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Found 6 papers, 3 papers with code
The Hard-Constraint PINNs for Interface Optimal Control Problems
We show that the physics-informed neural networks (PINNs), in combination with some recently developed discontinuity capturing neural networks, can be applied to solve optimal control problems subject to partial differential equations (PDEs) with interfaces and some control constraints.
A cusp-capturing PINN for elliptic interface problems
In this paper, we propose a cusp-capturing physics-informed neural network (PINN) to solve discontinuous-coefficient elliptic interface problems whose solution is continuous but has discontinuous first derivatives on the interface.
An efficient neural-network and finite-difference hybrid method for elliptic interface problems with applications
A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain with jump discontinuities on embedded irregular interfaces.
A shallow physics-informed neural network for solving partial differential equations on surfaces
To track the surface, we additionally introduce a prescribed hidden layer to enforce the topological structure of the surface and use the network to learn the homeomorphism between the surface and the prescribed topology.
A Shallow Ritz Method for Elliptic Problems with Singular Sources
We first introduce the energy functional of the problem and then transform the contribution of singular sources to a regular surface integral along the interface.
A Discontinuity Capturing Shallow Neural Network for Elliptic Interface Problems
In this paper, a new Discontinuity Capturing Shallow Neural Network (DCSNN) for approximating $d$-dimensional piecewise continuous functions and for solving elliptic interface problems is developed.
