Large language model agents are increasingly deployed as autonomous scientists that can design experiments and infer mechanistic world models with minimal human oversight. However, identifiability is often ignored: when an agent hits a plateau it must decide whether the limitation stems from its own capability or from the model being unidentifiable from the available data, in which case further experiments of the same kind are futile. We introduce the Identifiability‑Driven Experimental Agent (LLM‑IDEA), which closes the discovery loop with an identifiability engine that returns a three‑way verdict on plateaus: capability limit, resolvable within the current design class, or certified exhausted.
On ODEBench, 60 of the 62 systems with free constants are identifiable already at round 0; the RC circuit is certified exhausted for every experiment the protocol can run; and a harvesting model becomes resolvable by adding a single initial condition. The identifiability engine reproduces known verdicts on Lotka‑Volterra, Van der Pol, Lorenz, and a pharmacokinetic model, recommending the intravenous arm that pharmacologists use, and it ranks the depth scorer of our own benchmark last among four observation designs.
On the DiscoverPhysics benchmark, it uncovers two public worlds whose explanation rubric rewards a distinction that no legal experiment can make, and every model with accurate trajectories fails the explanation grade (15/15 failed, versus 5/9 passed in identifiable worlds, p = 0.012). In the Alien Universe two‑body testbed we propose, where a force law switches between a provably non‑identifiable and an identifiable protocol, LLM‑IDEA on the identifiable protocol reaches a discovery depth of at least three on 8/8 seeds versus 1/8 without it. Thus an autonomous discovery agent can compute—not guess—whether a plateau calls for deeper search, a better experiment of the same kind, or a different kind of experiment.
Review