Dynamic Volume Updating of Convex Polytopes via Random-Walk Sampling

This project explores the problem of estimating how the volume of a high-dimensional convex polytope changes under sequential constraint additions. In genome-scale metabolic models, this is prevalent. The feasible steady states form such a polytope, and biological interventions (gene deletions) correspond to additional linear constraints. Quantifying the resulting volume contraction provides a geometric measure of robustness and enables detection of synthetic lethality, but existing methods require recomputing volume from scratch after each update. A dynamic volume updating algorithm that estimates relative volume changes incrementally is proposed. The method introduces constraints via an annealing schedule of parallel hyperplanes and computes local volume ratios using sample reuse with selective resampling. To maintain efficiency as the polytope becomes thin or anisotropic, the approach incorporates Constrained Riemannian Hamiltonian Monte Carlo (CRHMC). Deliverables include an annealed update framework, an incremental relative volume estimator, integration into volesti with dingo interfaces, and validation on metabolic models for robustness analysis and synthetic lethality detection.