{"id":"savings-path-sampling-algorithms","title":"Algorithmic Compute-Savings in Path-Finding and Sampling Methods","subtitle":"Surrogate path methods, freezing and growing strings, single-ended searches, and replica economization.","category":"references","tags":["literature-review","savings-stack","path-finding","sampling","algorithms"],"source":"articles/lit-review/savings-path-sampling-algorithms.md","lang":"en","words":2429,"readMinutes":11,"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-19 (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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Chapter digest: Algorithmic compute-savings in path-finding and sampling methods

Evidence cut: 2026-07-21. Scope 2015–2026 (two foundational pre-2015 papers flagged where cited). All sources below were accessed this session; each entry states whether I read the full text or only the abstract.

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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 (read level)Evidence strength
ML-NEB with GPR surrogate + uncertainty-driven acquisitionPer-iteration force calls on all N images; image-count scaling5–25× fewer function calls vs classical NEB optimizers (Au/Al(111), Pt adatom, Pt7 island; Müller-Brown 243→11 calls ≈ 22×). Cost independent of # imagesGP extrapolation to short-distance/high-force configs degrades it (motivated the 2019 fix); LBFGS/MDMin baselines sometimes fail insteadarXiv:1811.08022v1; PRL 122, 156001 (2019) (full text)strong
GP-NEB with inverse-distance covarianceSame as above, more robust"Fewer energy and force evaluations" than 2017 GP-NEB on H₂/Cu(110), H₂O/ice, heptamer island — factor not in abstract[UNVERIFIED factor]: abstract gives no numberDOI 10.1021/acs.jctc.9b00692 (abstract only)moderate
On-the-fly GPR surrogate for massive NEB (GPR_calculator)Ab-initio calls inside NEB loops3–10× acceleration vs pure ab-initio NEB (surface diffusion/reaction benchmarks)Uncertainty-gated fallback to ab initioarXiv:2504.07319v2; CPC 316, 109781 (2025) (abstract only)moderate
Freezing string method + internal-coordinate interpolationFull band optimization; only ~1 opt step per new node, nodes then frozen~90 → ~39 total DFT gradient calls per TS search (conservative→aggressive, Baker set); ~50% cost cut vs prior FSM implementations; 100% success over 40+ reactionsFSM "deviates significantly from the MEP"; LST interpolation converges to wrong/2nd-order TS in 2/16 (conservative) and 7/24 (aggressive) Baker casesarXiv:2407.09763v2; JCTC 2025 (full text)strong
GNN-PES inside FSM growthAll DFT calls during string growth72% fewer ab-initio calls: 28.9 vs 103.7 avg per TS (7 organic reactions, ωB97X/6-31G(d))Pre-trained-only GNN fails 2/7 reactions (bad H–H/non-covalent chemistry); fine-tuning mandatoryarXiv:2501.06159v2 (full text)moderate (small test set)
Single-ended GSM (SE-GSM)Need for product state; double-ended machineryClaimed "even more computationally efficient than the already rapid double-ended method"; automated search found 165 reaction paths from 333 searches (NH₃BH₃ + (LiH)₄)Single-ended walks can find unintended chemistry; no per-call factor in abstractDOI 10.1002/jcc.23833, JCC 36, 601 (2015) (abstract only)moderate
GP-accelerated dimer (OT-GP / GPDimer)~90% of electronic-structure calls in minimum-mode saddle searchMedian 254 → 28 (OTGPD) / 30 (GPDimer) HF calls on 238 organic reactions (7–25 atoms); mean wall-time 12.6 min vs 23.7 (dimer) / 28.3 (GPDimer); OTGPD uniquely succeeds on 3.8–4.6% more systemsUnconstrained GP signal-variance explosion → unphysical configs, crashes electronic-structure code (documented failure cases); surrogate collapse can fragment moleculesarXiv:2510.06030v1 (full text)strong
ART nouveau (with interactive Lanczos + seeded starts, pARTn/r-ARTn)Hessian cost (Lanczos with few force calls); unbiased searchesLanczos eigenvector cost cut from 16 to <10 (<5 above inflection) force evals; 170 force calls avg per event (DFT, Al adatom on Al(100), 301 atoms); seeded r-ARTn: 50 force evals vs 463 unbiased (~9×)Random pushes oversample collective/soft modes; constrained pushes bias the event catalogue; unsuccessful events when relaxation drops below inflectionDOI 10.1016/j.commatsci.2022.111363 (full text)strong
VC-DESW / DESW (double-ended surface walking, Liu group)Iterative pathway optimization + Hessian; pseudopathway only"Much more efficient" than G-SSNEB for solid phase-transition TS (SiO₂, TiO₂ examples); per-image force-eval counts tabulated vs NEB — [UNVERIFIED factor: table rendered as image, numbers not extractable this session]Multi-TS pathways can yield a TS "not directly connected to the structure pairs provided"; pseudopath ≠ MEPDOI 10.1021/acs.jctc.5b00641, JCTC 11, 4885 (2015) (full text, table unreadable)moderate
SSW + global NN potential (LASP)First-principles cost in global PES explorationG-NN ≥100× faster than PW-DFT at 28 atoms; ≥1000× at >1000 atoms; CBD TS location ~50 energy/force evals from good guessNN accuracy ~10 meV/atom, 0.2 eV/Å over global set; potential generation itself costs 1–2 weeks × 1000 cores per systemWIREs Comput. Mol. Sci. 2019, 9, e1415 (full text)strong (for the NN speed claim; TS-eval count is author guidance)
Pre-trained GNN for dense NEB enumeration (CatTSunami, Meta FAIR)DFT inside NEB entirely28× speedup with 91% of TS energies within 0.1 eV of DFT (OC20NEB benchmark); 1500× for full reaction-network enumeration (174 reactions: 12 GPU-days vs ~52 GPU-years)9% of TSs >0.1 eV off; model never trained on reactions — transferability claim, chemistry-dependentarXiv:2405.02078v3 (abstract only)strong (large benchmark)
REST2 (solute tempering)Replicas wasted heating solventTrpcage: 10 replicas vs 48 for T-REMD; ≥9.6× total CPU speedup (4.8× replica count × ~2× per-replica CPU); exchange acceptance 30% vs 10%[pre-2015 foundational] Artificial protein collapse at high effective T documented later (Zhang et al. 2023, abstract-level)DOI 10.1021/jp204407d (full text); failure mode: PMID 36791464 (abstract snippet)strong
Non-reversible parallel tempering + optimized scheduleWasted replicas/round-trips from geometric schedules + reversible swapsProvable dominance of non-reversible over reversible PT; optimal annealing schedule; reversible PT can deteriorate when chains are added, non-reversible cannotGains are in round-trip rate/ESS, not a fixed "× fewer replicas" number; mostly demonstrated on statistical/inverse problems, not atomistic MDarXiv:1905.02939v4; JRSS B 84, 321 (2022) (abstract only)strong (theory), moderate (atomistic transfer)
OPES vs WTMetaDConvergence time of FES, esp. multi-dim/suboptimal CVs"Drastic improvement in convergence speed" (main-text claim); explores 6-CV alanine tetrapeptide space "much more efficiently" than MetaD — [UNVERIFIED numeric factor in main text; SI not read]Fast-converging bias ⇒ fewer transitions; FES estimate can look converged while basins are mis-weighted if CVs badarXiv:1909.07250v4; JPCL 11, 2731 (2020) (full text)strong (replicated by community)
OPES-exploreExploration time across metastable states~10× faster exploration than MetaD (alanine tetrapeptide, 8 basins); all methods ~100× slower with suboptimal CVsTrades convergence accuracy for exploration; systematic ΔF error when unconvergedarXiv:2201.09950v1; JCTC 18, 3988 (2022) (full text)strong
OneOPES (OPES-explore + MultiCV + MultiThermal replica exchange)CV-tuning effort + replica count vs PTMetaD8 replicas; trypsin–benzamidine ΔF converged for all 5 runs by ~100 ns; PT-WTE-MetaD off-target even at 250 ns (needs 60% trajectory discarded); alanine dipeptide with bad CV (ψ): converged ~50 nsExploratory replicas bypass TS region: "minima well reproduced, TS region unreliable" (stated in paper)DOI 10.1021/acs.jctc.3c00254 (full text)strong
Parallel-bias MetaDCurse of dimensionality in CV space (partitioned biases)Claimed efficient sampling of high-dim FES (trp-cage) — [UNVERIFIED factor: only abstract snippet accessed]More walkers/replicas to manageDOI 10.1021/acs.jctc.5b00846 (abstract snippet only)claim
GaMDCV selection; boost potential without RCChignolin folded in 3×300 ns; T4-lysozyme binding in 1800 ns — no baseline factor in abstract [UNVERIFIED "orders-of-magnitude" claim often made elsewhere]Reweighting noise (anharmonicity); boost distorts kinetics/TSDOI 10.1021/acs.jctc.5b00436, JCTC 11, 3584 (2015) (abstract only)moderate
Reinforced dynamics (RiD) — Princeton + IAPCM BeijingPrecise CV selection; NN bias over many CVsDemonstrated with 20 CVs (polyalanine-10, explicit solvent) where low-dim MetaD impractical — no factor in abstractNN bias accuracy sets FES accuracyarXiv:1712.03461v6; JCP 148, 124113 (2018) (abstract only)moderate
Enhanced-sampling-driven active learning (DEAL: OPES + GP + GNN)DFT dataset size for reactive MLPs~1,000 DFT calculations per reaction (ammonia decomposition on Fe–Co alloys)Uniform accuracy requires the two-stage GP→GNN scheme; misses rare channels outside explored CV spaceDOI 10.1038/s41524-024-01481-6, npj Comput. Mater. 10, 291 (2024) (abstract only, via ChemRxiv/plumID:24.035)strong
CI-NEB image-count economics (baseline observation)—Classical NEB: "several hundred function calls even for 10 images"; function calls grow steeply (empirically ~exponentially per their Fig. 4) with image count; surrogate methods flatten thisToo few images → corner-cutting, convergence failure on complex landscapes (their Fig. 4 + cited Sheppard & Henkelman)arXiv:1811.08022v1, Fig. 4 (full text)strong

3. Proven vs claimed

Replicated and trusted (multiple independent groups, public benchmarks):

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Single-paper claims to treat with care:

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Marketing-adjacent / unverified here: GaMD "orders of magnitude" acceleration (not in the abstract I accessed); VC-DESW numeric factor vs G-SSNEB (table not extractable); original GP-NEB 2017 reduction factor; dimer-vs-NEB head-to-head force-call counts (Olsen 2004, Heyden 2005 — pre-window, not accessed this session) [all UNVERIFIED].

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4. Openings for Lupine

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  1. Sparse anchors sit exactly where FSM/GSM already spend their budget. The measured cost profile of FSM is ~2 gradient calls per frontier node plus a 20–30-call local TS refinement. Lupine's 4–6-image sparse-anchor DFT around a uMLIP-predicted saddle is operationally identical to "FSM growth on the ML potential + DFT only on the 2–4 nodes bracketing the extremum." GNN-FSM currently spends 28.9 DFT calls per search mostly in P-RFO refinement; theorem-gated anchor placement (e.g., enforcing Hessian signature / single-imaginary-mode constraints formalized in Lean) could cut that refinement further and, more importantly, catch the known FSM failure mode — convergence to second-order saddles or wrong TS (2/16 and 7/24 in Marks et al.) — which is precisely a violated-theorem condition (wrong number of negative curvatures).
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  2. Union anchors vs per-search surrogates. GPR-NEB and OT-GP build a fresh, non-transferable surrogate per search — the 5–25× factor resets every time. Lupine's union-anchor result (154 shared vs 558 naive evaluations across uMLIPs) is orthogonal and multiplicative: shared DFT anchors can serve as common high-fidelity training points for any per-search GP, and anchor agreement across models gives a free uncertainty estimator that GPR papers show is the key acquisition signal. Nobody in the GP-saddle literature pools evaluations across searches or models; that is unclaimed territory with a measured 72.4% baseline.
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  3. Fix the documented TS-region blind spot of fast exploration. OneOPES explicitly reports that exploratory replicas converge basin free energies while skipping/distorting the TS region, and OPES can look converged while mis-weighting basins under bad CVs. Lupine could run OPES/OneOPES on the uMLIP, then apply theorem-gated sparse DFT anchors only at model-predicted barrier tops and at points where models disagree — a targeted TS-region correction layer on top of a converged-but-wrong-there FES, rather than DEAL-style blanket active learning (~1,000 DFT calls/reaction). A natural metric: ΔF error at the barrier region per DFT call, against DEAL's per-reaction budget.
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  4. Image-count economics without a surrogate's extrapolation risk. The PRL 2019 Fig. 4 result — classical NEB cost grows steeply with images while surrogate cost is image-independent — argues for running dense-band NEB entirely on the uMLIP (dense images are free) and letting theorem gates select the 4–6 images that actually need DFT. This beats ML-NEB's sequential-acquisition protocol in wall-clock parallelism (all anchors evaluable simultaneously, unlike active-learning loops) and avoids the replicated GP failure mode of extrapolating into short-contact configurations, since anchors are chosen by physical-law violations, not GP variance.
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Honesty note: this subdomain is not thin — it is one of the best-quantified corners of the compute-savings literature, with multiple independent groups (Stanford/SUNCAT, Iceland, Iowa, Fudan, IIT/ETH, Meta FAIR, Princeton+IAPCM) publishing head-to-head evaluation counts. The weakest cells in the table are flagged inline.

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