# What is a compact model?

I am a domain scientist and I study biophysical systems. When I asked a colleague in CS for suggestions about how to design a multi-scale simulator, he mentioned the term "compact model".

Now, I can't find a very good definition of this term. I can find the book "Compact Modeling" edited by Gildenblat but this is a collection of domain specific applications, similar to what I found on google scholar.

I haven't found a first-principles treatment of what a compact model is or the advantages of using one. It would be great to know where I could find this topic in a textbook or annual reviews type paper.

Q: What is a compact model, and when is it useful?

• The term model is incredibly overloaded. – reinierpost Feb 11 '15 at 14:06

This paper uses the phrases "compact model" and "multiscale simulation". Perhaps it is relevant. Indeed, Googling "multiscale simulation compact model" yielded lots of results.

The back cover of the book you refer to states:

Compact Models of circuit elements are models that are sufficiently simple to be incorporated in circuit simulators and are sufficiently accurate to make the outcome of the simulators useful to circuit designers. The conflicting objectives of model simplicity and accuracy make the compact modeling field an exciting and challenging research area for device physicists, modeling engineers and circuit designers.

My understanding is that a compact model is a parametric equation with certain parameters determined that models the phenomenon of interest to some degree of precision.

Compact model refers to modeling of current-voltage behavior electron device (like MOS transistor) using a set of equations and parameters. It is used for circuit simulation of integrated circuit (IC). Since the fabrication cost and time of IC chip is large, IC designers need to simulate the circuit function before hand out the layout of IC to fabrication company. So it need to be accurate. And, since the IC scale is large (billions of transistor in Intel newest CPU), the model need to be sufficiently simple. It is also referred as SPICE model, since most of the circuit simulators are based on SPICE language (https://en.wikipedia.org/wiki/SPICE).

Another model used in semiconductor field is physical model, or TCAD model. It can simulate the physical properties inner the electron device, like charge densities, electronic potential distribution, and also the current-voltage output, based on the physical rules of electron transport. It's a powerful tool to analyze the performance of the device and the physics behind it. However it's very time consuming, even for a single device.

Compact model is like a black box of the electron device. It doesn't care what happen internal, and only gives the output behavior of the device (current and voltage responses on its terminals). I don't who invented the phrase "compact model" and why. I think this might be what the word "compact" refers to.

fwiw- when I think of compact models, I tend to think of combinatorial games. The idea is that simple rules and fully definable parameters can be used to produce complexity akin to nature (computational intractability), and that the compactness of the models makes them suitable for mathematical analysis.

a recent example of the utility of these models in computer science is AlphaGo. in the future, i suspect these types of models will be useful in gauging relative strength of problem solving algorithms.

This is strange, haven't heard of 'compact model' before, maybe this refers to compactness in model theory (http://en.wikipedia.org/wiki/Compactness_theorem)? But it doesn't seem relevant to simulations.

• Based on the description on the wikipedia page This theorem is an important tool in model theory, as it provides a useful method for constructing models of any set of sentences that is finitely consistent. This is on the right track ... though I am interested in how it can be applied generally to model design – David LeBauer Feb 10 '15 at 18:09
• Hmm, I really don't think this is relevant, since these models are really about structures for logical sentences: en.wikipedia.org/wiki/Structure_(mathematical_logic). But this is the only place where I have heard of compactness. I think you should clarify what your colleague meant. – randomsurfer_123 Feb 10 '15 at 19:02

A compact model is a circuit model that "can fit into SPICE", meaning that it is composed only of branches whose current-voltage characteristics are time-independent linear or nonlinear functions, or time-dependent relationships where voltage is the derivative of current with respect to time (L) or vice-versa (C).

• What does "fit into SPICE" mean? – David Richerby Jan 18 '18 at 13:36

Do not attach too much meaning to this terminology. So called simple analytical models of the complex system elements that are used in the CAD design of the whole complex systems. Gennady Zebrev

• This is probably better as a comment, unless you could expand your answer. – Yuval Filmus Sep 6 '18 at 2:53