Development of Data-Driven Models

In previous chapters, we have mainly dealt with physics-based models represented by a general mapping $$\mathbf{u}=\mathcal{M}(\mathrm{}{\boldsymbol{\uptheta}}{}),$$ , where $$\mathbf{u}$$ denotes state variable(s), $$\mathcal{M}(\mathrm{}{\boldsymbol{\uptheta}}{})$$ is obtained from mathematical equation(s) describing the underlying physical processes, and $$\mathrm{}{\boldsymbol{\uptheta}}{}$$ is a set of unknown physical parameters that need to be estimated from measurements. As mentioned in Chap. 1, various data-driven models that connect model inputs and model outputs directly are also developed and extensively used in environmental and water resource (EWR) fields. They are most useful when there is no or little a priori knowledge about the form of the actual physical processes, or when it is desired to replace a physics-based model with a surrogate model for improving computational efficiency in optimization problems. The latter usage is referred to as reduced-order modeling or metamodeling.