In this work, we applied and evaluated modified inferential proper orthogonal decomposition (POD)/machine learning (ML) to a steam reformer for 5-kW high-temperature proton-exchange membrane fuel cells (HT-PEMFC) involving heterogeneous chemical reactions, combustion, and fluid flow. The number of snapshots is limited by the inverse problem of a steam reformer yielding an intractable computational burden, and a limited number of snapshots and modes can yield unfavorable POD subspace projection results. In order to solve this problem, characteristic vectors are derived from the residual after POD projection and employed to the feature. We analyzed the details and distribution of the characteristic vector and investigated the extent of its influence on the inferential POD. Consequently, inferential POD/ML is improved by adding the characteristic vector of observation to the feature for ML. (C) 2018 Elsevier Ltd. All rights reserved.