Deceptron: Learned Local Inverses for Fast and Stable Physics Inversion

TL;DR

Deceptron introduces a learned local inverse module for physical inverse problems, enabling faster and more stable convergence by approximating inverse mappings and improving iteration efficiency in solving ill-conditioned inverse tasks.

Contribution

The paper presents Deceptron, a novel bidirectional module that learns local inverses for inverse problems, incorporating a Jacobian Composition Penalty for improved stability and convergence.

Findings

D-IPG reaches fixed tolerance with 20x fewer iterations on Heat-1D.

D-IPG requires 2-3x fewer iterations on Damped Oscillator.

DeceptronNet demonstrates fast convergence in 2D inverse problems.

Abstract

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 $J_g(f(x))\,J_f(x)\!\approx\!I$ 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 $\sim$20$\times$ fewer iterations on Heat and $\sim$2-3$\times$ 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.