This paper proposes a hybrid framework for modeling and forecasting the term structure of Brent crude oil futures by integrating the dynamic Diebold-Li representation with neural network architectures. Using monthly data from 2001 to 2024, we decompose the futures curve into three latent factors—level, slope, and curvature—and model their temporal evolution through both Multilayer Perceptrons (MLP) and Kolmogorov-Arnold Networks (KAN). The methodology involves estimating the latent factors via the Diebold-Li model, followed by independent out-of-sample forecasts using neural network architectures specifically designed to capture nonlinear dependencies. Forecasting performance is evaluated over multiple horizons (1, 3, 6, and 12 months) using standard metrics such as MSE, MAE, and MAPE. The results reveal that while MLP and KAN architectures exhibit similar accuracy for smoother components like the level factor, KAN demonstrates clear advantages in capturing nonlinearities and short-term fluctuations, particularly in the curvature factor. These findings underscore the potential of interpretable neural network architectures like KAN for improving the transparency and robustness of financial time series forecasting.