# FlatSeek

Planning and control of differentially flat systems rests on a flat output, yet no general procedure writes one down for arbitrary nonlinear dynamics. FlatSeek reverses the reconstruction relation in the definition of flatness: fix an output and its reconstruction maps, close the dynamics differentially, and obtain system–output pairs with known certificates at scale. A Qwen3.5-2B model fine-tuned with LoRA proposes candidates that a symbolic verifier accepts or rejects. FlatSeek solves 74 literature and 171 synthetic systems, against 58 and 127 for the strongest traditional symbolic method.

Planning and control of differentially flat systems rests on a flat output, yet no general procedure writes one down for arbitrary nonlinear dynamics. FlatSeek reverses the reconstruction relation in the definition of flatness: fix an output and its reconstruction maps, close the dynamics differentially, and obtain system–output pairs with known certificates at scale. A Qwen3.5-2B model fine-tuned with LoRA proposes candidates that a symbolic verifier accepts or rejects. FlatSeek solves 74 literature and 171 synthetic systems, against 58 and 127 for the strongest traditional symbolic method.