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Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations

Home Page: https://maziarraissi.github.io/NumericalGP/

License: MIT License

MATLAB 71.05% Mathematica 28.66% M 0.03% Java 0.26%

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numericalgp's Issues

Questions about Solving Burger Equations with Noise

Taking Burger Equation as an example:
Starting from the given initial condition u(t=0,x), we assume it follows GP and from the joint distribution of u(t=0,x) and u(t=1,b), which follows GP(0, K) ,we use Likelihood to get the estimated parameter (hyp), and then to predict the u(t=1,x) given u(t=1,b). However, you are using u(t=0,x) as the mean of u(t=0,x) and using 0 to be the var-cov of u(t=0,x). It was treated as a constant. Which contradicts with our assumption which u(t=0,x) is GP. That is my question. How could we treat the initial condition as constant and assume it is GP? Hope I clarify my question clearly.

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