WIP added learning of the kernel. It's learning something, but I'm no…

…t entirely sure what - it seems to be learning autocorrelation-related thing rather than the kernel itself, but that may be somehow inherent to the problem setu[

examples/convolution_2d.py

@@ -114,3 +114,64 @@ def gaussian_function(x, y, sigma=1):
 ax.plot([1, 3], [1, 3])
 
 print(f"Relative difference between fourier convolution and direct convolution {torch.norm(convolved_at_points - convolved_by_hand) / np.linalg.norm(convolved_by_hand)}")
+
+
+
+##############################################################
+# Now let's see if we can learn the convolution kernel from the input and output point clouds.
+# To this end, let's first make a pytorch object that can compute a kernel convolution
+# on a point cloud.
+
+class FourierPointConvolution(torch.nn.Module):
+
+    def __init__(self, fourier_kernel_shape):
+        super().__init__()
+        self.fourier_kernel_shape = fourier_kernel_shape
+
+        self.build()    
+
+    def build(self):
+        self.register_parameter("fourier_kernel", 
+            torch.nn.Parameter(torch.randn(self.fourier_kernel_shape, dtype=torch.complex128)))
+        # ^ think about whether we need to scale this init in some better way
+
+    def forward(self, points, values):
+        fourier_transformed_input = pytorch_finufft.functional.finufft_type1.apply(points, values, self.fourier_kernel_shape)
+        fourier_convolved = fourier_transformed_input * self.fourier_kernel
+        convolved = pytorch_finufft.functional.finufft_type2.apply(points, fourier_convolved, None, {'isign': 1}).real / np.prod(self.fourier_kernel_shape)
+        return convolved
+
+
+##############################################################
+# Now we can use this object in a pytorch training loop to learn the kernel from the input and output point clouds.
+# We will use the mean squared error as a loss function.
+
+fourier_point_convolution = FourierPointConvolution(shape)
+optimizer = torch.optim.AdamW(fourier_point_convolution.parameters(), lr=0.005, weight_decay=0.001)
+
+ones = torch.ones(points.shape[1], dtype=torch.complex128)
+
+losses = []
+for i in range(25000):
+    points = np.random.rand(2, N) * 2 * np.pi
+    torch_points = torch.from_numpy(points)
+
+    fourier_points = pytorch_finufft.functional.finufft_type1.apply(torch.from_numpy(points), 
+                                                                    ones, shape)
+    convolved_at_points = pytorch_finufft.functional.finufft_type2.apply(
+            torch.from_numpy(points), fourier_points * fourier_shifted_gaussian_kernel,
+            None, {'isign': 1}
+                ).real / np.prod(shape)
+
+
+    optimizer.zero_grad()
+    convolved = fourier_point_convolution(torch_points, ones)
+    loss = torch.nn.functional.mse_loss(convolved, convolved_at_points)
+    losses.append(loss.item())
+    loss.backward()
+    optimizer.step()
+
+    if i % 100 == 0:
+        print(f"Loss: {loss.item()}")
+
+