Feasibility And Verification Analysis Of Deep Learning Model For Dynamic System Modeling

In the past few years,deep learning models have achieved great success in various applications.However,this data-driven approach is often criticized for lack of interpretability.The research on the universality of deep learning models provides strong theoretical support for the feasibility of deep learning models: it proves that the success of this kind of network in application so far is not accidental,but reflects the universal approximation ability of this kind of network,that is,denseness in mathematics.Thanks to their depth and special connection structure,the convolutional neural network(CNN)is a popular deep learning model to handle various complicated tasks.Recent years,approximation theory has achieved many results in the field of deep learning.However,these results and conclusions can rarely be directly applied to the solution of practical problems or directly guide the training and optimization of deep learning models in the actual context.To address this issue,we propose the construction of a generic CNN based on the universality theory.It is ensured that the approximation error of such CNN is bounded by an explicit approximation upper bound that is related to the hyperparameters of this model from the theoretical verification.Moreover,we generalize the conclusion of the universality property of convolutional neural network to a general case of multidimensional data sets,thereby making the CNNs suitable for not only one-dimensional,but also multidimensional inputs and outputs.Specifically,taking the operation of normalization as a widely used technique into consideration,we then show that this operation does not take effect on the approximation performance of the original neural network.In order to verify the relationship between the approximation upper bound of the network and hyperparameters,we conducted experiments with a practical problem in the field of inertial guidance as the background.At the same time,we demonstrated that the theory can directly guide the experimental process,optimize the experimental results,and actually break the barrier between theory and application.We use the curve similarity index defined by Frechet distance to prove that the experimental results are highly consistent with the functional relationship given by the theory,which also shows that we can use the approximation upper bound in the theory to guide the training process of CNN in some sense.This paper explores the theoretical feasibility of the deep learning model through the research of the universal approximation of the deep learning model.Based on the universality theory,we provide a specific CNN model with definite approximation ability.By modeling the appropriate dynamic model data,the approximation upper bound is verified.At the same time,it also provides an example for the application of the approximation theory of the convolutional neural network,and reveals that the approximation theory has guiding significance for practical training.