Differentiable Hybrid Modelling for Learning and Optimising Chemical Transport Processes from Experimental Data
Authors: Arthur Jessop, Mohammed Alsubeihi, Ben Moseley, Ashwin Kumar Rajagopalan
Organizations: Department of Chemical Engineering, The University of Manchester, Manchester, M13 9PL, United Kingdom. · Department of Earth Science and Engineering, Imperial College London, South Kensington, SW7 2BX, United Kingdom. · I-X Centre for AI in Science, Imperial College London, South Kensington, SW7 2BX, United Kingdom.
Reliable transport models are essential when modelling and optimising many chemical engineering processes, yet, most models assume hand-picked constitutive laws which may not reflect reality, and often assume initial conditions are known exactly. Both restrictions can significantly bias model predictions and lead to systematic error when used in predictive and control settings. Black-box neural surrogate alternatives for modelling can better match real example data, but are confined to the task they were trained on and cannot be interrogated for physical consistency. Here we introduce a general-purpose differentiable hybrid modelling framework for transport processes, specifically for the case of population balance equations. Our framework integrates a JAX finite volume population balance solver with learnable neural network components which are trained to both discover constitutive laws and fit initial conditions from real experimental data, allowing us to better model real experimental transport systems. Furthermore, we use our framework for process optimisation, using its differentiability to allow us to direct optimising experimental settings for quantities of interest. This work highlights the huge potential of such differentiable hybrid modelling frameworks for learning and optimising any given chemical separation which involves mass, energy, and/or momentum 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.
Matthew Marsh, Benoit Chachuat, Antonio del Rio Chanona
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.
Joshua W. Sin, David Ming Segura, Bojana Ranković +8
Accurate prediction of polymerization dynamics is essential for process design, control, and optimization. Yet, purely mechanistic models require labor-intensive parameterization of partially characterized kinetics, while purely data-driven models demand large, diverse datasets that are costly to obtain, particularly in early-design stages. We propose a hybrid Neural Ordinary Differential Equation (NODE) framework for data-efficient modeling of free-radical polymerization. Using batch polymerization of methyl methacrylate (MMA) as a case study, the mechanistic mass balances are retained explicitly, and only the partially-characterized effective radical concentration governing monomer consumption is learned from data through a neural network surrogate, while established reactions such as initiator decomposition, propagation, and termination remain physically modeled. The hybrid NODE is evaluated against a discrete-time feedforward neural network and a purely data-driven NODE under sparse data conditions, with models trained on as few as ten measurements under both regular and irregular sampling. The hybrid NODE consistently achieves lower prediction errors and more physically consistent extrapolations than both purely data-driven baselines. In a generalization scenario with noisy data and unseen operating conditions, the hybrid NODE achieves an RMSE of 0.013, compared to 0.31 for the data-driven NODE and 0.68 for the discrete-time model, demonstrating that learning only a closure term rather than the full dynamics is sufficient for reliable prediction under limited data availability.