2026/07/16 by V. R. Saiprasad, V. Troude, D. Sornette · 1 voice
#physics.data-an #cs.CG #nlin.CD
Across hydrodynamics, ecology, neuroscience, network dynamics, non-Hermitian physics, and socio-economic systems, asymptotically stable dynamics can exhibit large transient amplifications that are invisible to eigenvalue-based analyses. The mechanism is geometric rather than spectral: perturbations entering along one direction may be expressed transiently along another, allowing asymptotic decay to coexist with strong transient or noise-driven amplification. We introduce non-normal directional response inference, a data-driven method for detecting this geometry from multivariate time series when the governing operator is unknown. A local linear operator is estimated from sliding windows and projected onto the dominant two-dimensional input-response subspace. The reduced dynamics are summarized by the eigenvalue splitting Δ, eigenvector non-orthogonality K, and the scale-free ratio R=K/Kc(Δ), where Kc(Δ) is the two-dimensional threshold for transient amplification. Controlled benchmarks show that the reduced geometry, particularly R, can be recovered from finite data even when the full high-dimensional operator is poorly estimated. Tests across sample size, dimension, training horizon, spectral structure, and non-stationarity confirm that the relevant response geometry requires far fewer observations than full-matrix recovery. Applied in moving windows to electrohysterogram, seizure EEG, freezing-of-gait, and unstable push-up inertial recordings, the method reveals systematic changes around known physiological or behavioral episodes through shifts in R, changes in Δ, or stronger projection of fluctuations onto the inferred response direction. It thus exposes interpretable changes in local response geometry without framing the problem as supervised event detection.