Biotechnological Catalysts in Hybrid Analytical–Numerical–Machine Learning Architectures for Risk-Aware Decision-Making and Uncertainty Quantification in Nepalese Management Systems
Biotechnological catalysts; hybrid architectures; machine learning; risk-aware decision-making; uncertainty quantification; Nepalese management systems; stochastic PDEs; neural operators; conditional value-atrisk; Fourier Neural Operator.
AuthorsAbstractThe integration of biotechnological catalysts into management systems operating within structurally complex, hazard-prone environments demands theoretical frameworks that transcend traditional deterministic optimization. This paper develops a comprehensive mathematical theory for embedding biocatalytic processes within hybrid analytical–numerical–machine learning (HANN-ML) architectures, specifically tailored for risk-aware decisionmaking under uncertainty in Nepalese management contexts. We establish a measure-theoretic foundation on a filtered probability space Ω,ℱ,{ℱt}t≥0,ℙ, where biotechnological catalyst states evolve according to stochastic reaction–diffusion–advection equations perturbed by compound Poisson processes representing seismic and climatic shocks endemic to the Himalayan region. The central theoretical contribution is the formulation of a coupled operator system: an analytical asymptotic solver for fast biocatalytic reactions, a numerical finite-element discretization for spatial catalyst transport across Nepal’s topographically fractured domains, and a Fourier Neural Operator (FNO) that learns the discrepancy between lowfidelity numerical solutions and high-fidelity experimental observations. We prove existence, uniqueness, and regularity of weak solutions to the coupled stochastic partial differential equation (SPDE) system via Galerkin approximation and the stochastic compactness method. Risk-awareness is encoded through a dynamic conditional value-at-risk (CVaR) functional defined on the space of càdlàg stochastic processes, and we derive the corresponding Hamilton–Jacobi–Bellman (HJB) variational inequality governing optimal catalyst deployment policies. For uncertainty quantification, we develop a generalized polynomial chaos (gPC) expansion in tensorized Hermite–Legendre bases, augmented by a deep ensemble Bayesian neural network that captures epistemic uncertainty arising from Nepal’s sparse sensor networks. The paper establishes convergence rates for the hybrid solver, stability bounds for the risk-aware control under Lipschitz perturbations, and information-theoretic bounds on epistemic uncertainty. We contextualize the theory through three Nepalese management domains: agricultural biofertilizer distribution in the Terai and Hill regions, bioremediation catalyst deployment for glacial lake outburst flood (GLOF) mitigation, and enzyme-based pharmaceutical cold-chain logistics. The framework provides management scientists and operations researchers with rigorous tools for decision-making where biocatalytic efficiency, topological constraints, seismic risk, and data scarcity intersect. •••••••••••••••••••••••••••••••• ejprd.org - Published by Riset Publication Services LLC
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