The coefficient map, not the basis, limits how machine-learning surrogates of metal–organic framework water-adsorption beds transfer to unseen materials
- 1Faculty of Mechanical Engineering, Yıldız Technical University, Yıldız Campus, Barbaros Bulvarı, Beşiktaş, Istanbul, 34349
Abstract
Machine-learning surrogates could let designers of metal–organic framework (MOF) water harvesters screen many candidate adsorbents without solving the transport equations for each. A surrogate fails on an unseen material for one of two reasons: its reduced basis cannot represent the true field, or its map from material parameters to basis coefficients predicts the wrong coefficients. Which one limits accuracy decides where method development should go, yet it is rarely measured. We measure it for a one-dimensional, non-isothermal convection–dispersion–adsorption model of a packed bed, verified against 4 closed-form solutions and compared, unfitted, with a published MOF-303 breakthrough curve. Seven explanations of the error were registered in advance, each with the evidence that would eliminate it, and tested on 240 held-out materials in five folds, with a cluster bootstrap that corrects for choosing the best configuration on the test materials. Beyond the first few modes the map, not the basis, limits accuracy: refining the basis 90× changes a per-mode map’s error by 0.9 % and a DeepONet’s by 12 %. More training materials still help (error ∝ N_mat^(-0.222)) and larger models are not ruled out, while Kolmogorov–Arnold networks lose to a same-size perceptron in every comparison by point estimate (exploratory, 12 materials). A physics-residual loss at a small weight improves transfer by 9 % (48 materials); larger weights hurt. Learning beats fitted closed forms 2.44-fold, yet a coarse finite-volume solve is more accurate than the perceptron surrogates (3.1 % normalised error) and cheaper below about 25,400 queries. Effort is better spent on the coefficient map and on training data than on richer bases.
Related
- Machine learning surrogates for multi-geometry EDGE2D-EIRENE studies of MAST Upgrade
- Learning on-the-fly quasi-stationarity diagnostics from low-dimensional surrogates
- Fracture-Bench: A Controlled Benchmark Suite for Machine Learning Surrogates in Phase-Field Fracture Mechanics
- A Transport Framework for Evaluating Nanoscale Interconnect Materials
- A locally ab initio computational framework for arbitrary incommensurate materials interfaces
BibTeX
@misc{batayhi2026coefficient,
title = {{The coefficient map, not the basis, limits how machine-learning surrogates of metal–organic framework water-adsorption beds transfer to unseen materials}},
author = {Abdulhamid Batayhi},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15010365/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010365/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - The coefficient map, not the basis, limits how machine-learning surrogates of metal–organic framework water-adsorption beds transfer to unseen materials
AU - Abdulhamid Batayhi
PY - 2026
DA - 2026/10/13
PB - ChemRxiv
DO - 10.26434/chemrxiv.15010365/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010365/v1
AB - Machine-learning surrogates could let designers of metal–organic framework (MOF) water harvesters screen many candidate adsorbents without solving the transport equations for each. A surrogate fails on an unseen material for one of two reasons: its reduced basis cannot represent the true field, or its map from material parameters to basis coefficients predicts the wrong coefficients. Which one limits accuracy decides where method development should go, yet it is rarely measured. We measure it for a one-dimensional, non-isothermal convection–dispersion–adsorption model of a packed bed, verified against 4 closed-form solutions and compared, unfitted, with a published MOF-303 breakthrough curve. Seven explanations of the error were registered in advance, each with the evidence that would eliminate it, and tested on 240 held-out materials in five folds, with a cluster bootstrap that corrects for choosing the best configuration on the test materials. Beyond the first few modes the map, not the basis, limits accuracy: refining the basis 90× changes a per-mode map’s error by 0.9 % and a DeepONet’s by 12 %. More training materials still help (error ∝ N_mat^(-0.222)) and larger models are not ruled out, while Kolmogorov–Arnold networks lose to a same-size perceptron in every comparison by point estimate (exploratory, 12 materials). A physics-residual loss at a small weight improves transfer by 9 % (48 materials); larger weights hurt. Learning beats fitted closed forms 2.44-fold, yet a coarse finite-volume solve is more accurate than the perceptron surrogates (3.1 % normalised error) and cheaper below about 25,400 queries. Effort is better spent on the coefficient map and on training data than on richer bases.
ER -