To design an artificial neural network that estimates the phonon density of states from temperature dependent heat capacity data
Specific heat due to phonons is related to phonon density of states by the integral transform:
- heat capacity at constant volume;
- temperature;
- gas constant;
- phonon frequency;
- phonon density of states (DOS);
- kernel function.
One first discretizes the DOS by defining
such that the problem is reformulated as a matrix equation:
.
The kernel matrix K is given by
with
.
N.B. we set for the time being.
Therefore we have an input vector of
tuples, and
require an
output vector of the
components of the DOS,
.