When May a Model Replace the Experiment? Audits, Licenses, and the Price of Trust in Surrogate-Driven Design
Authors: Shuangxiu, Ma, Wenhe, Zhao
Organizations: Max · William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, Ohio 43210, United States · Zachary · Department of Physics, The Ohio State University, Columbus, Ohio 43210, United States
Abstract
Design campaigns in chemistry, materials science, and machine learning share a bottleneck: determining how good a candidate truly is requires an expensive evaluation - an experiment, a first-principles simulation, or a full training run. Machine-learning surrogates that predict these outcomes are increasingly used not only to propose candidates but to grade them, and even to feed their own predictions back into the search as though they were measurements. Through mathematical analysis validated on three exhaustively ground-truthed design tasks, we establish when this practice is safe, what any certificate of safety must cost, and when the substitution provably pays. Predictive accuracy cannot anchor trust: near-perfect R^2 is compatible with worst-possible selections, and screening N candidates inflates the over-prediction at the selected candidate by a quantifiable "selection tax" with matching upper and lower bounds. Safety follows instead from an architectural rule - predictions may propose and train without restriction, but every certified conclusion must rest on true evaluations - which is sufficient with no assumptions on the surrogate, and necessary, since admitting predictions into certification with the standing of measurements opens a deterministic self-confirmation failure mode. We derive the minimal criterion under which a model may act as an oracle (rank preservation, not accuracy), show that trust must be purchased through selection-aware audits that are optimal in query complexity, and prove a dichotomy fixing when audited surrogates cut certified evaluation cost. Across 432 surrogate fits over six task-regime conditions, the audit statistic tracks deployed search performance at Spearman rank correlation 0.80-0.99, while the rank correlation of R^2 with deployed regret falls as low as 0.33; audited screening reduces certified oracle cost by a measured factor of 25.
Closed-loop AI scientists can generate candidate designs at low marginal computational cost, whereas reliable feedback may require wet-lab synthesis, characterization, or high-fidelity computation. Addressing this imbalance through custom laboratory automation remains infrastructure-intensive and costly, while replacing new experiments with a fixed surrogate leaves persistent model errors that can be amplified by optimization. We propose \emph{online surrogate repair} (OSR), a closed-loop algorithm that uses sparse high-fidelity evaluations to update the surrogate throughout a longer agent search conducted primarily with inexpensive surrogate feedback. An acquisition rule selects which designs from the agent's accumulated proposals receive high-fidelity evaluation, and the resulting labels update the surrogate used in subsequent episodes. Across controlled synthetic environments, we demonstrate that improving global surrogate fit does not necessarily reduce maximum regret, whereas Q90-UCB and expected improvement (EI) substantially reduce regret by directing evaluations toward regions that determine the optimizer's decisions. On MADE, controls receiving high-fidelity feedback after every episode require 6.36--7.23× more oracle queries to match Online EI under two LLM orchestrators and 10.27× more under the non-LLM Chemeleon+MLIP workflow. Online surrogate repair introduces a novel third feedback regime between fixed-surrogate operation and high-fidelity feedback after every episode, separating the frequency of high-fidelity evaluation from the duration of the agent's search.
Scientific machine-learning (SciML) surrogates approximate expensive simulations, but exact expected outputs for arbitrary inputs are unavailable (the oracle problem). Metamorphic testing checks relations across executions, yet a candidate relation is not automatically valid: its preconditions, output mapping, and the numerical floor of the scoring operator determine whether a violation is meaningful. We study how candidate metamorphic relations (MRs) can be screened for domain validity and turned into executable, oracle-free test assets for SciML surrogates. We propose (i) a domain-validity rubric that admits a candidate only when its tolerance dominates the operator's numerical floor and its preconditions hold; (ii) an MR-card executable-asset format recording source cases, transformations, metrics, tolerances, and typed relation-level verdicts; and (iii) a case-study protocol on MeshGraphNets cylinder-flow surrogates, with a claim ledger binding every result to a tracked artifact. On a MeshGraphNets checkpoint, node permutation holds to machine precision, mirror-y is a bounded out-of-distribution stress finding rather than an exact symmetry, and absolute conservation stays deferred while a reference-relative guard passes. The same readings hold across held-out trajectories, a checkpoint roster, three further architectures, and PhysicsNeMo. On a second CFD task (compressible airfoil) the predicate instead rejects incompressible continuity on physical grounds, showing it reasons about domain validity rather than running a fixed checklist. On a second PDE family, FNO Burgers and heat surrogates run full admit/reject/execute verdicts. The evidence spans two CFD tasks and a second PDE family, supporting a validity-aware bridge from candidate MRs to auditable SciML test assets that separates model-level violations from out-of-domain applications.
Physics-informed machine learning is often assessed by curve error, although engineering use depends on downstream decisions: ranking candidates, avoiding infeasible designs and limiting regret. We introduce pinn-gym, an open benchmark for material-conditioned lattice design that couples a transparent reduced-order crush-and-impact oracle with five printable polymer cards, dimensionless force-response targets and a protocol spanning curve fidelity, physical admissibility, top-k retrieval and mass regret. Across per-material, pooled and cross-material settings, low nRMSE is frequently insufficient to identify useful design selections. Physics-informed losses alter trade-offs rather than monotonically improving all metrics, and dimensionless conditioning improves comparability without making transfer symmetric. The benchmark is not a certified material model; within the released oracle, candidate generator and material cards, pinn-gym provides a reproducible testbed for evaluating PIML surrogates as decision systems rather than curve predictors alone.