# coding=utf-8 # SPDX-FileCopyrightText: Copyright (c) 2024 The torch-harmonics Authors. All rights reserved. # SPDX-License-Identifier: BSD-3-Clause # # Redistribution and use in source and binary forms, with or without # modification, are permitted provided that the following conditions are met: # # 1. Redistributions of source code must retain the above copyright notice, this # list of conditions and the following disclaimer. # # 2. Redistributions in binary form must reproduce the above copyright notice, # this list of conditions and the following disclaimer in the documentation # and/or other materials provided with the distribution. # # 3. Neither the name of the copyright holder nor the names of its # contributors may be used to endorse or promote products derived from # this software without specific prior written permission. # # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" # AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE # IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE # DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE # FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL # DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR # SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER # CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, # OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE # OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. # import math import torch import torch.nn as nn import torch.amp as amp from torch_harmonics import RealSHT, InverseRealSHT from torch_harmonics import DiscreteContinuousConvS2, DiscreteContinuousConvTransposeS2 from torch_harmonics import ResampleS2 from torch_harmonics.examples.models._layers import MLP, SpectralConvS2, SequencePositionEmbedding, SpectralPositionEmbedding, LearnablePositionEmbedding from functools import partial # heuristic for finding theta_cutoff def _compute_cutoff_radius(nlat, kernel_shape, basis_type): theta_cutoff_factor = {"piecewise linear": 0.5, "morlet": 0.5, "zernike": math.sqrt(2.0)} return (kernel_shape[0] + 1) * theta_cutoff_factor[basis_type] * math.pi / float(nlat - 1) class DiscreteContinuousEncoder(nn.Module): r""" Discrete-continuous encoder for spherical neural operators. This module performs downsampling using discrete-continuous convolutions on the sphere, reducing the spatial resolution while maintaining the spectral properties of the data. Parameters ---------- in_shape : tuple, optional Input shape (nlat, nlon), by default (721, 1440) out_shape : tuple, optional Output shape (nlat, nlon), by default (480, 960) grid_in : str, optional Input grid type, by default "equiangular" grid_out : str, optional Output grid type, by default "equiangular" inp_chans : int, optional Number of input channels, by default 2 out_chans : int, optional Number of output channels, by default 2 kernel_shape : tuple, optional Kernel shape for convolution, by default (3, 3) basis_type : str, optional Filter basis type, by default "morlet" groups : int, optional Number of groups for grouped convolution, by default 1 bias : bool, optional Whether to use bias, by default False """ def __init__( self, in_shape=(721, 1440), out_shape=(480, 960), grid_in="equiangular", grid_out="equiangular", inp_chans=2, out_chans=2, kernel_shape=(3, 3), basis_type="morlet", groups=1, bias=False, ): super().__init__() # set up local convolution self.conv = DiscreteContinuousConvS2( inp_chans, out_chans, in_shape=in_shape, out_shape=out_shape, kernel_shape=kernel_shape, basis_type=basis_type, grid_in=grid_in, grid_out=grid_out, groups=groups, bias=bias, theta_cutoff=_compute_cutoff_radius(in_shape[0], kernel_shape, basis_type), ) def forward(self, x): dtype = x.dtype with amp.autocast(device_type="cuda", enabled=False): x = x.float() x = self.conv(x) x = x.to(dtype=dtype) return x class DiscreteContinuousDecoder(nn.Module): r""" Discrete-continuous decoder for spherical neural operators. This module performs upsampling using either spherical harmonic transforms or resampling, followed by discrete-continuous convolutions to restore spatial resolution. Parameters ---------- in_shape : tuple, optional Input shape (nlat, nlon), by default (480, 960) out_shape : tuple, optional Output shape (nlat, nlon), by default (721, 1440) grid_in : str, optional Input grid type, by default "equiangular" grid_out : str, optional Output grid type, by default "equiangular" inp_chans : int, optional Number of input channels, by default 2 out_chans : int, optional Number of output channels, by default 2 kernel_shape : tuple, optional Kernel shape for convolution, by default (3, 3) basis_type : str, optional Filter basis type, by default "morlet" groups : int, optional Number of groups for grouped convolution, by default 1 bias : bool, optional Whether to use bias, by default False upsample_sht : bool, optional Whether to use SHT for upsampling, by default False """ def __init__( self, in_shape=(480, 960), out_shape=(721, 1440), grid_in="equiangular", grid_out="equiangular", inp_chans=2, out_chans=2, kernel_shape=(3, 3), basis_type="morlet", groups=1, bias=False, upsample_sht=False, ): super().__init__() # set up upsampling if upsample_sht: self.sht = RealSHT(*in_shape, grid=grid_in).float() self.isht = InverseRealSHT(*out_shape, lmax=self.sht.lmax, mmax=self.sht.mmax, grid=grid_out).float() self.upsample = nn.Sequential(self.sht, self.isht) else: self.upsample = ResampleS2(*in_shape, *out_shape, grid_in=grid_in, grid_out=grid_out) # set up DISCO convolution self.conv = DiscreteContinuousConvS2( inp_chans, out_chans, in_shape=out_shape, out_shape=out_shape, kernel_shape=kernel_shape, basis_type=basis_type, grid_in=grid_out, grid_out=grid_out, groups=groups, bias=False, theta_cutoff=_compute_cutoff_radius(in_shape[0], kernel_shape, basis_type), ) def forward(self, x): dtype = x.dtype with amp.autocast(device_type="cuda", enabled=False): x = x.float() x = self.upsample(x) x = self.conv(x) x = x.to(dtype=dtype) return x class SphericalNeuralOperatorBlock(nn.Module): """ Helper module for a single SFNO/FNO block. Can use both FFTs and SHTs to represent either FNO or SFNO blocks. Parameters ---------- forward_transform : torch.nn.Module Forward transform to use for the block inverse_transform : torch.nn.Module Inverse transform to use for the block input_dim : int Input dimension output_dim : int Output dimension conv_type : str, optional Type of convolution to use, by default "local" mlp_ratio : float, optional MLP expansion ratio, by default 2.0 drop_rate : float, optional Dropout rate, by default 0.0 drop_path : float, optional Drop path rate, by default 0.0 act_layer : torch.nn.Module, optional Activation function to use, by default nn.GELU norm_layer : str, optional Type of normalization to use, by default "none" inner_skip : str, optional Type of inner skip connection to use, by default "none" outer_skip : str, optional Type of outer skip connection to use, by default "identity" use_mlp : bool, optional Whether to use MLP layers, by default True disco_kernel_shape : tuple, optional Kernel shape for discrete-continuous convolution, by default (3, 3) disco_basis_type : str, optional Filter basis type for discrete-continuous convolution, by default "morlet" bias : bool, optional Whether to use bias, by default False Returns ------- torch.Tensor Output tensor """ def __init__( self, forward_transform, inverse_transform, input_dim, output_dim, conv_type="local", mlp_ratio=2.0, drop_rate=0.0, drop_path=0.0, act_layer=nn.GELU, norm_layer="none", inner_skip="none", outer_skip="identity", use_mlp=True, disco_kernel_shape=(3, 3), disco_basis_type="morlet", bias=False, ): super().__init__() if act_layer == nn.Identity: gain_factor = 1.0 else: gain_factor = 2.0 if inner_skip == "linear" or inner_skip == "identity": gain_factor /= 2.0 # convolution layer if conv_type == "local": theta_cutoff = 2.0 * _compute_cutoff_radius(forward_transform.nlat, disco_kernel_shape, disco_basis_type) self.local_conv = DiscreteContinuousConvS2( input_dim, output_dim, in_shape=(forward_transform.nlat, forward_transform.nlon), out_shape=(inverse_transform.nlat, inverse_transform.nlon), kernel_shape=disco_kernel_shape, basis_type=disco_basis_type, grid_in=forward_transform.grid, grid_out=inverse_transform.grid, bias=bias, theta_cutoff=theta_cutoff, ) elif conv_type == "global": self.global_conv = SpectralConvS2(forward_transform, inverse_transform, input_dim, output_dim, gain=gain_factor, bias=bias) else: raise ValueError(f"Unknown convolution type {conv_type}") if inner_skip == "linear": self.inner_skip = nn.Conv2d(input_dim, output_dim, 1, 1) nn.init.normal_(self.inner_skip.weight, std=math.sqrt(gain_factor / input_dim)) elif inner_skip == "identity": assert input_dim == output_dim self.inner_skip = nn.Identity() elif inner_skip == "none": pass else: raise ValueError(f"Unknown skip connection type {inner_skip}") # normalisation layer if norm_layer == "layer_norm": self.norm = nn.LayerNorm(normalized_shape=(inverse_transform.nlat, inverse_transform.nlon), eps=1e-6) elif norm_layer == "instance_norm": self.norm = nn.InstanceNorm2d(num_features=output_dim, eps=1e-6, affine=True, track_running_stats=False) elif norm_layer == "none": self.norm = nn.Identity() else: raise NotImplementedError(f"Error, normalization {norm_layer} not implemented.") # dropout self.drop_path = DropPath(drop_path) if drop_path > 0.0 else nn.Identity() gain_factor = 1.0 if outer_skip == "linear" or inner_skip == "identity": gain_factor /= 2.0 if use_mlp == True: mlp_hidden_dim = int(output_dim * mlp_ratio) self.mlp = MLP( in_features=output_dim, out_features=input_dim, hidden_features=mlp_hidden_dim, act_layer=act_layer, drop_rate=drop_rate, checkpointing=False, gain=gain_factor, ) if outer_skip == "linear": self.outer_skip = nn.Conv2d(input_dim, input_dim, 1, 1) torch.nn.init.normal_(self.outer_skip.weight, std=math.sqrt(gain_factor / input_dim)) elif outer_skip == "identity": assert input_dim == output_dim self.outer_skip = nn.Identity() elif outer_skip == "none": pass else: raise ValueError(f"Unknown skip connection type {outer_skip}") def forward(self, x): residual = x if hasattr(self, "global_conv"): x, _ = self.global_conv(x) elif hasattr(self, "local_conv"): x = self.local_conv(x) x = self.norm(x) if hasattr(self, "inner_skip"): x = x + self.inner_skip(residual) if hasattr(self, "mlp"): x = self.mlp(x) x = self.drop_path(x) if hasattr(self, "outer_skip"): x = x + self.outer_skip(residual) return x class LocalSphericalNeuralOperator(nn.Module): r""" LocalSphericalNeuralOperator module. A spherical neural operator which uses both local and global integral operators to accureately model both types of solution operators [1]. The architecture is based on the Spherical Fourier Neural Operator [2] and improves upon it with local integral operators in both the Neural Operator blocks, as well as in the encoder and decoders. Parameters ---------- img_size : tuple, optional Input image size (nlat, nlon), by default (128, 256) grid : str, optional Grid type for input/output, by default "equiangular" grid_internal : str, optional Grid type for internal processing, by default "legendre-gauss" scale_factor : int, optional Scale factor for resolution changes, by default 3 in_chans : int, optional Number of input channels, by default 3 out_chans : int, optional Number of output channels, by default 3 embed_dim : int, optional Embedding dimension, by default 256 num_layers : int, optional Number of layers, by default 4 activation_function : str, optional Activation function name, by default "gelu" kernel_shape : tuple, optional Kernel shape for convolutions, by default (3, 3) encoder_kernel_shape : tuple, optional Kernel shape for encoder, by default (3, 3) filter_basis_type : str, optional Filter basis type, by default "morlet" use_mlp : bool, optional Whether to use MLP layers, by default True mlp_ratio : float, optional MLP expansion ratio, by default 2.0 drop_rate : float, optional Dropout rate, by default 0.0 drop_path_rate : float, optional Drop path rate, by default 0.0 normalization_layer : str, optional Type of normalization layer to use ("layer_norm", "instance_norm", "none"), by default "instance_norm" sfno_block_frequency : int, optional Frequency of SFNO blocks, by default 2 hard_thresholding_fraction : float, optional Hard thresholding fraction, by default 1.0 residual_prediction : bool, optional Whether to use residual prediction, by default False pos_embed : str, optional Position embedding type, by default "none" upsample_sht : bool, optional Use SHT upsampling if true, else linear interpolation bias : bool, optional Whether to use a bias, by default False Example ---------- >>> model = LocalSphericalNeuralOperator( ... img_shape=(128, 256), ... scale_factor=4, ... in_chans=2, ... out_chans=2, ... embed_dim=16, ... num_layers=4, ... use_mlp=True,) >>> model(torch.randn(1, 2, 128, 256)).shape torch.Size([1, 2, 128, 256]) References ---------- .. [1] Liu-Schiaffini M., Berner J., Bonev B., Kurth T., Azizzadenesheli K., Anandkumar A.; "Neural Operators with Localized Integral and Differential Kernels" (2024). ICML 2024, https://arxiv.org/pdf/2402.16845. .. [2] Bonev B., Kurth T., Hundt C., Pathak, J., Baust M., Kashinath K., Anandkumar A.; "Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere" (2023). ICML 2023, https://arxiv.org/abs/2306.03838. """ def __init__( self, img_size=(128, 256), grid="equiangular", grid_internal="legendre-gauss", scale_factor=3, in_chans=3, out_chans=3, embed_dim=256, num_layers=4, activation_function="gelu", kernel_shape=(3, 3), encoder_kernel_shape=(3, 3), filter_basis_type="morlet", use_mlp=True, mlp_ratio=2.0, drop_rate=0.0, drop_path_rate=0.0, normalization_layer="none", sfno_block_frequency=2, hard_thresholding_fraction=1.0, residual_prediction=False, pos_embed="none", upsample_sht=False, bias=False, ): super().__init__() self.img_size = img_size self.grid = grid self.grid_internal = grid_internal self.scale_factor = scale_factor self.in_chans = in_chans self.out_chans = out_chans self.embed_dim = embed_dim self.num_layers = num_layers self.encoder_kernel_shape = encoder_kernel_shape self.hard_thresholding_fraction = hard_thresholding_fraction self.normalization_layer = normalization_layer self.use_mlp = use_mlp self.residual_prediction = residual_prediction # activation function if activation_function == "relu": self.activation_function = nn.ReLU elif activation_function == "gelu": self.activation_function = nn.GELU # for debugging purposes elif activation_function == "identity": self.activation_function = nn.Identity else: raise ValueError(f"Unknown activation function {activation_function}") # compute downsampled image size. We assume that the latitude-grid includes both poles self.h = (self.img_size[0] - 1) // scale_factor + 1 self.w = self.img_size[1] // scale_factor # dropout self.pos_drop = nn.Dropout(p=drop_rate) if drop_rate > 0.0 else nn.Identity() dpr = [x.item() for x in torch.linspace(0, drop_path_rate, self.num_layers)] if pos_embed == "sequence": self.pos_embed = SequencePositionEmbedding((self.h, self.w), num_chans=self.embed_dim, grid=grid_internal) elif pos_embed == "spectral": self.pos_embed = SpectralPositionEmbedding((self.h, self.w), num_chans=self.embed_dim, grid=grid_internal) elif pos_embed == "learnable lat": self.pos_embed = LearnablePositionEmbedding((self.h, self.w), num_chans=self.embed_dim, grid=grid_internal, embed_type="lat") elif pos_embed == "learnable latlon": self.pos_embed = LearnablePositionEmbedding((self.h, self.w), num_chans=self.embed_dim, grid=grid_internal, embed_type="latlon") elif pos_embed == "none": self.pos_embed = nn.Identity() else: raise ValueError(f"Unknown position embedding type {pos_embed}") # encoder self.encoder = DiscreteContinuousEncoder( in_shape=self.img_size, out_shape=(self.h, self.w), grid_in=grid, grid_out=grid_internal, inp_chans=self.in_chans, out_chans=self.embed_dim, kernel_shape=self.encoder_kernel_shape, basis_type=filter_basis_type, groups=1, bias=False, ) # compute the modes for the sht modes_lat = self.h # due to some spectral artifacts with cufft, we substract one mode here modes_lon = (self.w // 2 + 1) - 1 modes_lat = modes_lon = int(min(modes_lat, modes_lon) * self.hard_thresholding_fraction) self.trans = RealSHT(self.h, self.w, lmax=modes_lat, mmax=modes_lon, grid=grid_internal).float() self.itrans = InverseRealSHT(self.h, self.w, lmax=modes_lat, mmax=modes_lon, grid=grid_internal).float() self.blocks = nn.ModuleList([]) for i in range(self.num_layers): block = SphericalNeuralOperatorBlock( self.trans, self.itrans, self.embed_dim, self.embed_dim, conv_type="global" if i % sfno_block_frequency == (sfno_block_frequency-1) else "local", mlp_ratio=mlp_ratio, drop_rate=drop_rate, drop_path=dpr[i], act_layer=self.activation_function, norm_layer=self.normalization_layer, use_mlp=use_mlp, disco_kernel_shape=kernel_shape, disco_basis_type=filter_basis_type, bias=bias, ) self.blocks.append(block) # decoder self.decoder = DiscreteContinuousDecoder( in_shape=(self.h, self.w), out_shape=self.img_size, grid_in=grid_internal, grid_out=grid, inp_chans=self.embed_dim, out_chans=self.out_chans, kernel_shape=self.encoder_kernel_shape, basis_type=filter_basis_type, groups=1, bias=False, upsample_sht=upsample_sht, ) @torch.jit.ignore def no_weight_decay(self): return {"pos_embed", "cls_token"} def forward_features(self, x): x = self.pos_drop(x) for blk in self.blocks: x = blk(x) return x def forward(self, x): if self.residual_prediction: residual = x x = self.encoder(x) if self.pos_embed is not None: x = self.pos_embed(x) x = self.forward_features(x) x = self.decoder(x) if self.residual_prediction: x = x + residual return x