This study develops a theoretical framework for optimising knowledge innovation portfolios by extending the production function to incorporate cognitive adaptation costs, piecewise interaction effects, and heterogeneous knowledge depreciation across basic research, applied innovation, and fusion innovation. Numerical optimisation under the baseline parameter calibration indicates that a balanced allocation approximating an equal distribution [0.333, 0.333, 0.333] outperforms traditional science-heavy strategies [0.50, 0.35, 0.15]. Robustness analysis confirms this qualitative pattern across reasonable variations in depreciation rates and interaction parameters. This finding reflects context-dependent optimisation, conditional on the assumed heterogeneous depreciation structure and piecewise interaction effects, rather than a universally applicable prescription. Three counterintuitive insights emerge: excessive concentration in basic research leads to productivity losses; simultaneous, balanced ‘leapfrogging’ strategies dominate sequential catching-up paths; and fusion innovation yields disproportionately high marginal returns despite receiving smaller optimal allocations due to cross-domain synergies. Dynamic and sensitivity analyses validate the heterogeneous depreciation mechanism and confirm the robustness of optimal allocation structures under parameter uncertainty. Based on these findings, the study provides actionable guidance for organisations and governments, emphasising gradual transitions towards balanced portfolios and a reorientation of public funding towards applied and fusion innovation. Overall, the results advance innovation theory and policy through a structural shift from linear specialisation models to dynamic portfolio optimisation grounded in knowledge heterogeneity, differential depreciation, and interaction synergies.
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