digital twin development from sparse and heterogeneous experimental data. This framework is built on a multi-scale probabilistic knowledge graph (pKG), formulated as a stochastic differential equation (SDE)-based foundational model that captures the nonlinear dynamics of bioprocesses. RAPTOR-GEN consists of two ingredients: (i) an interpretable metamodel integrating linear noise approximation (LNA) that exploits the structural information of bioprocessing mechanisms and a sequential learning strategy to fuse heterogeneous and sparse data, enabling inference of latent state variables and explicit approximation of the intractable likelihood function; and (ii) an efficient Bayesian posterior sampling method that utilizes Langevin diffusion (LD) to accelerate posterior exploration by exploiting the gradients of the derived likelihood. It generalizes the LNA approach to circumvent the challenge of step size selection, facilitating robust learning of mechanistic parameters with provable finite-sample performance guarantees. We develop a fast and robust RAPTOR-GEN algorithm with controllable error. Numerical experiments demonstrate its effectiveness in uncovering the underlying regulatory mechanisms of biomanufacturing processes.

RAPTOR-GEN: RApid PosTeriOR GENerator for Bayesian Learning in Biomanufacturing

TL;DR

RAPTOR-GEN presents a mechanism-informed Bayesian framework for biomanufacturing that combines a multi-scale probabilistic knowledge graph (pKG) with stochastic differential equations to model SRN-based Bio-SoS dynamics. It introduces a Bayesian Updating pKG-LNA metamodel to achieve tractable likelihoods from sparse, heterogeneous data and a Langevin-diffusion–based LD-LNA sampler to efficiently explore the posterior with finite-sample guarantees. The method yields provable error bounds, including a nonasymptotic bound and asymptotic Bernstein–von Mises consistency, and it is implemented via a one-stage or two-stage RAPTOR-GEN algorithm for fast, robust posterior sampling. Empirical studies on enzyme kinetics and a prokaryotic autoregulation network demonstrate accurate latent-state and parameter recovery with superior efficiency and stability compared to traditional LD-based MCMC and ABC approaches. The framework is positioned to accelerate digital twin development in biomanufacturing and offers adaptable extensions to other Bio-SoS domains and decision-guided control tasks.

Abstract

Biopharmaceutical manufacturing is vital to public health but lacks the agility for rapid, on-demand production of biotherapeutics due to the complexity and variability of bioprocesses. To overcome this, we introduce RApid PosTeriOR GENerator (RAPTOR-GEN), a mechanism-informed Bayesian learning framework designed to accelerate intelligent digital twin development from sparse and heterogeneous experimental data. This framework is built on a multi-scale probabilistic knowledge graph (pKG), formulated as a stochastic differential equation (SDE)-based foundational model that captures the nonlinear dynamics of bioprocesses. RAPTOR-GEN consists of two ingredients: (i) an interpretable metamodel integrating linear noise approximation (LNA) that exploits the structural information of bioprocessing mechanisms and a sequential learning strategy to fuse heterogeneous and sparse data, enabling inference of latent state variables and explicit approximation of the intractable likelihood function; and (ii) an efficient Bayesian posterior sampling method that utilizes Langevin diffusion (LD) to accelerate posterior exploration by exploiting the gradients of the derived likelihood. It generalizes the LNA approach to circumvent the challenge of step size selection, facilitating robust learning of mechanistic parameters with provable finite-sample performance guarantees. We develop a fast and robust RAPTOR-GEN algorithm with controllable error. Numerical experiments demonstrate its effectiveness in uncovering the underlying regulatory mechanisms of biomanufacturing processes.

Paper Structure

This paper contains 46 sections, 26 theorems, 124 equations, 7 figures, 5 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Problem Statement
  4. SDE-based pKG Mechanistic Model of SRN
  5. SDE-based pKG Mechanistic Model of SRN
  6. Likelihood-based Bayesian Inference
  7. Description of Proposed Bayesian Learning Framework
  8. Linear Noise Approximation (LNA) on SDEs with Enhancement
  9. LNA for General SDEs
  10. LNA for pKG of SRN
  11. Enhance LNA Metamodel through Bayesian Updating on the pKG
  12. Langevin Diffusion-Based Linear Noise Approximation (LD-LNA)
  13. Langevin Diffusion (LD) for Efficient Data Fusion and Posterior Inference
  14. LNA for LD
  15. Finite-Sample Convergence Analysis of LD-LNA
  16. ...and 31 more sections

Key Result

Proposition 1

The mean vector $\pmb{m}_t$ and the covariance matrix $\pmb{K}_t$ of the Gaussian variable $\pmb{M}_t$ for any $t > 0$ can be obtained by solving the ODEs in eq:general_SDE_mean and eq:general_SDE_cov with initial values $\pmb{m}_0$ and $\pmb{K}_0$:

Figures (7)

  • Figure 1: Simulated observations of prey using Gillespie algorithm and diffusion approximation with different values of $\Delta t$.
  • Figure 2: An illustration of the proposed Bayesian learning framework.
  • Figure 3: An illustration of Bayesian updating pKG-LNA metamodel.
  • Figure 4: Trajectory inference for four state variables by Bayesian updating pKG-LNA metamodel with three data sizes.
  • Figure 5: Trajectory inference for four state variables by Bayesian updating pKG-LNA metamodel with data size $H=100$.
  • ...and 2 more figures

Theorems & Definitions (55)

  • Example 1: Enzyme Kinetics
  • Remark 1
  • Example 2: Lotka-Volterra Model
  • Remark 2
  • Proposition 1
  • Remark 3
  • Theorem 1
  • Remark 4
  • Remark 5
  • Theorem 2
  • ...and 45 more