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Code Interpreter ChatGPT4 optimization of LTE modulation via Nelder-Mead or Gradient Descent algorithm on annualized tidal forcing
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using Optim | |
using Statistics | |
using Plots | |
using CSV | |
using DataFrames | |
# Load the data | |
data = CSV.read("pdocalibrate.dat", DataFrame, delim='\t', header=false) | |
# Split the data into X and Y | |
X = data[!, 1] | |
Y_new = data[!, 2] | |
# Exclude the X-interval -0.5 to 0.5 for cross-validation testing | |
mask = .|((X .< -0.5), (X .> 0.5)) | |
# Define the initial parameters | |
init_params = [2.1, 0.87809140071, 8.07355642507, 0.29870699876, 0.30054986726, 0.36448482265, 0.88622559015, -0.02035357756, 0.26863335561, -2.50580242036, -1219.96154266431, -21959.30776795751, -2.81164147677, 1.72299585823, 1.76372489203, 1.83632733108, -0.39098896337] | |
# Define the function to be optimized | |
function func(params, X, Y) | |
a0, a1, a2, a3, a4, a5, a6, b1, b2, b3, b4, b5, c1, c2, c3, c4, c5 = params | |
Y_pred = a0 - a1*X .+ a2*sin.(2*π*b1*X .+ c1) .+ a3*sin.(2*π*b2*X .+ c2) .+ a4*sin.(2*π*b3*X .+ c3) .+ a5*sin.(2*π*b4*X .+ c4) .+ a6*sin.(2*π*b5*X .+ c5) | |
return mean((Y .- Y_pred).^2) | |
end | |
# Perform the optimization | |
res = Optim.optimize(params -> func(params, X[mask], Y_new[mask]), init_params, NelderMead()) | |
# Get the optimal parameters | |
optimal_params = Optim.minimizer(res) | |
# Compute the Y values with the new parameters | |
Y_calibrated_new = func(X, optimal_params) | |
# Compute the correlation coefficient | |
correlation_coefficient_new = cor(Y_new, Y_calibrated_new) | |
# Create the plot | |
scatter(X, Y_new, label="Original Data") | |
scatter!(X, Y_calibrated_new, label="New Calibration Fit", color=:red) | |
title!("New Calibration Fit vs Original Data") | |
xlabel!("X") | |
ylabel!("Y") |
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# | |
# see https://chat.openai.com/share/41bb88c1-8a77-471a-a069-4b94c040a0c6 | |
# | |
import numpy as np | |
import pandas as pd | |
import matplotlib.pyplot as plt | |
from scipy.optimize import minimize | |
from sklearn.metrics import mean_squared_error | |
import os | |
# Load the data | |
data = pd.read_csv('/mnt/data/pdocalibrate.dat', delimiter='\t', header=None) | |
data.columns = ['X', 'Y', 'Y_Noise'] | |
# Split the data into X and Y | |
X = data['X'].values | |
Y_new = data['Y'].values | |
# Exclude the X-interval -0.5 to 0.5 for cross-validation testing | |
mask = (X < -0.5) | (X > 0.5) | |
# Define the initial parameters | |
init_params = np.array([2.1, 0.87809140071, 8.07355642507, 0.29870699876, 0.30054986726, 0.36448482265, 0.88622559015, -0.02035357756, 0.26863335561, -2.50580242036, -1219.96154266431, -21959.30776795751, -2.81164147677, 1.72299585823, 1.76372489203, 1.83632733108, -0.39098896337]) | |
# Define the function to be optimized | |
def func(params, X, Y): | |
a0, a1, a2, a3, a4, a5, a6, b1, b2, b3, b4, b5, c1, c2, c3, c4, c5 = params | |
Y_pred = a0 - a1*X + a2*np.sin(2*np.pi*b1*X + c1) + a3*np.sin(2*np.pi*b2*X + c2) + a4*np.sin(2*np.pi*b3*X + c3) + a5*np.sin(2*np.pi*b4*X + c4) + a6*np.sin(2*np.pi*b5*X + c5) | |
return mean_squared_error(Y, Y_pred) | |
# Perform the optimization | |
if os.getenv('NM', 'false').lower() in ['true', '1']: | |
result = minimize(func, init_params, args=(X[mask], Y_new[mask]), method='Nelder-Mead') | |
else: | |
result = minimize(func, init_params, args=(X[mask], Y_new[mask]), method='BFGS') | |
# Get the optimal parameters | |
optimal_params = result.x | |
# Compute the Y values with the new parameters | |
Y_calibrated_new = calibration_func(X, optimal_params) | |
# Compute the correlation coefficient | |
correlation_coefficient_new = np.corrcoef(Y_new, Y_calibrated_new)[0, 1] | |
# Create the plot | |
plt.figure(figsize=(10, 6)) | |
plt.scatter(X, Y_new, label='Original Data') | |
plt.scatter(X, Y_calibrated_new, color='red', label='New Calibration Fit', s=10) | |
plt.title('New Calibration Fit vs Original Data\nCorrelation Coefficient: {:.3f}'.format(correlation_coefficient_new)) | |
plt.xlabel('X') | |
plt.ylabel('Y') | |
plt.legend() | |
plt.grid(True) | |
plt.show() |
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1.829665430956240 -0.30 -0.099937551 | |
1.828846120466240 0.00 -0.234897308 | |
1.828026809976240 0.00 -0.438386024 | |
1.827207499486240 -0.44 -0.655730749 | |
1.826388188996240 -0.98 -0.838513987 | |
1.825568878506240 -0.92 0.277330966 | |
1.731698422028570 -0.73 0.186954012 | |
1.730879111538570 -0.76 -0.026722405 | |
1.730059801048570 0.00 0.000000000 |
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Figures from initial training run
cross-validation
Training excluded forcing values between -0.5 and 0.5, so the test evaluation includes this region
One simplification is that the two high frequency terms are close to integer multiples of the reciprocal of the difference between consecutive X values when X does not exhibit a large jump. Can you check this?
Do the integer multiple values turn out close to 1 and 18?
The integer multiple values for the first high-frequency term (1219.96154266431) are close to 1 for 803 instances. For the second high-frequency term (21959.30776795751), the integer multiple values are close to 18 for 803 instances. These results are based on a tolerance of 0.1. This suggests that the frequencies of these terms may indeed be related to the spacing of the X values, with the first term being associated with a frequency close to the reciprocal of the X spacing and the second term being associated with a frequency about 18 times higher.