  The spread of many infectious diseases is modeled using variants of the SIR
compartmental model, which is a coupled differential equation. The coefficients
of the SIR model determine the spread trajectories of disease, on whose basis
proactive measures can be taken. Hence, the coefficient estimates must be both
fast and accurate. Shaier et al. in the paper "Disease Informed Neural
Networks" used Physics Informed Neural Networks (PINNs) to estimate the
parameters of the SIR model. There are two drawbacks to this approach. First,
the training time for PINNs is high, with certain diseases taking close to 90
hrs to train. Second, PINNs don't generalize for a new SIDR trajectory, and
learning its corresponding SIR parameters requires retraining the PINN from
scratch. In this work, we aim to eliminate both of these drawbacks. We generate
a dataset between the parameters of ODE and the spread trajectories by solving
the forward problem for a large distribution of parameters using the LSODA
algorithm. We then use a neural network to learn the mapping between spread
trajectories and coefficients of SIDR in an offline manner. This allows us to
learn the parameters of a new spread trajectory without having to retrain,
enabling generalization at test time. We observe a speed-up of 3-4 orders of
magnitude with accuracy comparable to that of PINNs for 11 highly infectious
diseases. Further finetuning of neural network inferred ODE coefficients using
PINN further leads to 2-3 orders improvement of estimated coefficients.
