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Up to data, the multi-dimension sensors (e.g. multi-axis force/moment sensors) still were considered as linear systems and linear system theory based dynamic decoupling and compensating methods then has been used for improving their dynamic performance. In the paper, a novel and practical neural network based left-inverse system dynamic decoupling and compensating (NNLISDDC) method is proposed for generic nonlinear multi-dimension sensors instead of well-used linear ones. Consequently, the proposed method is not only of prime theoretical interest but also, in practical implementation, can obtain better dynamic performance. A six-axis wrist force sensor is illustrated as an example to validate that the proposed method can markedly improve dynamic performance of the multi-dimension sensors and is superior to previous methods.