Hybrid Modeling of the Reversed‐Phase Chromatographic Purification of an Oligonucleotide: Few‐Shot Learning From Differentiable Physics Solver‐in‐the‐Loop

Hybrid models integrate mechanistic and data-driven components, effectively addressing the challenges of limited process understanding and data availability typical of biopharmaceutical processes. In this study, we applied a hybrid modeling framework named differentiable physics solver-in-the-loop (DP-SOL) to describe the reversed-phase chromatographic purification of an oligonucleotide, overcoming the mentioned limitations of purely mechanistic and data-driven models. The framework establishes a connection between neural networks (NNs) and mechanistic models through differentiable physical operators and their gradients. We first collected a data set comprising six linear gradient elution experiments at different resin loadings and gradient slopes, split in three experiments each for training and testing, for few-shot learning. The hyperparameters were determined through a grid search, resulting in a NN with two hidden layers and 14 nodes. Compared to a calibrated mechanistic model used for initialization of NN, the DP-SOL hybrid model showed significant performance improvement on both training and testing sets, with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:mrow><mml:msup><mml:mi>R</mml:mi> <mml:mn>2</mml:mn></mml:msup> <mml:mspace></mml:mspace> <mml:mo>></mml:mo></mml:mrow> </mml:mrow> </mml:semantics> </mml:math> 0.97 for the former. The good predictivity of DP-SOL is attributed to the combination of mechanistic models and NNs at the solver level. As a novel and versatile hybrid modeling paradigm, DP-SOL has the potential to significantly impact modeling approaches in the downstream processing field and the broader biopharmaceutical sector.