  "AI for Science" aims to solve fundamental scientific problems using AI
techniques. As most physical phenomena can be described as Partial Differential
Equations (PDEs) , approximating their solutions using neural networks has
evolved as a central component of scientific-ML. Physics-Informed Neural
Networks (PINNs) is the general method that has evolved for this task but its
training is well-known to be very unstable. In this work we explore the
possibility of changing the model being trained from being just a neural
network to being a non-linear transformation of it - one that algebraically
includes the boundary/initial conditions. This reduces the number of terms in
the loss function than the standard PINN losses. We demonstrate that our
modification leads to significant performance gains across a range of benchmark
tasks, in various dimensions and without having to tweak the training
algorithm. Our conclusions are based on conducting hundreds of experiments, in
the fully unsupervised setting, over multiple linear and non-linear PDEs set to
exactly solvable scenarios, which lends to a concrete measurement of our
performance gains in terms of order(s) of magnitude lower fractional errors
being achieved, than by standard PINNs. The code accompanying this manuscript
is publicly available at,
https://github.com/MorganREN/Improving-PINNs-By-Algebraic-Inclusion-of-Boundary-and-Initial-Conditions
