Investigating the Correspondence between Original Parameter Space and Synaptic Weight Space for Parameter Space Estimation in Predicting Critical Transitions

This study explores the correspondence between original parameter space and synaptic weight space in the framework of parameter-space estimation, with the objective of achieving accurate and reliable prediction of critical transitions. Recent studies have increasingly used early warning signals as diagnostic tools for detecting critical transitions. However, although these signals have proven effective across a wide range of applications, they lack the precision necessary to accurately predict the timing of critical transitions. To address this limitation, parameter-space estimation has been used to reconstruct bifurcation diagrams from limited time-series data. The parameter space necessary for constructing these diagrams is inferred within the synaptic weight space through linear interpolation between two synaptic weight vectors, each trained on time-series datasets generated by systems with distinct parameter values. By reconstructing bifurcation diagrams, the timing of critical transitions can be identified precisely, particularly in cases exhibiting dynamics characteristic of saddle-node bifurcations. This study evaluates the validity of the linear interpolation approach by examining its consistency with underlying theoretical assumptions and assessing its practical applicability through numerical experiments. Based on the validation results, we propose an auxiliary technique that offers better predictive performance with greater accuracy and reliability.