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In the practice, there is a problem where the input can be a continuous line, like waveform, the output is also a continuous line, i.e., another waveform. In the sampling space, I can get 100 samples from waveform in the original continuous space. In other words, the problem can be transformed into finding the mapping function between a numerical sequence and another numerical sequence.

For instance, the input sequence is [-4.1288461e-16 -2.2452528e-15 -1.1717652e-14 -5.8685417e-14 -2.8203791e-13 -1.3006001e-12], the output sequence is [1.2080356e-01 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00 0.0000000e+00 ]

In practice, we can have thousands of this kind of input-output pairs for training purposes. In the machine learning field, are there any specific models aiming to solve this kind of problem. My feeling is that neural network maybe a fit, but what kind of architecture is a better option. Here, the output is not a categorical variables usually for classification problems.

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The general term for this kind of problem, in which you want to predict one variable using another, and you have input-output pairs with which to train a model, is "supervised learning". Supervised learning is the most common application of statistics and machine learning. Machine-learning people like to call supervised learning of a continuous variable "regression", although to statisticians, this term refers to a certain family of models. In any case, there's a wide array of tools available for such problems, from linear regression to neural networks.

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