# estimate parameter of complex function to predict target with neural network

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mohamed cheikh on 3 Apr 2023
Commented: mohamed cheikh on 4 Apr 2023
i have a data sets with target. i have debvelopped a complex function with some parameters to predict the target using the data. i would estimates this parameters with neural networks. but i don't know how to proceed.

Jack on 3 Apr 2023
To estimate the parameters of your complex function using a neural network, you can follow these general steps:
1. Prepare your data: Prepare your dataset by splitting it into training, validation, and test sets. You can use the training set to train your neural network, the validation set to optimize the hyperparameters of your neural network, and the test set to evaluate the performance of your neural network.
2. Choose a neural network architecture: Choose an appropriate neural network architecture that can learn the complex function you have developed. You can use various types of neural networks such as feedforward neural networks, convolutional neural networks, or recurrent neural networks. You can also choose the number of hidden layers and the number of neurons in each layer.
3. Define a loss function: Define a loss function that measures the difference between the predicted output of your neural network and the actual output in your training set. Some commonly used loss functions include mean squared error, mean absolute error, and binary cross-entropy.
4. Train your neural network: Train your neural network by optimizing the weights and biases of your neural network using the backpropagation algorithm. You can use various optimization algorithms such as stochastic gradient descent, Adam, or RMSprop.
5. Evaluate your neural network: Evaluate the performance of your neural network on the validation set and the test set. You can use various metrics such as mean squared error, mean absolute error, or R-squared to evaluate the performance of your neural network.
6. Tune your neural network hyperparameters: If your neural network does not perform well, you can tune the hyperparameters of your neural network such as the learning rate, the number of epochs, the batch size, or the regularization parameters.
7. Use your neural network to estimate the parameters: Once your neural network has been trained and optimized, you can use it to estimate the parameters of your complex function for new data points.
You can use MATLAB's Deep Learning Toolbox to implement your neural network. The toolbox provides various functions for creating, training, and evaluating neural networks. You can also use MATLAB's hyperparameter tuning tools to automate the hyperparameter tuning process.
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Torsten on 4 Apr 2023
Parameter estimation in a fixed functional form (in your case f(x)=exp(a*x1)+log(b*x2)+c*x3^2) is not done using neural networks.
It's done using a curve-fitting tool, e.g. "lsqcurvefit", "fit" or similar functions.
mohamed cheikh on 4 Apr 2023
Many thanks