Knowledge Manifold Optimization for Scientific Discovery

The rapid expansion and specialization of scientific literature make it increasingly difficult to identify not only what is known, but where new and still supportable knowledge may emerge. We introduce Knowledge Manifold Optimization (KMO), a discovery-oriented extension of the Knowledge Manifold framework that treats scientific discovery as a multiobjective search over a continuous, literature-derived knowledge space. Candidate locations are evaluated using four complementary objectives: persistent knowledge-regime boundary strength, band-pass white-space novelty, semanticgradient magnitude, and evidential support. Rather than collapsing these criteria into a single weighted score, KMO identifies Pareto-optimal Supported Knowledge Gaps, defined as corpus-relative unoccupied regions that remain sufficiently supported by surrounding literature. The method is demonstrated on a 99-paper corpus in aerodynamics and aerodynamic design. On a 21 x 21 grid, exact Pareto analysis produced 19 non-dominated points, of which 16 formed the practical front after excluding points with zero white-space score. These solutions exhibited distinct discovery modes, including methodology bridges, aero-structural topology/FSI integration, functional aerodynamic-device integration, and rear-wake/vehicle flow-control integration. A distance-maximization baseline preferentially selected extrapolative regions with substantially lower support and reliability, demonstrating why emptiness alone is insufficient. Representative Pareto locations were converted into auditable evidence packages and then verbalized by a constrained large language model into candidate research hypotheses. The results show that scientific discovery can be formulated as structured multi-objective search in an explicit knowledge space, while keeping novelty corpus-relative and separating numerical discovery from downstream language generation.