Learning acyclicity and reproducibility on directed graphs for scientific applications
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Scientific domains often possess partial knowledge of functional dependencies derived from domain expertise or preliminary structure learning. However, these priors are frequently incomplete, uncertain, or contain erroneous cycles. This limits upstream-to-downstream prediction and reduced-order modeling. We introduce DG2DAG (Directed-Graph-to-Directed-Acyclic-Graph), a method for refining potentially cyclic directed priors into directed acyclic graphs (DAGs) optimized for functional reconstruction. Given an initial directed graph, DG2DAG jointly learns edge orientations and per-node regression functions using Gumbel-Softmax parametrization for gradient-based edge direction exploration and a cycle-enumeration constraint that exploits prior sparsity. On synthetic benchmarks, DG2DAG refines the outputs of existing structure learning methods, achieving substantially improved reconstruction accuracy. In materials science applications, the method resolves microstructure cycles, enabling scientists to predict properties from fewer experiments. The approach provides a practical tool for converting exploratory structure discovery into predictive models.
