Oil Production Forecasting Under Asymmetric Temporal Dynamics Using Signature-Weighted Kolmogorov–Arnold Network

Accurate production forecasting of oil wells is of great significance for reservoir management, production optimization, and investment decisions. However, complex subsurface dynamics and sudden operational interventions frequently break the temporal symmetry of production sequences, generating highly asymmetric data distributions. Standard deep sequence architectures often suffer from severe phase lag and limited adaptability when modeling such asymmetric regime transitions. To resolve these bottlenecks, we introduce the Signature-Weighted Kolmogorov–Arnold Network with Gated Recurrent Units (SigKAN-GRU). The architecture replaces static node activations with adaptive edge–spline mappings, enabling robust approximation of asymmetric nonlinearities. Path signatures compress high-order asymmetric temporal trajectories into invariant geometric features, a learnable gating kernel filters critical variations, and a final GRU layer enforces explicit sequential memory. This integration bridges long-term depletion trends with abrupt asymmetrical perturbations while maintaining structurally controlled complexity and an interpretable decomposition of nonlinear response and temporal weighting. Validated on two real-world wells with contrasting data characteristics, SigKAN-GRU consistently minimizes absolute error metrics and phase distortions against prevailing baselines. In addition, event-sensitive evaluations further confirm its reliability in peak regions and abrupt shock intervals. The resulting framework translates erratic historical data into robust deterministic forecasts, offering a rigorous quantitative tool for field-level reservoir optimization.