Inverse modeling of porous flow through deep neural networks: the case of coffee percolation
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912709056921600 |
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| author | Barletta, Antoniorenee Cuomo, Salvatore Egidi, Nadaniela Giacomini, Josephin Maponi, Pierluigi |
| author_facet | Barletta, Antoniorenee Cuomo, Salvatore Egidi, Nadaniela Giacomini, Josephin Maponi, Pierluigi |
| contents | This work addresses the inverse problem of espresso coffee extraction, in which one aims to reconstruct the brewing conditions that generate a desired chemical profile in the final beverage. Starting from a high-fidelity multiphysics percolation model, describing fluid flow, solute transport, solid, liquid reactions, and heat exchange within the coffee bed, we derive a reduced forward operator mapping controllable brewing parameters to the concentrations of the main chemical species in the cup. From a mathematical standpoint, we formalize the structural requirements for the local solvability of inverse problems, providing a minimal analytical condition for the existence of a (local) inverse map: continuous differentiability of the forward operator and a locally constant, nondegenerate Jacobian rank. Under these assumptions, the Constant Rank Theorem ensures that the image of the forward operator is a smooth embedded manifold on which well-defined local right-inverses exist.
Extensive experiments, including off-grid validation, show that the learned inverse map accurately reconstructs brewing temperature, grind size, and powder composition. The resulting framework combines rigorous analytical guarantees with modern data-driven methods, providing a principled and computationally efficient solution to the inverse extraction problem and enabling personalised brewing, recipe optimisation, and integration into smart coffee-machine systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11194 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverse modeling of porous flow through deep neural networks: the case of coffee percolation Barletta, Antoniorenee Cuomo, Salvatore Egidi, Nadaniela Giacomini, Josephin Maponi, Pierluigi Numerical Analysis This work addresses the inverse problem of espresso coffee extraction, in which one aims to reconstruct the brewing conditions that generate a desired chemical profile in the final beverage. Starting from a high-fidelity multiphysics percolation model, describing fluid flow, solute transport, solid, liquid reactions, and heat exchange within the coffee bed, we derive a reduced forward operator mapping controllable brewing parameters to the concentrations of the main chemical species in the cup. From a mathematical standpoint, we formalize the structural requirements for the local solvability of inverse problems, providing a minimal analytical condition for the existence of a (local) inverse map: continuous differentiability of the forward operator and a locally constant, nondegenerate Jacobian rank. Under these assumptions, the Constant Rank Theorem ensures that the image of the forward operator is a smooth embedded manifold on which well-defined local right-inverses exist. Extensive experiments, including off-grid validation, show that the learned inverse map accurately reconstructs brewing temperature, grind size, and powder composition. The resulting framework combines rigorous analytical guarantees with modern data-driven methods, providing a principled and computationally efficient solution to the inverse extraction problem and enabling personalised brewing, recipe optimisation, and integration into smart coffee-machine systems. |
| title | Inverse modeling of porous flow through deep neural networks: the case of coffee percolation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2511.11194 |