How do I correct the following errors in this code that converts keypoints to a gene tree

Question

I used AI to convert a math formula into an example code to test how facial features could be converted to genetic traits and output as a family tree of genes. It output the following that can run correctly due to errors: "`

import numpy as np
from scipy.spatial import cKDTree
from scipy.interpolate import griddata
from scipy.optimize import minimize
import matplotlib.pyplot as plt

# 1. Represent phenotype as function u(x,y)
# Use (x,y) coordinates of 3D face scan
x = [1, 2, 4, 5, 7, 8] 
y = [3, 1, 7, 6, 9, 4]
u = [0.1, 0.3, 0.5, 0.4, 0.2, 0.7] 

# 2. Detect key points by finding local minima/maxima
tree = cKDTree(np.c_[x, y])
query_point = np.array([[0, 10], [5, 5]])  # Query points as a 2D array
keypts_indices = tree.query(query_point, k=3)[1]

print("Indices of Key Points:", keypts_indices)

# 3. Encode genotype as vector
v1, v2 = 0.7, 1.5 

# 4. Relate genotype and phenotype through PDE
def laplacian(u):
    du_dx = np.gradient(u, axis=0)
    du_dy = np.gradient(u, axis=1)
    d2u_dx2 = np.gradient(du_dx, axis=0)[0]
    d2u_dy2 = np.gradient(du_dy, axis=1)[0]
    return d2u_dx2 + d2u_dy2

def phenotype(v1, v2, x, y, u):
    u_2d = u.reshape(grid_x.shape)  # Reshape u to match the grid dimensions
    return (v1 * np.array(x) + v2 * np.array(y)) * laplacian(u_2d)

# 5. Solve PDE to predict u(x,y) from genotype  
grid_x, grid_y = np.mgrid[0:10:100j, 0:10:100j]
u_pred = griddata((x, y), u, (grid_x, grid_y), method='cubic')

# 6. Optimize v1, v2 to fit observed u(x,y) 
def loss_function(params):
    v1, v2 = params
    predicted_u = phenotype(v1, v2, x, y, u_pred)
    loss = np.sum((u - predicted_u)**2)
    return loss

initial_guess = [0.5, 1.0]  # Initial guess for v1 and v2
optimized_params = minimize(loss_function, initial_guess, method='L-BFGS-B').x
optimal_v1, optimal_v2 = optimized_params

print("Optimized v1:", optimal_v1)
print("Optimized v2:", optimal_v2)

# 7. Validate model, visualize results
u_optimal = phenotype(optimal_v1, optimal_v2, grid_x, grid_y, u_pred)

plt.figure(figsize=(12, 5))

# Original phenotype
plt.subplot(1, 2, 1)
plt.scatter(x, y, c=u, marker='o', cmap='viridis')
plt.colorbar(label='Phenotype u')
plt.title('Observed Phenotype')

# Predicted phenotype after optimization
plt.subplot(1, 2, 2)
plt.imshow(u_optimal.T, extent=(0, 10, 0, 10), origin='lower', cmap='viridis',
           vmin=min(u), vmax=max(u), aspect='auto', interpolation='nearest')
plt.colorbar(label='Phenotype u')
plt.title('Predicted Phenotype after Optimization')

plt.tight_layout()
plt.show()`

The errors were as follows: "--->

47 optimized_params = minimize(loss_function, initial_guess, method='L-BFGS-B').x
48 optimal_v1, optimal_v2 = optimized_params
49

in phenotype(v1, v2, x, y, u)
31 def phenotype(v1, v2, x, y, u):
32     u_2d = u.reshape(grid_x.shape)  # Reshape u to match the grid dimensions
\---\> 33     return (v1 \* np.array(x) + v2 \* np.array(y)) \* laplacian(u_2d)
34
35 # 5. Solve PDE to predict u(x,y) from genotype

ValueError: operands could not be broadcast together with shapes (6,) (100,)

I asked many different AI code model to suggest corrects but none of them fixed anything.