Neural Network Solves A Classic Risk Mode

Efficient calculation of the bankruptcy probability is useful for guiding enterprise decision making and can effectively prevent bankruptcy and reduce risk,while using traditional numerical methods can only roughly estimate the range of bankruptcy probability,and the precision of traditional extreme learning machine methods is not high enough.Therefore,it is of great theoretical and practical importance to solve the classical risk model with continuous time.The main research results are as follows:(1)An effective optimal adaptive particle swarm optimization triangular neural network(AR-PSO-TNN)is established,which consists of three parts: the particle swarm optimization algorithm(PSO)improved triangular neural network(PSO-TNN),the extreme learning machine with initial conditions(IELM),and an improved reduction algorithm.The results show that PSO-TNN outperforms triangulated neural networks(TNNs)as well as Physics-informed Neural Network(PINNs),and PSO outperforms Aquila Optimizer(AO),Smell Agent Optimization(SAO),African Vultures Optimization Algorithm(AVOA),and Arithmetic Optimization Algorithm(AOA).Considering that the introduction of PSO increases the computational cost,the adaptive reduction algorithm(AR)is proposed to simplify the network structure.The AR-PSO-TNN and PSO-TNN has a significant improvement in accuracy and efficiency.(2)A deep extreme learning machine model(D-ELM)is proposed.It consists of three parts: the traditional extreme learning machine,Bayesian triangular polynomial,and trust region algorithm.The first layer of the hidden layer uses a triangular polynomial optimized by Bayesian optimization algorithm as the activation function,and the initial weights of the second layer are obtained using the traditional extreme learning machine model and the trust region algorithm is used to optimize the loss function.Deepening the network while retaining the advantages of the extreme learning machine.Numerical experiments show that D-ELM outperforms ELM in terms of mean square error,relative error and computation time.