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

Macroscopic transport modelling aims to predict traffic flows after proposed public policy interventions, such as a new road or railway section or a temporary road closure. As such, it is a vital step in infrastructure planning and development. Traditionally, building a transport model has relied on complex understanding of socio-economic characteristics of the population requiring expensive data collection via surveys, which are prone to biases. Previous numerical frameworks to optimize transport models to fit observed traffic flows are not easily-interpretable and can lead to overfit. We present here an alternative: a data-driven modelling protocol with objective function based on traffic counts, which can be nowadays cheaply and reliably obtained; explainable model weights; and a controlled path to increase model complexity and accuracy. We demonstrate our approach on several toy and realistic examples, and suggest ways to generalize to multimodal systems including public transport.

Machine learning models are increasingly used to model chemical process systems, yet they often lack principled uncertainty quantification and mechanisms to enforce physical constraints. We propose a probabilistic neural network framework that guarantees satisfaction of linear equality constraints within a given tolerance, while capturing aleatoric uncertainty. Compared to state-of-the-art methods, our formulation demonstrates improved predictive accuracy, uncertainty calibration, and adherence to constraints on reduced data. It also demonstrates competitive performance, but with significantly faster training times when evaluated on large data regimes. We evaluated this on two batch reactor case studies, enforcing mass balances.

Optimising chemical reactions across multiple objectives, such as yield, selectivity, and safety, is central to chemical synthesis, and model-driven approaches depend critically on how reaction components are represented. Established featurisations are either chemically uninformative, as with one-hot encodings, or, as with molecular descriptors, do not readily extend across chemically distinct components. For structurally and functionally diverse components, it is therefore unclear what a shared representation should contain. Constructing such a representation is itself a challenging research undertaking that must be revisited for each new reaction system. Here we bypass this step by learning the reaction representation dynamically from text. Textual descriptions of reaction conditions are encoded by a fine-tuned language model trained jointly with Gaussian process surrogates, yielding task-adaptive representations within a multi-objective Bayesian optimisation loop. Across nickel- and palladium-catalysed cross-couplings in both sequential and parallel experimentation regimes, this approach reaches optimisation convergence in fewer experiments than descriptor libraries or one-hot encoding. Applied prospectively to a palladium-catalysed cyanation spanning mixed ligand denticity and heterogeneous additives, and to a three-objective asymmetric hydrogenation across chiral iridium and ruthenium catalyst families, two rounds of high-throughput experimentation (192 reactions, under 3% of each design space) delivered conditions translating directly to gram scale in 94% and 84% isolated yield, the latter at 99.6% enantiomeric excess.