# Differentiable Hybrid Modelling for Learning and Optimising Chemical Transport Processes from Experimental Data

arXiv: https://arxiv.org/abs/2609.04011 · HTML: https://mlsanity.com/paper/2609.04011/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 45 references that are in the map.
- First posted on arXiv 3 Sep 2026.

## Builds on (most cited first, 7 of 7)

- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Physics-based Deep Learning](https://mlsanity.com/paper/2109.05237/) (2021)
- [On structural and practical identifiability](https://mlsanity.com/paper/2102.05100/) (2021)
- [A Hybrid Science-Guided Machine Learning Approach for Modeling and Optimizing Chemical Processes](https://mlsanity.com/paper/2112.01475/) (2021)
- [Physics-Constrained Machine Learning for Chemical Engineering](https://mlsanity.com/paper/2508.20649/) (2025)
- [Modern, Efficient, and Differentiable Transport Equation Models using JAX: Applications to Population Balance Equations](https://mlsanity.com/paper/2411.00742/) (2024)
- [Modeling Batch Crystallization under Uncertainty Using Physics-informed Machine Learning](https://mlsanity.com/paper/2602.07184/) (2026)

## Abstract (arXiv)

Transport models underpin the design and optimisation of chemical processes, yet their constitutive laws are typically hand-picked, their experimental initial conditions are assumed exact, and their computational cost restricts optimisation to a handful of process variables. Here we introduce a differentiable hybrid modelling framework that embeds neural networks within a GPU-accelerated population balance equation solver to discover constitutive laws and assimilate initial conditions directly from experimental crystallisation data. Using thirteen real experiments with multi-dimensional size and shape measurements, we show that treating measured initial conditions as exact yields a physically inconsistent rate law despite improved predictive accuracy, whereas assimilating them recovers a physically consistent, non-linear law and reduces trajectory error sevenfold relative to conventional modelling. End-to-end differentiability further enables gradient-based optimisation of high-dimensional operating profiles, identifying a 300-variable temperature profile that reduces crystal aspect ratio by 25% at constant mass, facilitating superior product attributes. Our framework augments, rather than replaces, mechanistic modelling, offering a general route to learning transport models from data and optimising processes with them.