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To overcome this difficulty, in this paper we propose a new, nonlinear approach relying on deep learning (DL) algorithms-such as deep feedforward neural networks and convolutional autoencoders-to obtain accurate and efficient ROMs, whose dimensionality matches the number of system parameters. We show that the proposed DL-ROM framework can efficiently provide solutions to parametrized electrophysiology problems, thus enabling multi-scenario analysis in pathological cases. We investigate four challenging test cases in cardiac electrophysiology, thus demonstra