{"id":"savings-surrogate-neb","title":"Surrogate-Accelerated Transition-State and Pathway Search","subtitle":"GPR-NEB and variants, ML-surrogate NEB, surrogate dimer methods, and uMLIP-warmed practice, 2015–2026; costs counted in electronic-structure evaluations.","category":"references","tags":["literature-review","savings-stack","neb","surrogate","transition-state"],"source":"articles/lit-review/savings-surrogate-neb.md","lang":"en","words":2697,"readMinutes":12,"toc":[{"depth":2,"text":"1. Executive result","id":"1-executive-result"},{"depth":2,"text":"2. Savings table","id":"2-savings-table"},{"depth":2,"text":"3. Proven vs claimed","id":"3-proven-vs-claimed"},{"depth":2,"text":"4. Openings for Lupine","id":"4-openings-for-lupine"}],"html":"
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Provenance: explore agent agent-13 (director-commissioned deep research, swarm of 7, 2026-07-21) — materialized verbatim, then editorially corrected only to replace the retracted 624/132 union-anchor figures with the reproducible primary-record values (558/154). Quantitative literature claims are as reported by the research agent from sources it accessed; see citations inline. Citation-verification pass pending before any external publication.

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Deep-research digest: Surrogate-accelerated transition-state and pathway search

Scope covered: GPR-NEB and variants, NN/ML-surrogate NEB, surrogate-assisted dimer / minimum-mode following, and uMLIP-warmed NEB practice, 2015–2026 (evidence cut 2026-07-21). Cost accounting throughout follows the literature convention: number of energy+force (electronic structure) evaluations to convergence, since that dominates wall time ("the overall computational effort is well characterized by simply the number of times the energy and force need to be evaluated," Koistinen et al. 2017). 22 real sources accessed this session; abstract-only vs full-text status is stated per row.

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1. Executive result

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2. Savings table

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TechniqueWhat cost it removesMeasured savings factor (system/size context)Accuracy cost / failure modeCitation (access level)Evidence strength
GP-NEB, squared-exponential kernel, one-image-evaluated acquisitionIterative force calls on all images during band relaxation~10× fewer energy+force evaluations vs regular NEB; 13 rearrangement transitions of a heptamer island on FCC(111) (EAM); uncertainty-targeted evaluation halves calls furtherNone measured for converged MEP; stationary kernel fails when training data includes close-contact, large-force configsKoistinen et al., JCP 147, 152720 (2017), arXiv:1706.04606v2 (abstract)Strong (peer-reviewed; later replicated by other groups)
GP-NEB, inverse-interatomic-distance kernel + early stoppingSame; plus failures/restarts on repulsive regionsFewer evaluations than 2017 version on the same heptamer benchmark; enables cases where 2017 fails: H₂ dissociation on Cu(110) (216-atom slab, EAM), H₂O hop on ice Ih(0001); per-system call counts not in abstract [UNVERIFIED — abstract-level only]Fixes, not introduces, failure modesKoistinen et al., JCTC 15, 6738 (2019), DOI 10.1021/acs.jctc.9b00692; ChemRxiv full text (full text read)Strong
ML-NEB (CatLearn GP surrogate, acquisition-function NEB)Cost scaling with number of images; image-count tuning243→11 force calls on Müller-Brown (≈22×); ~5–25× fewer function calls vs FIRE/LBFGS/MDMin on Au adatom/Al(111), Pt adatom/stepped Pt, Pt heptamer island/Pt(111) (all EMT); "order of magnitude faster… no accuracy loss for converged energy barriers"Demonstrated rigorously only on EMT/toy PES; DFT validation confined to SI; LBFGS baseline occasionally failsGarrido Torres et al., PRL 122, 156001 (2019), arXiv:1811.08022 / full text (full text read)Strong (toy/EMT); moderate (DFT)
NN surrogate saddle search (Amp)Intermediate ab initio force calls during saddle search"Dramatic reduction" on two simple examples; exact factor not in abstract [UNVERIFIED]No in-time validation; uncertainty unavailable (criticized by later work)Peterson, JCP 145, 074106 (2016), DOI 10.1063/1.4960708 (abstract)Moderate (seminal, superseded)
GP minimum-mode following (GPR-accelerated dimer)Rotation-phase force evaluations (5–15 per translation step)Evaluations "reduced to less than a third" vs conventional; starts near saddles for H₂/Cu(110) dissociative adsorption + 3 gas-phase reactions—Koistinen et al., JCTC 16, 499 (2020), DOI 10.1021/acs.jctc.9b01038 (abstract)Strong
GPR TS search (local, molecular)Gradient evaluations vs dimer and P-RFO"Significant decrease" in energy/gradient evaluations on 27 test systems (exact factor not in abstract)Local method; needs decent starting point (they supply one)Denzel & Kästner, JCTC 2018, DOI 10.1021/acs.jctc.8b00708 (abstract)Moderate
Physical prior-mean GP + CI-NEBOptimizer steps vs FIRE~10× fewer optimization steps than FIRE across gas-phase, bulk-phase, and interfacial reaction benchmarksSurrogate PES "high accuracy vs true PES"; single-group resultTeng, Wang, Bao, JCTC 20, 4308 (2024), DOI 10.1021/acs.jctc.4c00291 (abstract)Moderate
GP-dimer production implementation (eOn/gpr_optim, C++)Electronic structure calls in single-ended searchOrder-of-magnitude fewer electronic structure evaluations than dimer across a 500-molecular-reaction benchmark (Hermez et al. set); Cartesian GP competitive with Sella internal coordinates; wall time reduced in 3/4 cases even at cheap HF levelGP hyperparameter overhead can dominate cheap oracles; failures if search strays outside data regionGoswami et al., JCTC 21, 7935 (2025), arXiv:2505.12519v2, DOI 10.1021/acs.jctc.5c00866 (abstract)Strong (large benchmark)
Adaptive-pruning OT-GP (Wasserstein farthest-point subset, trust radius)GP update overhead and instability as data growsMean computational time reduced to less than half on 238 challenging reaction configurations—Goswami & Jónsson, ChemPhysChem 2025, arXiv:2510.06030v3, DOI 10.1002/cphc.202500730 (abstract)Moderate→strong
On-the-fly GPR hybrid calculator (ASE add-on)Fraction of DFT calls inside NEB replaced by surrogate predictions3–10× acceleration vs pure ab initio NEB on surface diffusion and reactions (per-system breakdown not in abstract)Uncertainty-threshold behavior governs accuracy; one-shot MLFFs criticized as unsuitable for high-accuracy exploratory tasksOnyango, Kang & Zhu, Comput. Phys. Commun. 2025, arXiv:2504.07319v2 (abstract + methods full text)Moderate
GPR + LI-NEB instanton path optimizationOn-the-fly electronic structure calls in ring-polymer instanton searchOrder of magnitude faster than traditional instanton algorithms; H + CH₄ → H₂ + CH₃, malonaldehyde, aminopropenalTunneling rates in "excellent agreement" (no degradation reported)Zhang et al., JCTC 21, 7517 (2025), DOI 10.1021/acs.jctc.5c00673 (abstract)Moderate (single group, new area)
Gradient-enhanced Kriging TS/constrained optimizationEnergy/gradient evaluations in TS and reaction-path optimization"Outperforms current standard in efficiency and robustness" on a reaction benchmark set (counts not in abstract [UNVERIFIED])—Raggi, Fdez. Galván, Lindh, JCTC 17, 193 (2021), DOI 10.1021/acs.jctc.0c01163 (abstract)Moderate
GPR surrogate + gentlest ascent dynamics, OED active learningTrue-gradient evaluations in single-ended saddle search"Competitive performance" on three examples; no DFT system, no factor in abstractMath/test-function levelGu, Wang, Zhou, J. Sci. Comput. 93, 78 (2022), arXiv:2108.04698 (abstract)Claim
On-the-fly targeted MLIP inside ART nouveau (single-ended saddle sampling)Reference-potential evaluations during activated-mechanism explorationTargeted on-the-fly MLIP gives highest barrier precision while "remaining cost-effective" (no factor in abstract); SW Si vacancy + SiGe zincblendeGeneral-purpose potentials underperform targeted ones for barriersSanscartier et al., JCP 158, 244110 (2023), DOI 10.1063/5.0143211, arXiv:2301.08630 (abstract)Moderate
AL-trained GAP MLFF + NEB (system-specific)Nearly all DFT-NEB force calls for a reaction set622 total DFT single-points yield all five CO₂→methanol/In₂O₃ barriers within 45 meV (after 6 NEB-AL iterations); DFT-NEB restarted from ML MEP converges in 0 optimization steps (projected force < 0.05 eV/Å); found 40%-lower rate-limiting barrier than literaturePre-AL MLFF: mean barrier error 50 meV; protocol-specific, needs MD+AL pipelineSchaaf et al. 2023, arXiv:2301.09931v2 (abstract + full-text excerpts)Strong
Pretrained GNN (OC20) as NEB calculator (CatTSunami)All per-image DFT calls in catalytic NEB28× speedup; TS within 0.1 eV of DFT in 91% of OC20NEB cases (932 DFT NEBs); 174-reaction network at 40 meV resolution: 12 GPU-days vs 52 GPU-years (1500×)9% of cases miss 0.1 eV; no explicit reaction training; fixed to OC20 DFT settingsWander et al., arXiv:2405.02078v3 (abstract)Strong (large public benchmark; journal version exists, venue detail [UNVERIFIED])
GNN surrogate NEB for molecules (PaiNN/Transition1x)DFT calls in organic-reaction NEBBarrier MAE 0.13 ± 0.03 eV on unseen reactions; outperforms DFTB on accuracy and costQM9/ANI1x-trained models fail to converge (data in TS region is the binding constraint)Schreiner et al., arXiv:2207.09971v3 (abstract)Strong
uMLIP-NEB as-is (MACE-MP-0, MACE-OMAT, Orb-v3, SevenNet, CHGNet, M3GNet)All DFT-NEB calls, if trusted574 literature migration paths (battery materials): full-replacement at MAE 0.310–0.349 eV; classification (good/bad conductor, 500 meV) ≤84.8% (Orb-v3); warm-start: better-than-LI initial paths in >66% (MACE/SevenNet >71%), fewer DFT steps in 5/6 restarts0.2–0.35 eV MAE ≈ 3–6× the intrinsic DFT-NEB error (~60 meV ≈ 10× in diffusivity at 298 K); CHGNet/M3GNet underestimate 73–78%; all models degrade at high barriers (≤21% within 0.1 eV above ~1.3 eV); geometry and barrier accuracy uncorrelatedBheemaguli, Xiao, Gautam, Digital Discovery 2026, DOI 10.1039/D5DD00534E, arXiv:2512.03642 (full text read)Strong (largest uMLIP-NEB benchmark)
Fine-tuned uMLIP NEB/MD (dual framework)DFT calls in high-throughput Li-ion screeningHigh-throughput barrier prediction "balancing speed and accuracy," validated on NASICON-type Li electrolytes; no call counts in abstractPretrained uMLIPs explicitly inaccurate on high-energy states → fine-tuning requiredLian et al., J. Mater. Chem. A 13, 34918 (2025), DOI 10.1039/D5TA05355B, arXiv:2507.02334 (abstract)Moderate
uMLIP grid-PES sampling, no NEB images (FastTrack)NEB machinery and all per-image DFT calls~10²× speedup over DFT-NEB; barriers within "tens of meV" of DFT/experiment; 12 electrode/electrolyte materials (LiCoO₂, LiFePO₄, LGPS); GPTFF/CHGNet/MACE comparedPreprint; single paper; confined to single-ion hops in crystalsLiu et al., arXiv:2508.10505 (abstract)Claim
AL + CI-NEB slip-pathway workflow (interlayer slip PES)Dense DFT sampling of slip PESAutomated slip-pathway identification across several ductile inorganic semiconductors; no factor in abstractWorkflow-level, not per-call accountingLuo et al., npj Comput. Mater. 11, 41 (2025), DOI 10.1038/s41524-025-01531-7 (abstract)Moderate
Agentic DFT TS workflow (LLM-driven, UMA-warmed)Human-in-the-loop cost; some wasted DFT via replanning83% TS success on 100-reaction OC20NEB subset; vs human experts 70% vs 73±12% on 10 held-out; baseline ~10,000 CPU-hours per DFT TS searchNot a call-count method; shows current DFT cost baselineMadhavan et al., arXiv:2605.14154v1 (abstract)Claim (preprint)
Unified BO/GP framing of minimization–dimer–NEB (review)—Consensus estimate: "roughly an order of magnitude" reduction in electronic structure evaluations; ~30 evaluations per saddle search typical with analytical forces; gains shrink for cheap oracles / short searches / energy-only dataVariance ≠ accuracy; trust regions required; GP overhead O(M³), M~30Goswami, arXiv:2603.10992v5 (2026; full text read)Strong (review of the field)

Sighted but not verified (citation only, no abstract read): Fang, Zhu, Cheng, Hao, Richardson, "Robust Gaussian Process Regression Method for Efficient Tunneling Pathway Optimization: Application to Surface Processes," JCTC 20, 3766 (2024) — relevant GPR-pathway work from a Chinese group (USTC) + ETH; numbers [UNVERIFIED]. Denzel et al., JPCA 2019 (GPR for MEP optimization + TS search, DOI 10.1021/acs.jpca.9b08239) — fetch failed [UNVERIFIED].

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3. Proven vs claimed

Replicated and trusted (multiple independent groups, peer-reviewed, large benchmarks):

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Single-paper claims, plausible but not independently replicated:

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Marketing or thin:

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4. Openings for Lupine

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  1. Theorem-gated anchors can replace the weakest part of the GP-NEB acquisition loop: the uncertainty signal. The 2026 review admits GP variance is only a sampling-density proxy, not an accuracy bound, and the field patches this with hand-tuned trust radii and early-stopping rules. Lupine's physical-law theorems (formalized in Lean) are exactly the missing correctness gate: they can certify when a surrogate/uMLIP prediction near a saddle violates a physical constraint (energy ordering, curvature sign, Hessian mode structure), deciding the next DFT call on physics rather than kernel distance. This directly addresses the failure mode documented for raw uMLIP-NEB (0.2–0.35 eV bias, systematic underestimation) without retraining anything.
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  2. Sparse-anchor DFT (~4–6 images near the predicted saddle) is the minimal-cost fix for the exact regime where uMLIP-NEB fails. Digital Discovery 2026 shows all six uMLIPs share 17 common >1 eV outliers and degrade above ~1.3 eV barriers. A Lupine layer on top of MACE-MP-0/Orb-v3 NEB — run the cheap band, theorem-gate the saddle region, evaluate DFT only at 4–6 anchor images near the model-predicted maximum — should convert the uMLIP's 0.2–0.35 eV MAE into DFT-grade barriers at a small fraction of the ~10² evaluations/image × 10² steps of CI-NEB. This is a cleaner, quantified value proposition than "another surrogate," because the failure set is now public and enumerated (github.com/sai-mat-group/mlips-migration-barriers, 574 paths).
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  3. Union anchors attack the one cost the entire surrogate literature cannot: per-search surrogate retraining. Every GP-NEB/GP-dimer run builds its surrogate from zero data and discards it ("the surrogate is discarded after each search completes," arXiv:2603.10992). In panel studies (reaction networks, screening campaigns, multi-model comparisons), Lupine's 154-shared-vs-558-naive-anchor result (72.4% fewer DFT calls) compounds multiplicatively with the per-search ~10×: different uMLIPs warm-start different bands, and wherever their predicted extrema coincide, one theorem-gated DFT anchor validates all of them. Nobody in this literature shares anchor data across searches or across models — Schaaf's protocol comes closest (622 points amortized over 5 reactions) but is single-model and system-specific.
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  4. Complement, don't fight, the GP-dimer line for single-ended search. Goswami's ~30-evaluations-per-saddle on a corrected oracle is already near the floor for single searches; Lupine's edge there is to run the dimer/minimum-mode walk on the uMLIP and spend theorem-gated DFT only at the converged saddle (plus a curvature-sign check), rather than correcting every surrogate step. Where Lupine should not compete: single isolated reactions with cheap oracles — local GP surrogates win outright with zero pretraining, and the honest literature says so. Lupine's wedge is amortized, multi-path, multi-model workloads — precisely the regime (CatTSunami-scale networks, battery screening panels) where per-search surrogates restart from scratch and pretrained-model bias is fixed and uncorrected.
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