diff --git a/graph_weather/models/graphs/hexagonal.py b/graph_weather/models/graphs/hexagonal.py
index 00ee82f5..aa9af20a 100644
--- a/graph_weather/models/graphs/hexagonal.py
+++ b/graph_weather/models/graphs/hexagonal.py
@@ -1,6 +1,8 @@
 """Generate hexagonal global grid using Uber's H3 library."""
 import h3
 import numpy as np
+import torch
+from torch_geometric.data import Data
 
 
 def generate_hexagonal_grid(resolution: int = 2) -> np.ndarray:
@@ -15,3 +17,59 @@ def generate_hexagonal_grid(resolution: int = 2) -> np.ndarray:
     base_h3_grid = sorted(list(h3.uncompact(h3.get_res0_indexes(), resolution)))
     base_h3_map = {h_i: i for i, h_i in enumerate(base_h3_grid)}
     return np.array(base_h3_grid), base_h3_map
+
+def generate_h3_mapping(lat_lons: list, resolution: int = 2) -> dict:
+    """Generate mapping from lat/lon to h3 index.
+
+    Args:
+        lat_lons: List of (lat,lon) points
+        resolution: H3 resolution level
+    """
+    num_latlons = len(lat_lons)
+    base_h3_grid = sorted(list(h3.uncompact(h3.get_res0_indexes(), resolution)))
+    base_h3_map = {h_i: i for i, h_i in enumerate(base_h3_grid)}
+    h3_grid = [h3.geo_to_h3(lat, lon, resolution) for lat, lon in lat_lons]
+    h3_mapping = {}
+    h_index = len(base_h3_grid)
+    for h in base_h3_grid:
+        if h not in h3_mapping:
+            h_index -= 1
+            h3_mapping[h] = h_index + num_latlons
+    # Now have the h3 grid mapping, the bipartite graph of edges connecting lat/lon to h3 nodes
+    # Should have vertical and horizontal difference
+    h3_distances = []
+    for idx, h3_point in enumerate(h3_grid):
+        lat_lon = lat_lons[idx]
+        distance = h3.point_dist(lat_lon, h3.h3_to_geo(h3_point), unit="rads")
+        h3_distances.append([np.sin(distance), np.cos(distance)])
+    h3_distances = torch.tensor(h3_distances, dtype=torch.float)
+    return base_h3_map, h3_mapping, h3_distances
+
+
+def generate_latent_h3_graph(base_h3_map: dict, base_h3_grid: dict) -> torch.Tensor:
+    """Generate latent h3 graph.
+
+    Args:
+        base_h3_map: Mapping from h3 index to index in latent graph
+        h3_mapping: Mapping from lat/lon to h3 index
+        h3_distances: Distances between lat/lon and h3 index
+
+    Returns:
+        Latent h3 graph
+    """
+    # Get connectivity of the graph
+    edge_sources = []
+    edge_targets = []
+    edge_attrs = []
+    for h3_index in base_h3_grid:
+        h_points = h3.k_ring(h3_index, 1)
+        for h in h_points:  # Already includes itself
+            distance = h3.point_dist(h3.h3_to_geo(h3_index), h3.h3_to_geo(h), unit="rads")
+            edge_attrs.append([np.sin(distance), np.cos(distance)])
+            edge_sources.append(base_h3_map[h3_index])
+            edge_targets.append(base_h3_map[h])
+    edge_index = torch.tensor([edge_sources, edge_targets], dtype=torch.long)
+    edge_attrs = torch.tensor(edge_attrs, dtype=torch.float)
+    # Use heterogeneous graph as input and output dims are not same for the encoder
+    # Because uniform grid now, don't need edge attributes as they are all the same
+    return Data(edge_index=edge_index, edge_attr=edge_attrs)
diff --git a/graph_weather/models/graphs/ico.py b/graph_weather/models/graphs/ico.py
index b9302f69..90009fc7 100644
--- a/graph_weather/models/graphs/ico.py
+++ b/graph_weather/models/graphs/ico.py
@@ -32,6 +32,8 @@
 """
 
 import numpy as np
+import torch
+from torch_geometric.data import Data
 
 
 def icosphere(nu=1, nr_verts=None):
@@ -294,5 +296,60 @@ def generate_icosphere_graph(resolution=1):
     vertices, faces = icosphere(resolution)
     edges = np.r_[faces[:, :-1], faces[:, 1:], faces[:, [0, 2]]]
     edges = np.unique(np.sort(edges, axis=1), axis=0)
-    return NotImplementedError("TODO: Make into PyTorch Tensors and return")
     return vertices, edges
+
+
+def generate_icosphere_mapping(lat_lons, resolution=1):
+    """
+    Generate mapping from lat/lon to icosphere index.
+
+    Args:
+        lat_lons: List of (lat,lon) points
+        resolution: Icosphere resolution level
+    """
+    num_latlons = len(lat_lons)
+    vertices, faces = icosphere(resolution)
+    # TODO Actually make this work
+    h3_mapping = {}
+    h_index = len(vertices)
+    for h in vertices:
+        if h not in h3_mapping:
+            h_index -= 1
+            h3_mapping[h] = h_index + num_latlons
+    # Now have the h3 grid mapping, the bipartite graph of edges connecting lat/lon to h3 nodes
+    # Should have vertical and horizontal difference
+    h3_distances = []
+    for idx, h3_point in enumerate(h3_grid):
+        lat_lon = lat_lons[idx]
+        distance = h3.point_dist(lat_lon, h3.h3_to_geo(h3_point), unit="rads")
+        h3_distances.append([np.sin(distance), np.cos(distance)])
+    h3_distances = torch.tensor(h3_distances, dtype=torch.float)
+    return h3_mapping, h3_distances
+
+def generate_latent_ico_graph(h3_mapping, h3_distances):
+    """
+    Generate latent h3 graph.
+
+    Args:
+        base_h3_map: Mapping from h3 index to index in latent graph
+        h3_mapping: Mapping from lat/lon to h3 index
+        h3_distances: Distances between lat/lon and h3 index
+
+    Returns:
+        Latent h3 graph
+    """
+    # Get connectivity of the graph
+    edge_sources = []
+    edge_targets = []
+    edge_attrs = []
+    for h3_index in h3_mapping:
+        h_points = h3.k_ring(h3_index, 1)
+        for h in h_points:  # Already includes itself
+            distance = h3.point_dist(h3.h3_to_geo(h3_index), h3.h3_to_geo(h), unit="rads")
+            edge_attrs.append([np.sin(distance), np.cos(distance)])
+            edge_sources.append(h3_mapping[h3_index])
+            edge_targets.append(h3_mapping[h])
+    edge_sources = np.array(edge_sources)
+    edge_targets = np.array(edge_targets)
+    edge_attrs = np.array(edge_attrs)
+    return edge_sources, edge_targets, edge_attrs
\ No newline at end of file
diff --git a/graph_weather/models/layers/encoder.py b/graph_weather/models/layers/encoder.py
index 916a6523..f4c82f80 100644
--- a/graph_weather/models/layers/encoder.py
+++ b/graph_weather/models/layers/encoder.py
@@ -48,6 +48,8 @@ def __init__(
         hidden_layers_processor_edge=2,
         mlp_norm_type="LayerNorm",
         use_checkpointing: bool = False,
+        input_graph: Data = None,
+        latent_graph: Data = None,
     ):
         """
         Encode the lat/lon data inot the isohedron graph
@@ -65,6 +67,8 @@ def __init__(
             mlp_norm_type: Type of norm for the MLPs
                 one of 'LayerNorm', 'GraphNorm', 'InstanceNorm', 'BatchNorm', 'MessageNorm', or None
             use_checkpointing: Whether to use gradient checkpointing to use less memory
+            input_graph: Input graph to use, if None, will generate a default one
+            latent_graph: Latent graph to use, if None, will generate a default one
         """
         super().__init__()
         self.use_checkpointing = use_checkpointing
diff --git a/graph_weather/models/losses.py b/graph_weather/models/losses.py
index 5e5d27ec..c417e3b6 100644
--- a/graph_weather/models/losses.py
+++ b/graph_weather/models/losses.py
@@ -61,3 +61,115 @@ def forward(self, pred: torch.Tensor, target: torch.Tensor):
         out = out * self.weights.expand_as(out)
         assert not torch.isnan(out).any()
         return out.mean()
+
+
+# Copyright (c) 2023, NVIDIA CORPORATION & AFFILIATES. All rights reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import math
+
+import torch
+import torch.nn as nn
+from torch.autograd.function import once_differentiable
+
+
+class CellAreaWeightedLossFunction(nn.Module):
+    """Loss function with cell area weighting.
+
+    Parameters
+    ----------
+    area : torch.Tensor
+        Cell area with shape [H, W].
+    """
+
+    def __init__(self, area):
+        super().__init__()
+        self.area = area
+
+    def forward(self, invar, outvar):
+        """
+        Implicit forward function which computes the loss given
+        a prediction and the corresponding targets.
+
+        Parameters
+        ----------
+        invar : torch.Tensor
+            prediction of shape [T, C, H, W].
+        outvar : torch.Tensor
+            target values of shape [T, C, H, W].
+        """
+
+        loss = (invar - outvar) ** 2
+        loss = loss.mean(dim=(0, 1))
+        loss = torch.mul(loss, self.area)
+        loss = loss.mean()
+        return loss
+
+
+class CustomCellAreaWeightedLossAutogradFunction(torch.autograd.Function):
+    """Autograd fuunction for custom loss with cell area weighting."""
+
+    @staticmethod
+    def forward(ctx, invar: torch.Tensor, outvar: torch.Tensor, area: torch.Tensor):
+        """Forward of custom loss function with cell area weighting."""
+
+        diff = invar - outvar  # T x C x H x W
+        loss = diff**2
+        loss = loss.mean(dim=(0, 1))
+        loss = torch.mul(loss, area)
+        loss = loss.mean()
+        loss_grad = diff * (2.0 / (math.prod(invar.shape)))
+        loss_grad *= area.unsqueeze(0).unsqueeze(0)
+        ctx.save_for_backward(loss_grad)
+        return loss
+
+    @staticmethod
+    @once_differentiable
+    def backward(ctx, grad_loss: torch.Tensor):
+        """Backward method of custom loss function with cell area weighting."""
+
+        # grad_loss should be 1, multiply nevertheless
+        # to avoid issues with cases where this isn't the case
+        (grad_invar,) = ctx.saved_tensors
+        return grad_invar * grad_loss, None, None
+
+
+class CustomCellAreaWeightedLossFunction(CellAreaWeightedLossFunction):
+    """Custom loss function with cell area weighting.
+
+    Parameters
+    ----------
+    area : torch.Tensor
+        Cell area with shape [H, W].
+    """
+
+    def __init__(self, area: torch.Tensor):
+        super().__init__(area)
+
+    def forward(self, invar: torch.Tensor, outvar: torch.Tensor) -> torch.Tensor:
+        """
+        Implicit forward function which computes the loss given
+        a prediction and the corresponding targets.
+
+        Parameters
+        ----------
+        invar : torch.Tensor
+            prediction of shape [T, C, H, W].
+        outvar : torch.Tensor
+            target values of shape [T, C, H, W].
+        """
+
+        return CustomCellAreaWeightedLossAutogradFunction.apply(
+            invar, outvar, self.area
+        )
\ No newline at end of file