  We present a machine-learning approach to a long-standing issue in quantum
many-body physics, namely, analytic continuation. This notorious
ill-conditioned problem of obtaining spectral function from imaginary time
Green's function has been a focus of new method developments for past decades.
Here we demonstrate the usefulness of modern machine-learning techniques
including convolutional neural networks and the variants of stochastic gradient
descent optimiser. Machine-learning continuation kernel is successfully
realized without any 'domain-knowledge', which means that any physical 'prior'
is not utilized in the kernel construction and the neural networks 'learn' the
knowledge solely from 'training'. The outstanding performance is achieved for
both insulating and metallic band structure. Our machine-learning-based
approach not only provides the more accurate spectrum than the conventional
methods in terms of peak positions and heights, but is also more robust against
the noise which is the required key feature for any continuation technique to
be successful. Furthermore, its computation speed is 10$^4$-10$^5$ times faster
than maximum entropy method.
