# Voice Simulation: The Next Generation
## 3 Results
### High-Dimensional Simulations with Pre-Computations  
High-dimensional finite-element simulations are becoming ever more feasible to solve the entire production-perception chain of events with few simplifying assumptions [22; 23; 24; 25]. Hundreds to thousands of spatial elements are used to represent tissue and air continua. Execution is generally on arrays of supercomputers. If both air and tissue dynamics are three-dimensional across the entire airway and no simplifying assumptions are made, a  
Figure 5: Cusp catastrophe from Equation (16) [20].  
Figure 6: Oscillation frequency when moving across the fold in Figure 5. The arrows indicate frequency jumps, forming a hysteresis loop [20].  
few cycles of oscillation may take days to compute. However, exploration with computer simulation often calls for hundreds, if not thousands, of repetitions with incremental steps of a parameter. This is especially the case if optimization of an output is the goal. Computation speed is therefore still an issue, even if arrays of supercomputers are used. Practitioners in our field may not have access to supercomputer facilities, or they prefer to work on laptops or desktops. That brings up the question of pre-computation for high-cost portions of the simulation that are repeated over and over again.  
Some pre-calculations can be made in the next generation with the use of computational learning: (1) Acoustic targets can be pre-determined from perceptual targets, (2) Biomechanical parameters can be pre-determined from acoustic targets, (3) A large variety of feed-forward biomechanic-to-acoustic mappings can be pre-calculated, (4) Deep learning with acoustic and somatosensory feedback can be implemented to predict novel acoustic outputs from a training set, and (5) Vocal fold driving pressures in a complex glottis can be predicted with a neural network from a pre-calculated data base. These driving pressures are the costliest in high-dimensional simulations with high fidelity.  
As an example, a large variety of normal mode surface vibrations with different contact islands and diverse flow channels (confluent, di-fluent, convergent, divergent) can be used to generate a data base. Deep learning can then be applied to predict a new pressure profile from the pre-computed data base. Figure 7 shows one of many possible cases. Each of the four rectangles represents the glottal surface, left to right being inferior to superior (direction of airflow) and bottom to top being posterior to anterior. In left to right sequence, we show glottal contact (two black areas), glottal width, calculated glottal pressure with a high-fidelity immersed boundary solution, and measured glottal pressure from a scaled-up physical model. This mapping between a glottal shape and the corresponding driving pressures can be pre-calculated for hundreds of glottal shapes, from which a neural network can then predict the pressure pattern for a novel shape. It is evident from Figure 7 that a single channel Bernoulli approach cannot capture the pressure profile on the glottal surfaces. Airflow is multi-directional and therefore the pressure gradients are also multi-directional.  
All machine learning approaches require training data that are likely to occur in phonation. This is a bit of a \"lifting by the bootstrap\" approach. A priori, we do not know which normal modes of vibration will be excited by the predicted pressures, and we do not  
Figure 7: Four variables depicted in a rectangular glottis with inferior (left), superior (right), posterior (bottom) and anterior (top) boundaries. (**a**) vocal fold contact regions, (**b**) glottal width, (**c**) calculated surface pressure with high-dimensional computation, and (**d**) measured pressure with an up-scaled static model [26].  
know how often these modes exist in self-sustained oscillation. With a large training set and assigned weights, the neural network will likely converge on the realistic cases that occur in self-sustained oscillation.