Coupled, nonlinear sets of ODEs, of the sort that describe most physical processes, do not always have well-behaved numerical solutions (as we saw in the last chapter). In addition, there is certain physical behavior that cannot be (or at any rate has not been) rendered into well-defined, deterministic, ODEs. Whatever the source, there are some problems where we have a large amount of data, but no good rule for generating output from input. Suppose we have an electromagnetic signal that is supposed to propagate through space to an antenna on the ground – as the signal enters the Earth's atmosphere … things happen. The signal is scattered by the atmosphere, for example, and the properties of the air that govern that scattering change as the light makes its way to an antenna on the Earth. Now there is nothing physically obscure about this process, and yet one can imagine that the particular model of the atmosphere plays a large role in taking us from an observed signal to properties of its source. If we had associated pairs of known source signals together with ground-based measurements of them, we could side-step the model-dependent portion of the problem, and simply estimate the signal given the measurement by comparing with the previously observed data.