Controlled Neural Koopman Machine for Interpretable Longitudinal Personalized Alzheimer’s Disease Forecasting

Effective longitudinal prediction of cognitive decline requires more than extrapolating present cognitive scores; it should also aim to infer the future trajectory of cognition. Nevertheless, performing longitudinal future forecasting using existing heterogeneous biological data, accommodating irregular and incomplete observations, and generalizing across cohorts is a challenging task in both biological sciences and machine learning. In this paper, we introduce the Neural Koopman Machine (NKM), a multimodal forecaster that integrates group-wise biological encoders, subject-conditioned control, and a spectrally normalized shared Koopman transition. NKM explicitly separates stable population-level dynamics from individualized, observation-driven forecasting while omitting past cognitive-history inputs. In subject-level five-fold outer evaluation with model selection restricted to an inner validation split on 949 participants from the Alzheimer's Disease Neuroimaging Initiative (ADNI), NKM achieves an outer-test macro Pearson correlation of ${0.622\pm0.053}$ across three different cognitive score metrics (CDRSB, MMSE, and ADAS13), exceeding various competitive multi-target baselines in every outer fold within the experimental setup (paired fold bootstrap $\Delta r=+0.059$, 95\% percentile CI $[0.038,0.079]$). Further, when evaluated in zero-shot transfer from ADNI data to data from 141 participants from the Australian Imaging, Biomarkers and Lifestyle (AIBL) study, NKM attains the lowest MMSE MAE (${1.902\pm0.169}$) and the highest Pearson correlation ($r={0.392\pm0.092}$) among all benchmarked forecasters. In-depth analysis of the learned operators reveals rapidly decaying autonomous dynamics, while ablations identify the subject-conditioned control mechanism as the model's most influential component. Together, these results show that controlled contractive dynamics provide an effective and interpretable inductive bias for multimodal cognitive forecasting.