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Center for Nonlinear Studies |
Function approximation is relatively simple compared to many other continuous numerical problems, such as solving (stochastic and/or partial) differential equations. Interpolation is often used in the case of noiseless data, and regression can handle the case of noisy data. For functions of one variable, collecting sufficient data is often straightforward, but for functions of many variables the function must satisfy some simplifying structure for approximation to be successful. The problem is even more difficult when functions values are costly, such as when they are generated by some complex computer simulation. This talk highlights some of the challenges of approximating functions of many variables and the strategies for overcoming these challenges.
Host: James Hyman