Deceptron: Learned Local Inverses for Fast and Stable Physics Inversion

Inverse problems in the physical sciences are often ill-conditioned in input space, making progress step-size sensitive. We propose the Deceptron, a lightweight bidirectional module that learns a local inverse of a differentiable forward surrogate. Training combines a supervised fit, forward-reverse consistency, a lightweight spectral penalty, a soft bias tie, and a Jacobian Composition Penalty (JCP) that encourages Jg(f(x)),Jf(x)!≈!I via JVP/VJP probes. At solve time, D-IPG (Deceptron Inverse-Preconditioned Gradient) takes a descent step in output space, pulls it back through g, and projects under the same backtracking and stopping rules as baselines. On Heat-1D initial-condition recovery and a Damped Oscillator inverse problem, D-IPG reaches a fixed normalized tolerance with ~20× fewer iterations on Heat and ~2-3× fewer on Oscillator than projected gradient, competitive in iterations and cost with Gauss-Newton. Diagnostics show JCP reduces a measured composition error and tracks iteration gains. We also preview a single-scale 2D instantiation, DeceptronNet (v0), that learns few-step corrections under a strict fairness protocol and exhibits notably fast convergence.