Multi-domain physics-informed neural network for solving heat conduction and conjugate natural convection with discontinuity of temperature gradient on interface

Deep learning has been increasingly recognized as a promising tool in solving kinds of physical problems beyond powerful approximations. A multi-domain physics-informed neural network(mPINN) is proposed to solve the non-uniform heat conduction and conjugate natural convection with the discontinuity of temperature gradient on the interface. Local radial basis function method(LRBF) is applied to compute the case without the analytical solution and is regarded as the benchmark solver.Each physical domain matches a private neural network and all neural networks are connected by the shared information of temperature and heat flux on the interface. Joint training and separate training are utilized to minimize the loss function, which usually consists of the residual of boundary conditions, interface conditions and governing equations. Joint training minimizes the sum of all losses from neural networks with one shared optimizer, while separate training owns its private optimizer. Local adaptive activation function(LAAF) is used to accelerate the convergence and acquire a lower loss value when compared with its fixed counterpart. The numerical experiments on three types of residual points, uniform, Gauss-Lobatto and random, are conducted and it can be concluded that the uniform residual points can obtain the most accurate solution than the random and Gauss-Lobatto. Joint training is more accurate than the separate training when the number of residual points is relatively small,while the separate training performs better than the joint training for the large number of residual points. Numerous test cases on multi-domain heat transfer and fluid flow show the accuracy of the proposed m PINN. Local and global heat transfer rates show good agreements with the results from LRBF. Excepting the forward problems, the thermal conductivity ratio, the constant source and the characteristic parameters of natural convection are accurately learned from sparsely distributed data points.