PositPR-PINNs-code

Julia codes for experiments with Posit arithmetic in Physics-Informed Neural Networks (PINNs).
Requires the custom PositPR.jl library, currently available only locally.

Differential Equations used in the experiments

eq1 (ode)

Differential equation

$$ \frac{du}{dt} = \cos(2\pi t) $$

Condition

$$ u(0) = 0 $$

Analytical solution

$$ u(t) = \frac{\sin(2\pi t)}{2\pi} $$

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eq2 (pde)

Differential equation

$$ \frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2} $$

Conditions

$$ u(0,t) = u(1,t) = 0, \qquad u(x,0) = \sin(\pi x) $$

Analytical solution

$$ u(x,t) = \sin(\pi x), e^{-\pi^2 t} $$