Efficient hybrid modeling and sorption model discovery for non-linear advection-diffusion-sorption systems - A systematic scientific machine learning approach

Aug 6, 2026

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This study proposes a systematic scientific machine learning framework to build efficient hybrid models and to discover sorption uptake kinetics in non-linear advection-diffusion-sorption systems. The method trains models with gradient-based optimizers, adjoint sensitivity analysis, and JIT-compiled vector Jacobian products, paired with spatial discretization and adaptive integration. Sparse and symbolic regression are used to identify missing terms inside an artificial neural network, while robustness is evaluated on noisy in-silico breakthrough curve data for fixed-bed adsorption.

LanguageEnglish

CategoryResearch & Report

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Pages25

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Introduction

Hybrid modeling in chemical engineering

Universal Differential Equations and universal approximators

Efficient hybrid modeling and sorption model discovery for non-linear advection-diffusion-sorption systems: A systematic scientific machine learning approach arXiv :2303 . 13555v1 [ cs .CE] 22 Mar 2023 Vinicius Viena Santana* LSRE–LCM †, ALiCE‡ Faculty of Engineering University of Porto [up201700649@edu.fe.up.pt](up201700649@edu.fe.up.pt) Erbet Costa Department of Chemical Engineering Norwegian University of Science and Technology Carine de Menezes Rebello Department of Chemical Engineering Norwegian University of Science and Technology Ana Mafalda Ribeiro LSRE–LCM †, ALiCE‡ Faculty of Engineering University of Porto Christopher Rackauckas JuliaLab Computer Science and Artiﬁcial Intelligence Laboratory Massachusetts Institute of Technology Idelfonso B.R. Nogueira* Department of Chemical Engineering Norwegian University of Science and Technology idelfonso .b.d .r.nogueira@ntnu .no March 27, 2023 Abstract This study presents a systematic machine learning approach for creating eﬃcient hybrid models and discovering sorption uptake models in non-linear advection-diﬀusion-sorption systems. It demonstrates an eﬀective method to train these complex systems using gradientbased optimizers, adjoint sensitivity analysis, and JIT-compiled vector Jacobian products, combined with spatial discretization and adaptive integrators. Sparse and symbolic regression were employed to identify missing functions in the artiﬁcial neural network. The robustness of the proposed method was tested on an in-silico data set of noisy breakthrough curve observations of ﬁxed-bed adsorption, resulting in a well-ﬁtted hybrid model. The study successfully reconstructed sorption uptake kinetics using sparse and symbolic regression, and accurately predicted breakthrough curves using identiﬁed polynomials, highlighting the potential of the proposed framework for discovering sorption kinetic law structures. ∗ To whom correspondence should be addressed †LSRE-LCM (Laboratory of Separation and Reaction Engineering – Laboratory of Catalysis and Materials, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal) ‡ALiCE (Associate Laboratory in Chemical Engineering,, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal) A preprint March 27, 2023 Keywords Hybrid Modeling 􀀁 Scientiﬁc Machine Learning 􀀁 Sparse Regression 􀀁 Advection-DiﬀusionSorption 􀀁 Partial Diﬀerential Equations 1 Introduction Mathematical modeling has been an essential part of science and engineering since its early stages. The use of mathematical models for problem-solving in chemical engineering has become increasingly important due to the exponential growth of computer power. Two main approaches have been used to model systems in chemical engineering: The mechanistic/classical and the empirical approaches [1] . The classical approach encompasses conservation equations, transport, and thermodynamic expressions and can accurately describe the problem. However, simpliﬁcations are often employed to make the problem computationally tractable. The empirical/data-driven models do not make any assumptions about the physics behind the observations, making them ﬂexible. Nevertheless, they are suitable for use in a limited range of process conditions due to their limited extrapolation power [2] . On the other hand, empirical models have gained substantial attention in the last few years with machine learning and deep learning. At the same pace, it is becoming more accepted that mechanistic model errors caused by simpliﬁcations can be compensated with other forms of knowledge, e.g., empirical models [3] . In this sense, hybrid models have received considerable attention in engineering [4, 5] . The "hybrid" term refers to a structure where empirical equations and physics knowledge (conservation laws, operation invariance, etc.) are merged. The merging process for engineering appl

FAQs

What is the main goal of the proposed method?

The approach builds efficient hybrid models and discovers sorption uptake kinetics for non-linear advection-diffusion-sorption systems.

How are the hybrid models trained and optimized?

Training uses gradient-based optimizers, adjoint sensitivity analysis, and JIT-compiled vector Jacobian products, together with spatial discretization and adaptive integrators.

How are missing functions or kinetics terms identified?

Sparse and symbolic regression are employed to reconstruct missing functions inside the artificial neural network and recover sorption uptake kinetics structures.

Aug 6, 2026

Upload by Jiven