Conclusion

High-fidelity resolution of complex problems, at reasonable cost in terms of computing resources and time, seemed out of reach for several decades. The uninterrupted growth in computing power we were witnessing, accompanied by a reduction in price, seemed at the time to be the only possible way out.

However, large-scale computing resources are out of everyone's reach, especially for small and medium-sized companies, and this is a real handicap to their survival, which depends on responsiveness in terms of innovation. However, innovation can only take place if the field of design parameters can be explored "on-line" and in real time.

Abacuses have made this possible in the past, but they were applied to systems and models that were less complex than those we are currently interested in. Model reduction is now emerging as an alternative for...