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This work belongs to a series of articles which have been dedicated to thecombination of signed particles and neural networks to speed up thetime-dependent simulation of quantum systems. More specifically, the suggestednetworks are utilized to compute the function known as the Wigner kernel. Inthe first paper, we suggested a network which is completely definedanalytically and which does not necessitate any training process. Although veryuseful, this approach keeps the same complexity as the more standard finitedifference methods. In the second work, we presented a different architecturewhich has generalization capabilities. Although more convenient in terms ofcomputational time, it still uses a similar structure compared to the previousapproach, with less neurons in the hidden layer but with the same expensiveactivation functions (sine functions). In this work, we focus on neuralnetworks without any prior physics based knowledge. In more details, thenetwork now consists of different hidden layers which are based on more common,and less computationally expensive, activation functions such as rectifiedlinear units, and which focus on predicting only one column of the discretizedWigner kernel at a time. This new suggested architecture proves to accuratelylearn the transform from the space of potential functions to the space ofWigner kernels and performs very well during the simulation of quantum systems(20 times faster). Finally, we simulate a one-dimensional quantum systemconsisting of a wave packet impinging on a potential barrier for validationpurposes. This represents one further step ahead to achieve fast and reliablesimulations of time-dependent quantum systems.

Combining neural networks and signed particles to simulate quantum systems more efficiently, Part III