Unsatz: Evaluating Scientific Discovery Without a Given Ansatz

Before a scientist fits any parameter, they must decide what the model contains: which quantities exist, which are hidden, how they interact, and how they are measured. Physicists call such a trial form an ansatz. Benchmarks for automated equation discovery mostly supply it, by fixing the variables, a library of candidate terms, or a law to be modified. We introduce Unsatz, a benchmark in which an LLM agent must construct the ansatz itself. Each task is a simulated system, generated from a private seed as a program in a small modeling language: ordinary, delay, or partial differential equations, discrete maps, static and causal models, or stochastic processes, possibly with hidden states, distorted sensors, and uninformative measurement channels. The agent buys experiments within a budget, writes candidate programs in the same language, obtains their coefficients from the benchmark's fitter, and is scored only on how its final program predicts experiments it never saw: conditions outside the range it could explore, interventions, and longer runs. Across 80 systems in 20 domains, nine language models solve between 21% and 60%. On 44 of these systems, classical equation-discovery methods almost never succeed, although the same data usually suffice once the true equations are given with unknown coefficients; the difficulty lies in finding the structure, not in estimating it. Because mechanisms recur across systems, we also hand agents the program they discovered for a related system; it helped only when the new system shared the mechanism and the first investigation had succeeded. Stronger agents make fewer unscientific errors; beyond these, agents find which variables a system has but not how they act, and prefer revisions that lower the training error to revisions that predict better.