Computational Hypergraph Discovery, a framework for connecting the dots
Abstract
We propose the development of a comprehensive, interpretable computational framework designed to radically simplify and transform the resolution of most complex problems within and beyond the scientific domain. This ambition mirrors the transformative impact of calculators on arithmetic, with the potential to reshape the boundaries of what we perceive as achievable in Science. Unlike prevalent empirically driven research, it will come with simple and transparent theoretical and computational guarantees. While these objectives may appear overly ambitious, they can be achieved by developing a framework for completing and discovering of computational hypergraphs. These hypergraphs are generalized graphs representing functional dependencies between groups of variables (node clusters) and functions through directed hyperedges linking these clusters. They offer a natural platform for organizing, communicating, and processing computational knowledge. While most Computational Sciences and Engineering (CSE) and Scientific Machine Learning (SciML) problems can be framed as the data-driven discovery of unknown functions in a computational hypergraph whose structure is known, manyproblems in Science require the data-driven discovery of the structure (nodes and connectivity) of the hypergraph itself. Here, we plan to master the completion and discovery of computational hypergraphs through a generalization of Gaussian Process (GP) and, morebroadly, of (possibly non-Gaussian) Optimal Recovery (OR) methods inheriting the guarantees of kernel/OR methods. Hypergraph discovery is enabled by the UQ capabilities of GPs (and of OR methods) used as a sensing mechanism for overcoming the curse of combinatorial complexity. Our approach contrasts sharply with the complexity of causal inference methods for such problems, which grows super-exponentially with the number of variables. By enabling polynomial complexity in hypergraph discovery, this sensing mechanism, absentin ANN-based methods, unlocks immediate application at an unprecedented scale across various domains, including reasoning with raw data (identifying a network of hidden relationships between variables without a parametrized model), intelligence gathering and material/chemical reaction discovery. We aim to evolve this framework towards applications of extreme complexity emerging from both concrete and abstract applications encompassing high-dimensional nonlinear singular black-box systems, algorithm discovery, the co-design of computing platforms, and the discovery of new forms of computation.Approved for Public Release.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Dec 14, 2024
- Source ID
- N000142512035
Entities
People
- Houman Owhadi
Organizations
- California Institute of Technology
- Office of Naval Research
- United States Navy