Getting Started
===============

A series of notebooks are available to help run the code using VaYu. There are located within the notebook directory, additionally the python scripts are within the example directory.

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   :maxdepth: 1
   :caption: Notebooks

   notebooks

Introductory examples
---------------------
We now introduce basic concepts, which helps in demonstaring the usage of library. 

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   :maxdepth: 1
   :caption: Introductory examples

   basic_exp
   


Spectral Methods 
----------------

We now dive into constrting spectral methods for integer-order differential equations.  

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   :maxdepth: 1
   :caption: Spectral methods for integer-order differential equations

   spec_int


We now dive into constrting spectral methods for fractional differential equations via convolution orthogonality   

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   :maxdepth: 1
   :caption: Spectral methods for General fractional PDE via convolution orthogonality 

   frac_int


Reduced Order Modeling
----------------------

We now dive into Reduced order modeling (ROM). ROM aims at speeding up simulations, by dimensionality reduction of the problem. 

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   :maxdepth: 1
   :caption: Reduced Order Modeling

   rom


Physics-informed Neural Networks
--------------------------------

We now dive into Physics-informed Neural Netorks (PINNs). PINNs solves differential equations by invoking a neural network. The governing equation is a part of the loss function, hence data is not required everywhere, only at the boundries.  

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   :maxdepth: 1
   :caption: Physics-informed Neural Networks

   pinns