Hierarchical Methodology for Inverse Problems
Technical Report,01 Apr 2017,31 Mar 2020
CALIFORNIA INSTITUTE OF TECHNOLOGY PASADENA United States
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Predictive mechanistic models have a long and rich history, stretching back through centuries of human knowledge development. The wealth of data now available presents an opportunity to leverage these models to new levels of predictive capability, through careful calibration, and also presents new ways of thinking about modelling, which are data-driven, and which have emerged over the last two decades in the machine learning community. Calibration of models to data is often referred to in the mathematics literature as an inverse problem. The goal of the funded work was to marry the best features of mechanistic modelling and data-driven modelling via the development of novel hierarchical algorithms for inverse problems. Hierarchical methods are attractive because, at the cost of relatively cheap outer optimization loop, typically for a small number of parameters, greater predictive capability is achieved. The result of the work is new computational methodologies for inverse problems, both classical and statistical, founded on theoretical understanding and with demonstrable applicability to important inverse problems in the physical sciences.
- Theoretical Mathematics