… framework is provided in Section 3 where coarse-graining efforts for an Ising lattice system
… results on the predictive uncertainty as a function of the level of coarse graining, and the …

… progress around the basic theory for coarse-graining. In so doing, we hope to clarify the
fundamental origin of challenges that arise in systematic coarse-graining. Moreover, we hope to …

… This image focuses on electronic coarse graining occupying … We will develop the rationale
for efficient, predictive models … vastly improved transferability and predictive value, including …

… In CG modeling, the transferability issue naturally emerges from the differences between
the FG and CG Hamiltonians and can be defined as a measure of how predictive or …

… To illustrate the estimation step of our data-driven coarsegraining framework, we perform a
numerical experiment based on a computer-generated time series. Specifically, we consider …

… phase materials and, as a predictive tool, enable computational design of … Coarse-graining
methods allow larger systems to be … Coarse-graining involves two coupled learning problems: …

… Without a connection to known physical law, it is very unlikely that coarse-graining can
become a predictive, quantitative methodology in any field of science. Fortunately, the theoretical …

… to this problem is the systematic coarse-graining of less relevant degrees of … spatial
coarse-graining. In the second part of the thesis, we analyze the problem of crystal structure …

… Beyond predictive and practical reasons for coarse-graining, another growing motivation in
… theory associated with the coarse-graining process. Indeed, coarse-graining can be viewed …

… As with any coarse-graining process, we recognize that this would unavoidably imply
some information loss which in turn will give rise to predictive uncertainty [48]. In this work, we …