A Context-aware Gated Convex Mixtures of LSTM Experts for Nonlinear System Identification
This work addresses nonlinear and nonstationary system identification using one-step-ahead prediction on the nonlinear autoregressive moving average benchmark with ten-step memory (NARMA-10). Baseline models, including autoregressive models with exogenous input (ARX), nonlinear ARX using a multilayer perceptron (NARX--MLP), and a single long short-term memory network (LSTM), are used to contextualize prediction performance. To improve robustness, multiple LSTM experts are combined through a convex mixture. A standard adaptive convex mixture updates the mixing weights using an error-driven rule with simplex projection, but this mechanism is reactive, hand-tuned, and not end-to-end learnable. The proposed method introduces a context-aware end-to-end mixture-of-experts (MoE) framework in which a differentiable softmax gating network learns context-aware mixing weights jointly with the expert parameters. On stationary NARMA-10, the proposed MoE gating approach achieves performance comparable to the adaptive convex mixture. Under regime-switching dynamics, a controlled frozen-experts ablation isolates the mixing-weight update mechanism and shows that the MoE gate significantly improves robustness, achieving approximately fivefold lower overall test error and about two-and-a-half-fold lower after-switch error.