Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations
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We prove that deep neural networks are capable of approximating solutions of semilinear Kolmogorov PDE in the case of gradient-independent, Lipschitz-continuous nonlinearities, while the required number of parameters in the networks grow at most polynomially in both dimension d ∈ℕ and prescribed reciprocal accuracy ε. Previously, this has only been proven in the case of semilinear heat equations.
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