We solve a system of ordinary differential equations with an unknown functional form of a sink (reaction rate) term. We assume that the measurements (time series) of state variables are partially available, and we use recurrent neural network to “learn” the reaction rate from this data. This is achieved by including a discretized ordinary differential equations as part of a recurrent neural net...

Neural networks have become increasingly popular for the task of language modeling. Whereas feed-forward networks only exploit a fixed context length to predict the next word of a sequence, conceptually, standard recurrent neural networks can take into account all of the predecessor words. On the other hand, it is well known that recurrent networks are difficult to train and therefore are unlik...