Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay di...Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay differential equations(DDEs)and delay integrodifferential equations(DIDEs)with constant delays,primarily due to their low regularity at delayinduced breaking points.In this paper,a DNN method that combines multi-task learning(MTL)which is proposed to solve both the forward and inverse problems of DIDEs.The core idea of this approach is to divide the original equation into multiple tasks based on the delay,using auxiliary outputs to represent the integral terms,followed by the use of MTL to seamlessly incorporate the properties at the breaking points into the loss function.Furthermore,given the increased training dificulty associated with multiple tasks and outputs,we employ a sequential training scheme to reduce training complexity and provide reference solutions for subsequent tasks.This approach significantly enhances the approximation accuracy of solving DIDEs with DNNs,as demonstrated by comparisons with traditional DNN methods.We validate the effectiveness of this method through several numerical experiments,test various parameter sharing structures in MTL and compare the testing results of these structures.Finally,this method is implemented to solve the inverse problem of nonlinear DIDE and the results show that the unknown parameters of DIDE can be discovered with sparse or noisy data.展开更多
提出了适用于无共享结构并行数据库实时多版本两阶段封锁并发控制协议.该协议具有多版本并发控制机制与两阶段封锁机制的优点,使用如下策略以减少延误截止时间事务数量:若冲突集中有比持锁事务Ti优先级高的事务,且Ti重启动不会延误截止...提出了适用于无共享结构并行数据库实时多版本两阶段封锁并发控制协议.该协议具有多版本并发控制机制与两阶段封锁机制的优点,使用如下策略以减少延误截止时间事务数量:若冲突集中有比持锁事务Ti优先级高的事务,且Ti重启动不会延误截止时间,则Ti重启动,冲突集中优先级最高的事务获得锁;否则,冲突集中其他事务等待.通过仿真模拟,与HP2PL和OCC TI WAIT 50协议进行比较,结果表明:在正常负载、长短事务混合的情况下,并发控制协议能有效地降低事务延误截止时间率、事务重启动率,减少同步开销,该协议比HP2PL和OCC TI WAIT 50协议性能更好,同时具有较强的扩展性.展开更多
文摘Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay differential equations(DDEs)and delay integrodifferential equations(DIDEs)with constant delays,primarily due to their low regularity at delayinduced breaking points.In this paper,a DNN method that combines multi-task learning(MTL)which is proposed to solve both the forward and inverse problems of DIDEs.The core idea of this approach is to divide the original equation into multiple tasks based on the delay,using auxiliary outputs to represent the integral terms,followed by the use of MTL to seamlessly incorporate the properties at the breaking points into the loss function.Furthermore,given the increased training dificulty associated with multiple tasks and outputs,we employ a sequential training scheme to reduce training complexity and provide reference solutions for subsequent tasks.This approach significantly enhances the approximation accuracy of solving DIDEs with DNNs,as demonstrated by comparisons with traditional DNN methods.We validate the effectiveness of this method through several numerical experiments,test various parameter sharing structures in MTL and compare the testing results of these structures.Finally,this method is implemented to solve the inverse problem of nonlinear DIDE and the results show that the unknown parameters of DIDE can be discovered with sparse or noisy data.
文摘提出了适用于无共享结构并行数据库实时多版本两阶段封锁并发控制协议.该协议具有多版本并发控制机制与两阶段封锁机制的优点,使用如下策略以减少延误截止时间事务数量:若冲突集中有比持锁事务Ti优先级高的事务,且Ti重启动不会延误截止时间,则Ti重启动,冲突集中优先级最高的事务获得锁;否则,冲突集中其他事务等待.通过仿真模拟,与HP2PL和OCC TI WAIT 50协议进行比较,结果表明:在正常负载、长短事务混合的情况下,并发控制协议能有效地降低事务延误截止时间率、事务重启动率,减少同步开销,该协议比HP2PL和OCC TI WAIT 50协议性能更好,同时具有较强的扩展性.
