Emerging power generation technologies such as solid oxide fuel cells (SOFCs) offer promising pathways for clean and efficient energy conversion. However, their material instability accelerates unexpected degradation, which remains a major barrier to large-scale commercialization. As a practical solution, control and diagnosis systems are integral to optimizing SOFCs’ lifetime and efficiency in real-world operations. Degradation mechanisms induce nonlinear, time-varying patterns in running fuel cells, affecting the effectiveness of control and diagnosis strategies. This study introduces a data-driven machine learning framework for predicting SOFC performance under degradation. Four lab-scale SOFCs were subjected to accelerated degradation tests, generating diverse run-to-failure datasets. To capture the complex, nonstationary dynamics in these data, a dynamic neural network based on Kolmogorov–Arnold approximation theory (DKAN) is developed. DKAN employs univariate splines as learnable activation functions, hierarchically adapting low-dimensional functions to diverse nonlinearities and temporal patterns. Comparative experiments against state-of-the-art sequence models, including LSTM, TCN, WaveNet, DGRU, Informer, and ConvRec, show that DKAN achieves on average 30% lower prediction error (across RMSE, WAPE, and MASE) and 55% faster inference relative to the baselines, while demonstrating superior generalization to unseen degradation patterns. Furthermore, statistical analyses using the Friedman–Nemenyi and ANOVA-Tukey tests confirm the significance of DKAN’s performance improvements across multiple datasets and metrics. These results highlight DKAN’s potential as a lightweight and scalable solution for real-time SOFC diagnostics and control.