Davide Papapicco | Searcharxiv

arXiv2026

Likelihood estimation of an interpretable early-warning sign of critical transitions

A critical transition is a sudden, abrupt and potentially unforeseen change in the state of a complex system often associated with catastrophic collapses and irreversability. Here we introduce a novel, interpretable early-warning signal of bifurcation-induced critical transitions. The proposed indicator can be readily computed from timeseries observations by maximum likelihood estimation and it has the advantage of providing immediate insight on the state of the system. We showcase its applicability by assessing its performance using models of ecosystems and ocean circulation collapse.

math.DS↗

arXiv2021

The Neural Network shifted-Proper Orthogonal Decomposition: a Machine Learning Approach for Non-linear Reduction of Hyperbolic Equations

Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate the Kolmogorov N-width decay thereby obtaining smaller linear subspaces with improved accuracy. These methods however must rely on the knowledge of the characteristic speeds in phase space of the solution, limiting their range of applicability to problems with explicit functional form for the advection field. In this work we approach the problem of automatically detecting the correct pre-processing transformation in a statistical learning framework by implementing a deep-learning architecture. The purely data-driven method allowed us to generalise the existing approaches of linear subspace manipulation to non-linear hyperbolic problems with unknown advection fields. The proposed algorithm has been validated against simple test cases to benchmark its performances and later successfully applied to a multiphase simulation.

math.NA↗