New results of deterministic learning-based knowledge fusion

Identifying the unknown dynamics of dynamical systems from observed data is common in science and engineering. Recently, deterministic learning has the ability to achieve locally-accurate modeling of unknown dynamics via neural network. However, locally-accurate modeling only contains local, limited dynamics knowledge along the input trajectory data, making it difficult to adapt to tasks in complex environments. To obtain broader dynamics knowledge, deterministic learning-based knowledge fusion is studied in this paper, i.e., the dynamics knowledge modeled from each individual trajectory via deterministic learning is integrated into a fusion network. Specifically, the fusion problem is formulated as an optimization problem by minimizing a global discrepancy measure over learned local models, which naturally leads to a weighted least-squares formulation with a properly designed weighting matrix that characterizes the optimal fusion dynamics and improves the reliability of the resulting fusion model. Additionally, the fusion algorithm is extended to a distributed fusion algorithm. By using the zero-gradient-sum strategy, the network weight of each node is proven to converge exponentially to the global optimal solution relying only on the weight information of adjacent nodes. Numerical and real-world benchmark results demonstrate the effectiveness of the proposed fusion algorithms.