Among the most interesting observations one can make about some (but not all) physical modeling methods concerns their relationship to abstract methods, which is somewhat deeper than it might appear to be. Abstract techniques, and especially those described in §1.1, set the stage for many later developments, and determined some of the basic building blocks for synthesis, as well as the accompanying notation, which is derived from digital signal processing. This influence has had its advantages and disadvantages, as will be detailed below.
As mentioned earlier, digital waveguides, certainly the most successful physical modeling technique to date, can be thought of as a physical interpretation of wavetable synthesis. Perhaps even more important than the direct association between a lossless string and a wavetable was the recognition that systems with a low degree of inharmonicity could be efficiently modelled using a pair of delay lines terminated by lumped low-order digital filters--this effectively led the way to efficient synthesis algorithms for many 1D musical systems producing pitched tones. No such efficient techniques have been reported for similar systems in the mainstream literature, and it is clear that such efficiency gains were made possible only by association with abstract synthesis methods (and digital signal processing in particular). On the other hand, such lumped modeling of effects such as loss and inharmonicity is also a clear departure from physicality; this is also true of newer developments such as banded waveguides and commuted synthesis.
Similarly, modal synthesis may be viewed as a direct physical interpretation of additive synthesis; a modal interpretation (like that of any physical model) has the advantage of drastically reducing the amount of control information which must be supplied. On the other hand, it is restrictive in the sense that, with minor exceptions, it may only be applied to linear and time invariant systems, which is a side-effect of a point of view informed by Fourier decomposition.
As mentioned above, there is not always a direct link between abstract and physical modeling techniques. Lumped network models and direct simulation methods, unlike the other techniques mentioned above, have distinct origins in numerical solution techniques, and not in digital signal processing. Those working on hybrid KW methods have gone a long way towards viewing such methods in terms of abstract synthesis concepts. Similarly, there is not a strong physical interpretation (to the knowledge of this author) of abstract techniques such as FM or granular synthesis.