Appendix B
Input Format for Training Data

Example:

B.1 File Header

The input file begins—neglecting any comments—with the integer number of neural networks that will be simultaneously trained. Subsequently, for each of these neural networks the preferred topology is specified. This is done by giving, for each network, the total integer number of layers¹ K + 1, followed by a list of integer numbers N₀ ... N_K for the width of each layer. The number of network inputs N₀ must be equal for all networks, and the same holds for the number of network outputs N_K.

Example:

These neural network specifications are followed by data about the device or subcircuit that is to be modelled. First the number of controlling (independent) input variables of a device or subcircuit is specified, given by an integer which should—for consistency—equal the number of inputs N₀ of the neural networks. It is followed by the integer number of (independent) output variables, which should equal the N_K of the neural networks.

Example:

After stating the number of input variables and output variables, a collection of data blocks is specified, in an arbitrary order. Each data block can contain either dc data and (optionally) transient data, or ac data. The format of these data blocks is specified in the sections B.2 and B.3. However, the use of neural networks for modelling electrical behaviour leads to additional aspects concerning the interpretation of inputs and outputs in terms of electrical variables and parameters, which is the subject of the next section.

B.1.1 Optional Pstar Model Generation

Very often, the input variables will represent a set of independent terminal voltages, like the v discussed in the context of Eq. (3.19), and the output variables will be a set of corresponding independent (target) terminal currents . In the optional automatic generation of models for analogue circuit simulators, it is assumed that we are dealing with such voltage-controlled models for the terminal currents. In that case, we can interpret the above 3-input, 3-output examples as referring to the modelling of a 4-terminal device or subcircuit with 3 independent terminal voltages and 3 independent terminal currents. See also section 2.1.2. Proceeding with this interpretation in terms of electrical variables, we will now describe how a neural network having more inputs than outputs will be translated during the automatic generation of Pstar behavioural models. It is not allowed to have fewer inputs than outputs if Pstar models are requested from the neural modelling software.

If the number of inputs N₀ is larger than or equal to the number of outputs N_K, then the first N_K (!) inputs will be used to represent the voltage variables in v. In a Pstar-like notation, we may write the elements of this voltage vector as a list of voltages V(T0,REF) ... V(T< N_K - 1 >,REF). Just as in Fig. 2.1 in section 2.1.2, the REF denotes any reference terminal preferred by the user, so V(T<i>,REF) is the voltage between terminal (node) T<i> and terminal REF. The device or subcircuit actually has N_K + 1 terminals, because of the (dependent) reference terminal, which always has a current that is the negative sum of the other terminal currents, due to charge and current conservation. The N_K outputs of the neural networks will be used to represent the current variables in , of which the elements can be written in a Pstar-like notation as terminal current variables I(T0) ... I(T< N_K - 1 >). However, any remaining N₀ - N_K inputs are supposed to be time-independent parameters PAR0 ... PAR< N₀ - N_K - 1 >, which will be included as such in the argument lists of automatically generated Pstar models.

To clarify this with an example: N₀ = 5 and N_K = 3 would lead to automatically generated Pstar models having the form

with 3 independent input voltages V(T0,REF), V(T1,REF), V(T2,REF), 3 independent terminal currents I(T0), I(T1), I(T2), and 2 model parameters PAR0 and PAR1.

B.2 DC and Transient Data Block

The dc data block is represented as a special case of a transient data block, by giving only a single time point 0.0 (which may also be interpreted as a data block type indicator), corresponding to t_s,is=1 = 0 in Eq. (3.18), followed by input values that are the elements of x_s,is⁽⁰⁾, and by target output values that are the elements of _s,is.

In modelling electrical behaviour in the way that was discussed in section B.1.1, the x_s,is⁽⁰⁾ of Eq. (3.18) will become the voltage vector v of Eq. (3.19), of which the elements will be the terminal voltages V(T0,REF) ... V(T< N_K - 1 >,REF), while the x_s,is of Eq. (3.18) will become the current vector _s,is of Eq. (3.19), of which the elements will be the terminal currents I(T0) ... I(T< N_K - 1 >).

Example:

However, it should be emphasized that an interpretation in terms of physical quantities like voltages and currents is only required for the optional automatic generation of behavioural models for analogue circuit simulators. It does not play any role in the training of the underlying neural networks.

Extending the dc case, a transient data block is represented by giving multiple time points t_s,is, always starting with the value 0.0, and in increasing time order. Time points need not be equidistant. Each time point is followed by the elements of the corresponding x_s,is⁽⁰⁾ and _s,is.

In the electrical interpretation, this amounts to the specification of voltages and currents as a function of time.

Example:

B.3 AC Data Block

The small-signal ac data block is distinguished from a dc or transient data block by starting with a data block type indicator value -1.0. This number is followed by the dc bias represented by the elements of x_b⁽⁰⁾ as in Eq. (3.59).

In the electrical interpretation, the elements of x_b⁽⁰⁾ are the dc bias voltages V(T0,REF) ... V(T< N_K - 1 >,REF).

After specifying the dc bias, the frequency values f_b,ib are given, each of them followed by the real and imaginary values of all the elements of an N_K ×N_K target transfer matrix _b,ib. The required order of matrix elements is the normal reading order, i.e., from left to right, one row after the other².

In the electrical interpretation, the transfer matrix contains the real and imaginary parts of Y-parameters³. _b,ib is then equivalent to the so-called admittance matrix Y of the device or subcircuit that one wants to model. The frequency f_b,ib and the admittance matrix Y have the same meaning and element ordering as in the Pstar specification of a multiport YNPORT, under the assumption that a common reference terminal REF had been selected for the set of ports [13, 14]:

where the r denotes a real value, and the i an imaginary value. The admittance matrix Y has size N_K ×N_K; N_K is here denoted by m. The ykl≡y<k><l> = (Y )_kl can be interpreted as the complex-valued ac current into terminal T<k> of a linear(ized) device of subcircuit, resulting from an ac voltage source of amplitude 1 and phase 0 between terminal T<l> and terminal REF.

Frequency values may be arbitrarily selected. A zero frequency is also allowed (which can be used for modelling dc conductances). The matrix element order corresponds to the normal reading order, i.e., from left to right, one row after the other:

Contrary to Pstar, the application is here not restricted to linear multiports, but includes nonlinear multiports, which is why the dc bias had to be specified as well.

Example:

Optional alternative ac data block specifications:

Alternatively, ac data blocks may also be given by starting with a data block type indicator value -2.0 instead of -1.0. The only difference is that pairs of numbers for the complex-valued elements in Y are interpreted as (amplitude, phase) instead of (real part, imaginary part). The amplitude given must be the absolute (positive) amplitude (not a value in decibel). The phase must be given in degrees. If a data block type indicator value -3.0 is used, the (amplitude, phase) form with absolute amplitude is assumed during input processing, with the phase expressed in radians.

B.4 Example of Combination of Data Blocks

Taking the above example parts together, one obtains, for an arbitrary order of data blocks:

The present experimental software implementation can read an input file containing the text of this example.

Only numbers are required in the input file, since any other (textual) information is automatically discarded as comment. In spite of the fact that no keywords are used, it is still easy to locate any errors due to an accidental misalignment of data as a consequence of some missing or superfluous numbers. For this purpose, a -trace software option has been implemented, which shows what the neural modelling program thinks that each number represents.