@@ -171,7 +171,7 @@ Here, $x_j \in [-1,1]$ are the quadrature nodes with the respective quadrature w
...
@@ -171,7 +171,7 @@ Here, $x_j \in [-1,1]$ are the quadrature nodes with the respective quadrature w
### Discrete-continuous convolutions on the sphere
### Discrete-continuous convolutions on the sphere
torch-harmonics now provides local discrete-continuous (DISCO) convolutions as outlined in [4] on the sphere. These are use in local neural operators to generalize convolutions to structured and unstructured meshes on the sphere.
torch-harmonics now provides local discrete-continuous (DISCO) convolutions as outlined in [5] on the sphere. These are use in local neural operators [2] to generalize convolutions to structured and unstructured meshes on the sphere.
### Spherical (neighborhood) attention
### Spherical (neighborhood) attention
...
@@ -276,14 +276,22 @@ Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere;
...
@@ -276,14 +276,22 @@ Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere;
International Conference on Machine Learning, 2023. [arxiv link](https://arxiv.org/abs/2306.03838)
International Conference on Machine Learning, 2023. [arxiv link](https://arxiv.org/abs/2306.03838)
<a id="1">[2]</a>
<a id="1">[2]</a>
Liu-Schiaffini M., Berner J., Bonev B., Kurth T., Azizzadenesheli K., Anandkumar A.;
Neural Operators with Localized Integral and Differential Kernels;
International Conference on Machine Learning, 2024. [arxiv link](https://arxiv.org/abs/2402.16845)
<a id="1">[3]</a>
Schaeffer N.;
Schaeffer N.;
Efficient spherical harmonic transforms aimed at pseudospectral numerical simulations;
Efficient spherical harmonic transforms aimed at pseudospectral numerical simulations;
G3: Geochemistry, Geophysics, Geosystems, 2013.
G3: Geochemistry, Geophysics, Geosystems, 2013.
<a id="1">[3]</a>
<a id="1">[4]</a>
Wang B., Wang L., Xie Z.;
Wang B., Wang L., Xie Z.;
Accurate calculation of spherical and vector spherical harmonic expansions via spectral element grids;
Accurate calculation of spherical and vector spherical harmonic expansions via spectral element grids;
Adv Comput Math, 2018.
Adv Comput Math, 2018.
<a id="1">[4]</a>
<a id="1">[5]</a>
Ocampo, Price, McEwen, Scalable and equivariant spherical CNNs by discrete-continuous (DISCO) convolutions, ICLR (2023), arXiv:2209.13603
Ocampo, Price, McEwen, Scalable and equivariant spherical CNNs by discrete-continuous (DISCO) convolutions, ICLR (2023), arXiv:2209.13603
<a id="1">[6]</a>
Bonev B., Rietmann M., Paris A., Carpentieri A., Kurth T.; Attention on the Sphere; [arxiv link](https://arxiv.org/abs/2505.11157)
