Adaptive Learning Networks (ALNs) are algebraic, nonlinear multinomials whose structure and coefficients are learned from empirical data. Over the past several years, their application to quantitative NDE problems has become widespread. The major advantage of the ALN approach is that only a modest data base of experiments is needed, from which the ALN models can be trained. In this work, ALNs are used as a nonlinear, empirical inversion procedure for various defect geometries. Measurements from a sparselypopulated ultrasonic transducer array are input to the ALNs which estimate the defect characteristics. The defects considered are (1) elliptical cracks, (2) irregular-shaped voids, and (3) surface-breaking semielliptical cracks. The models are synthesized from theoretically-generated, forward-scattering data, then evaluated on actual experimental data recorded from titanium and carbon steel samples. The advantage of using theoretical data to train the models is that ultrasonic responses can be generated quickly and inexpensively in a digital computer, thereby avoiding, or greatly minimizing, the expense of calibration sample fabrication. The size and orientation estimates for the experimental evaluation are in excellent agreement with the true defect characteristics.