Starting with the effects to discover the causes has concerned physicists for centuries. A historical example is the calculations of Adams and Le Verrier which led to the discovery of Neptune from … See more

Since Newton, scientists have extensively attempted to model the world. In particular, when a mathematical model is available (for instance, Newton's … See more

The inverse problem is the "inverse" of the forward problem: instead of determining the data produced by particular model parameters, we … See more

In the case of a linear forward map and when we deal with a finite number of model parameters, the forward map can be written as a See more

Non-linear inverse problems constitute an inherently more difficult family of inverse problems. Here the forward map $${\displaystyle F}$$ is a non-linear operator. Modeling of physical phenomena often relies on the solution of a partial differential equation … See more

Inverse problem theory is used extensively in weather predictions, oceanography, hydrology, and petroleum engineering. Another application is inversion of elastic waves for non … See more

• Atmospheric inverse problem
• Backus–Gilbert method
• Computed tomography
• Data assimilation See more