Sequential Importance Sampling for Hybrid Model Bayesian Inference to Support Bioprocess Mechanism Learning and Robust Control

Abstract

Driven by the critical needs of biomanufacturing 4.0, we present a probabilistic knowledge graph hybrid model characterizing complex spatial-temporal causal interdependencies of underlying bioprocessing mechanisms. It can faithfully capture the important properties, including nonlinear reactions, partially observed state, and nonstationary dynamics. Given limited process observations, we derive a posterior distribution quantifying model uncertainty, which can facilitate mechanism learning and support robust process control. To avoid evaluation of intractable likelihood, Approximate Bayesian Computation sampling with Sequential Monte Carlo (ABC-SMC) is developed to approximate the posterior distribution. Given high stochastic and model uncertainties, it is computationally expensive to match process output trajectories. Therefore, we propose a linear Gaussian dynamic Bayesian network (LG-DBN) auxiliary likelihood-based ABC-SMC algorithm. Through matching observed and simulated summary statistics, the proposed approach can dramatically reduce the computation cost and improve the posterior distribution approximation.

Integrate Bioprocess Mechanisms into Modeling, Analytics, and Control Strategies to Advance Biopharmaceutical Manufacturing and Delivery Processes

“…x θ θ θ where p(θ θ θ ) represents the prior distribution. Since the likelihood evaluation of KG hybrid model with high fidelity, that can faithfully capture the critical properties of bioprocess, is intractable, i.e., p(τ τ τ x |θ θ θ ) = • • • p(τ τ τ|θ θ θ )dz z z 1 • • • dz z z H+1 , approximate Bayesian computation sampling with Sequential Monte Carlo (ABC-SMC) is developed to approximate the posterior distribution [77,80]. In the naive ABC implementation, we draw a candidate sample from the prior θ θ θ ∼ p(θ θ θ ) and then generate a simulation dataset D from the hybrid model.…”

“…The ABC-sequential Monte Carlo (ABC-SMC) methods [81,82] can improve the sampling efficiency through: (1) generating candidate samples from updated posterior approximates by using sequential importance sampling (SIS); and (2) matching selected summary statistics, denoted by η(D), instead trajectory observations. Following the spirit of the auxiliary likelihood-based ABC [82], we create a linear Gaussian dynamic Bayesian network (LG-DBN) auxiliary model to derive summary statistics for ABC-SMC that can accelerate online inference on hybrid models with high fidelity characterizing complex bioprocessing mechanisms and rich properties [80]. This simple LG-DBN auxiliary model, in conjunction with SIS, can capture the critical dynamics and variations of bioprocess trajectory, ensure the computational efficiency, and enable high quality of inference, which can facilitate mechanism online learning and support robust process control.…”