Syllabus
* 1. Neural networks
Neuron and neural network - biological neuron, formal neuron, biological and mathematical neural network. Classical models of neural networks - perceptron network, multilayer network, backpropagation. Learning of neural networks - training set, supervised learning, self-organization, learning of recurrent neural networks, overfitting. Complexity of neural networks - threshold function, logical circuits, recurrent neural networks. Neural networks and genetic algorithms. Use neural networks in image processing. Further physical applications of neural networks. Fuzzy logic - basics. Combination of fuzzy logic and neural networks.
* 2. Wavelet transform
Properties of Fourier transform - summary, other non-local integral transforms. Partially local integral transforms - windowed Fourier and Gabor transform, basic properties, physical applications. Wavelet transform - continuous and discrete wavelet transform, basic properties, wavelet, complex wavelet, wavelets in multiple dimensions. Relationship between wavelet and fourier transform. Use of wavelet transform in physics.
Annotation
The lecture deals with selected algorithms of computational physics - neural networks and wavelet transform.