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Update docs for OperatorConv
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docs/src/apis.md

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@@ -17,8 +17,9 @@ v'(x) = \mathcal{F}^{-1} \{ F'(s) \}
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```
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where ``v(x)`` and ``v'(x)`` denotes input and output function,
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``\mathcal{F} \{ \cdot \}``, ``\mathcal{F}^{-1} \{ \cdot \}`` are Fourier transform, inverse Fourier transform, respectively.
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Function ``g`` is a linear transform for lowering Fouier modes.
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``\mathcal{F} \{ \cdot \}``, ``\mathcal{F}^{-1} \{ \cdot \}`` are transform,
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inverse transform, respectively.
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Function ``g`` is a linear transform for lowering spectrum modes.
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```@docs
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OperatorConv
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v_{t+1}(x) = \sigma(W v_t(x) + \mathcal{K} \{ v_t(x) \} )
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```
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where ``v_t(x)`` is the input function for ``t``-th layer and ``\mathcal{K} \{ \cdot \}`` denotes spectral convolutional layer.
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where ``v_t(x)`` is the input function for ``t``-th layer and
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``\mathcal{K} \{ \cdot \}`` denotes spectral convolutional layer.
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Activation function ``\sigma`` can be arbitrary non-linear function.
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```@docs
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v_{t+1}(x_i) = \sigma(W v_t(x_i) + \frac{1}{|\mathcal{N}(x_i)|} \sum_{x_j \in \mathcal{N}(x_i)} \kappa \{ v_t(x_i), v_t(x_j) \} )
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```
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where ``v_t(x_i)`` is the input function for ``t``-th layer, ``x_i`` is the node feature for ``i``-th node and ``\mathcal{N}(x_i)`` represents the neighbors for ``x_i``.
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where ``v_t(x_i)`` is the input function for ``t``-th layer,
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``x_i`` is the node feature for ``i``-th node and
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``\mathcal{N}(x_i)`` represents the neighbors for ``x_i``.
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Activation function ``\sigma`` can be arbitrary non-linear function.
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```@docs
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NeuralOperators.construct_subnet
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```
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---
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### NOMAD
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Nonlinear manifold decoders for operator learning

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