Model Calibration and Parameter Estimation
For Environmental and Water Resource Systems
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13 Result(s)
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Alexander Sun
Mathematics
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Book
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Chapter
Multiobjective Inversion and Regularization
After incorporating prior information, the inverse problem becomes a bi-criterion optimization problem. The use of prior information in such a way can be seen as a special case of the regularization method int...
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Chapter
Model Differentiation
In the previous chapters, we showed that an inverse problem ultimately becomes an optimization problem, regardless the type of framework (deterministic or statistical) used to formulate it. Gradient-based algo...
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Chapter
Model Structure Identification
In practice, determination of the model structure is the first problemthat a modeler has to deal with when modeling a complicatedphysical system. Model structure error is often the major cause ofmodel failure....
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Chapter
Data Assimilation for Inversion
Many EWR applications are data centric and naturally call for the ability to fuse spatial and temporal information from multiple sources and in different formats and scales. With the rapid advance of in situ a...
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Chapter
Model Uncertainty Quantification
Uncertainty quantification (UQ) is the analytic process of determining the effect of input uncertainties (both their magnitudes and sources) on system outcomes. Traditionally applied in engineering r...
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Chapter
Goal-Oriented Modeling
Two criteria are traditionally used for model parameter estimation and model structure identification: (C-1) fitting observation data; and (C-2) honoring prior information. As we have shown in Chaps. 3 and 7, ...
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Chapter
The Classical Inverse Problem
The classical inverse problem (CIP) assumes no model structure error and, thus, only model parameters need to be identified. In this chapter, we consider the solution of CIP for single state variable models. U...
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Chapter
Statistical Methods for Parameter Estimation
In this chapter, the CIP is formulated in a statistical framework. Byusing the Bayesian inference theory, we cast the CIP asaninformation transfer problem, in which the prior information andtheinformation tran...
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Chapter
Model Dimension Reduction
A real system, especially a distributed parameter system, may havehigh or even infinite dimensions of freedom (DOF). When the DOF ofa model is too high, all inversion methods that we have learnedbecome ineffic...
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Chapter
Development of Data-Driven Models
In previous chapters, we have mainly dealt with physics-based models represented by a general map** $$\mathbf{u}=\mathcal{M}(\mathrm{}{\boldsymbol{\uptheta...
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Chapter
Optimal Experimental Design
In environmental and water resource (EWR) engineering, different types of design problems exist, such as operation design, monitoring design, detection design, and remediation design. This chapter is devoted t...
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Chapter
Introduction
In this chapter, commonly seen models in environmental and water resources (EWR) study are shown. A general form of mathematical models and their classifications are then provided. Different mathematical model...
