In our uncertain and ever-changing world, many systems face the danger of crossing tipping thresholds in the future. Therefore, there is a growing interest in developing swift and reliable early warning methods to signal such crossings ahead of time. Until now, most approaches have relied on critical slowing down, typically assuming white noise and neglecting spatial effects.

We introduce a data-driven method that reconstructs the linearised reaction–diffusion dynamics directly from spatio-temporal data. From the inferred model, we compute the dispersion relation and analyse the stability of Fourier modes, allowing early detection of both homogeneous and spatial instabilities.

By framing early detection as a data-driven stability analysis, this approach provides a unified and quantitative way to indicate whether and when a system is approaching a tipping point or a Turing-type transition.