基于物理信息神经网络求解带自由边界条件的DCIS问题OA

Solving the ductal carcinoma in situ(DCIS)problem with free boundary conditions can better reveal the changing law of Ductal Carcinoma in situ,mean while reducing the cost of experiments and improving the accuracy of numerical results.This paper exploits physics-informed neural networks(PINNs)to solve the problem of ductal carcinoma in situ with free boundary conditions.We construct two independent deep neural networks to respectively approximate the nutrient concentration and the free boundary,the loss function is represented by the residuals of the partial differential equations,initial and boundary conditions,and solved using the Adam optimization algorithm.In order to verify the accuracy and computational efficiency of the solution of the free boundary problem by PINNs,numerical simulation was performed.The results not only show the effectiveness of PINNs in solving the problem,but also verify that the numerical solution agrees well with the exact solution.