Add to ORKGMulti-level methods are widely used for the solution of large-scale problems, because of their computational advantages and exploitation of the complementarity between the involved sub-problems. After a re-interpretation of multi-level methods from a block-coordinate point of view, we propose a multi-level algorithm for the solution of nonlinear optimization problems and analyze its evaluation complexity. We apply it to the solution of partial differential equations using physics-informed neural networks (PINNs) and show on a few test problems that the approach results in better solutions and significant computational savings
Abstract Physics-informed neural networks (PINNs) leverage data and knowledge about a problem. They ...
A multiscale method is described in the context of binary Hopfield--type neural networks. The approp...
A novel multi-level method for partial differential equations with uncertain parameters is proposed....
Multi-level methods are widely used for the solution of large-scale problems, because of their compu...
Recent works have shown that neural networks can be employed to solve partial differential equations...
International audienceIn this paper, we propose a new multilevel Levenberg–Marquardt optimizer for t...
International audienceThis paper is concerned with the approximation of the solution of partial diff...
[[abstract]]This study aims at utilizing the dynamic behavior of artificial neural networks (ANNs) t...
Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like ...
[[abstract]]This study aims at utilizing the dynamic behavior of artificial neural networks (ANNs) t...
Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like ...
Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bri...
Recent works have shown that deep neural networks can be employed to solve partial differential equa...
A novel modified method for obtaining approximate solutions to difficult optimization problems withi...
Recent works have shown that deep neural networks can be employed to solve partial differential equa...
Abstract Physics-informed neural networks (PINNs) leverage data and knowledge about a problem. They ...
A multiscale method is described in the context of binary Hopfield--type neural networks. The approp...
A novel multi-level method for partial differential equations with uncertain parameters is proposed....
Multi-level methods are widely used for the solution of large-scale problems, because of their compu...
Recent works have shown that neural networks can be employed to solve partial differential equations...
International audienceIn this paper, we propose a new multilevel Levenberg–Marquardt optimizer for t...
International audienceThis paper is concerned with the approximation of the solution of partial diff...
[[abstract]]This study aims at utilizing the dynamic behavior of artificial neural networks (ANNs) t...
Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like ...
[[abstract]]This study aims at utilizing the dynamic behavior of artificial neural networks (ANNs) t...
Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like ...
Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bri...
Recent works have shown that deep neural networks can be employed to solve partial differential equa...
A novel modified method for obtaining approximate solutions to difficult optimization problems withi...
Recent works have shown that deep neural networks can be employed to solve partial differential equa...
Abstract Physics-informed neural networks (PINNs) leverage data and knowledge about a problem. They ...
A multiscale method is described in the context of binary Hopfield--type neural networks. The approp...
A novel multi-level method for partial differential equations with uncertain parameters is proposed....
