Computational graph completion

We introduce a framework for generating, organizing, and reasoning with computational knowledge. It is motivated by the observation that most problems in Computational Sciences Engineering (CSE) can be described as of completing (from data) graph (or hypergraph) representing dependencies between functions variables. In setting nodes represent variables edges hyperedges) functionals). Functions may known, unknown, or random. Data come form observations distinct values finite number subsets (satisfying its functional dependencies). The underlying problem combines regression (approximating unknown functions) matrix completion (recovering unobserved data). Replacing Gaussian processes conditioning on observed data provides simple but efficient approach to such graphs. Since proposed highly expressive, it has vast potential application scope. process automatized, one solves $$\sqrt{\sqrt{2}+\sqrt{3}}$$ pocket calculator without thinking about it, could, framework, solve complex CSE drawing diagram. Compared traditional regression/kriging, used recover much scarcer exploiting interdependencies multiple (CGC) addressed could therefore also interpreted generalization solving linear systems equations approximating noisy, incomplete, nonlinear dependencies. Numerous examples illustrate flexibility, scope, efficacy, robustness CGC show how pathway identifying solutions classical problems. These include seamless representation known methods (for solving/learning PDEs, surrogate/multiscale modeling, mode decomposition, deep learning) discovery new ones (digital twin dimension reduction).