Solving the nonlinear Schrodinger equation with an unsupervised neural network.
We solve the nonlinear Schrodinger equation with an unsupervised neural network with the optical axis position z and time t as inputs. The network outputs the real and imaginary components of the solution. Unsupervised training aims to minimize a non-negative energy function derived from the equation and the boundary conditions. The trained network is generalizing - a solution value is determined at any (z, t)-combination including those not considered during training. Solutions with normalized mean-squared errors of order 10;-2, are obtained when the average energy is reduced to 10;-2 from order 10;4. The NN method is universal and applies to other complex differential equations.
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Monterola
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Saloma