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Following recent advances in direct modeling of the speech waveform using a deep neural network, we propose a novel method that directly estimates a physical model of the vocal tract from the speech waveform, rather than magnetic resonance imaging data. This provides a clear relationship between the model and the size and shape of the vocal tract, offering considerable flexibility in terms of speech characteristics such as age and gender. Initial tests indicate that despite a highly simplified physical model, intelligible synthesized speech is obtained. This illustrates the potential of the combined technique for the control of physical models in general, and hence the generation of more natural-sounding synthetic speech.