Natural and Engineering Systems: A Taxonomy of Failure Modes in Inverse-Problem Diagnostics

This volume collects seven technical notes applying a common inverse-problem framework to different natural and engineering systems: dam seepage, volcanic tremor, network flows, structural health monitoring, chaotic data assimilation, ultrasonic testing of composites, and turbulent intermittency. The results are deliberately mixed: four negative, one positive, two partial. This introduction explains what the seven notes have in common, why their differences matter, and what they jointly say about the limits of inverse-problem diagnostics. The unifying lesson is simple: a diagnostic is a detector, not an oracle. It can tell you where a system is fragile; it cannot tell you when it will break without external physics.