Predicting rare events is a challenging problem in many complex systems arising in physics, chemistry, biology, and materials science. Simulating rare events is often prohibitive in such systems due to their high dimensionality and the numerical cost of their simulation, yet analytical expressions for rare event probabilities are usually not available. This dissertation tackles the problem of approximation of the probability of rare catastrophic events in optical communication systems and spin-torque magnetic nanodevices. With the application of the geometric minimum action method, the probability of pulse position shifts or other parameter changes in a model of an actively mode-locked laser subject to noise from amplified spontaneous emission can be quantified. Similarly, by applying importance sampling with biasing functions motivated by optimal control, read and write soft error rates of macrospin and coupled-spin systems of spin-torque magnetic nanodevices can be efficiently estimated
