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Assessment and optimization of the fast inertial relaxation engine (FIRE) for energy minimization in atomistic simulations and its implementation in LAMMPS

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A modified fast inertial relaxation engine, fire 2.0, reaches a fixed force threshold in fewer force evaluations than FIRE in all eight test cases and beats conjugate gradient in five of six direct minimizations.

desk verdict A genuinely useful methods paper: FIRE 2.0 is clearly specified, implemented in LAMMPS, and mostly faster than FIRE/CG, but the parameter recommendations rest on a single test case and a few speedup ratios are measured at non-identical stopping points. read the letter →

arxiv 1908.02038 v4 pith:DQIZRLNJ submitted 2019-08-06 physics.comp-ph cond-mat.mtrl-sci

Julien Guénolé , Wolfram G. Nöhring , Aviral Vaid , Frédéric Houllé , Zhuocheng Xie , Aruna Prakash , Erik Bitzek This is my paper · ORCID
classification physics.comp-phcond-mat.mtrl-sci MSC 65K0565K10 PACS 02.70.Ns
keywords FIREalgorithmenergyminimizationatomisticsimulationLAMMPStimeintegrationconjugategradientnudgedelasticbanddislocationrelaxation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to show that the fast inertial relaxation engine, a pseudo-dynamics minimizer widely used in atomistic simulation, is limited less by its mixing idea than by how it is integrated and how it handles overshoot. It presents fire 2.0, a LAMMPS implementation that switches from explicit Euler to semi-implicit Euler or Velocity Verlet, moves the configuration back by half a timestep whenever the discrete power $P = F \cdot v$ turns non-positive, and delays the timestep and mixing adjustments after such events. On eight materials-science test cases covering dislocations, surfaces, ionic melts, and nudged elastic band paths, the paper reports that fire 2.0 reaches the chosen force threshold in fewer force evaluations than the standard FIRE in every case, and beats conjugate gradient in five of six direct minimizations. If this transfers to other systems, routine energy minimization of defects and reaction paths becomes faster and less likely to stall in shallow valleys.

What carries the argument

The load-bearing mechanism is the half-step back correction. FIRE accelerates along the force direction but must detect the turn where the power $P = F \cdot v$ changes sign; by the time a discrete step sees $P \le 0$, the trajectory has overshot uphill. FIRE 2.0 responds with $x(t) \leftarrow x(t) - 0.5 \, \Delta t \, v(t)$ before setting $v = 0$, which counters most of that overshoot while staying closer to the turning point than a full-step reversal. The other essential component is the time integrator: with explicit Euler the corrected algorithm behaves like steepest descent, whereas semi-implicit Euler or Velocity Verlet make the variable-timestep descent robust, and the paper identifies this choice as the most important parameter affecting FIRE's performance.

What would settle it

Relax the Mg dislocation–precipitate system (case 6) with the dislocation started at several distances from the precipitate, using the same $f_{2\,\mathrm{norm}}=10^{-8}$ eV/$\AA$ stopping criterion for FIRE, CG, and fire 2.0. The claim that fire 2.0 reaches lower-energy structures would fail if fire 2.0 does not consistently move the dislocation toward the precipitate while the other algorithms do, or if conjugate gradient with different line-search settings reaches that configuration in no more force evaluations.

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Extended reading notes

Core claim

fire 2.0 is a modification of the FIRE algorithm built on four changes: a symplectic integrator (semi-implicit Euler or Velocity Verlet) instead of the explicit Euler used by LAMMPS's standard FIRE; a half-step backward coordinate correction when the discrete power $P = F \cdot v$ becomes non-positive, before velocities are zeroed; a short delay before timestep growth and mixing-coefficient decay resume after a negative-power step; and a stopping rule that exits after too many consecutive negative-power steps. With these changes the paper reports that fire 2.0 reaches the target force norm in fewer force evaluations than standard FIRE in all eight tests, with finite speedups from 1.8x to more than 30x, and outperforms conjugate gradient in five of six direct minimizations, the exception being the non-periodic nanoporous gold pillar. In the Mg dislocation–precipitate test, FIRE and CG leave the dislocation in the matrix while fire 2.0 relaxes it toward the precipitate; the paper presents this as evidence that fire 2.0 can reach lower-energy structures that other algorithms do not find.

Load-bearing premise

The performance claims rest on the assumption that the eight chosen test systems and the comparison by force-evaluation counts represent typical energy-minimization problems; in particular, the paper's recommended parameter ranges are extrapolated from a parameter sweep run on only one of the eight cases (silicon vacancies).

Editorial extensions

If this is right

  • LAMMPS users can expect fire 2.0 to reach a given force norm in fewer force evaluations than the standard FIRE on typical defect, surface, and NEB relaxation tasks; the reported gain grows with the complexity of the NEB path.
  • On systems with long-range electrostatics or long-range elastic fields, conjugate gradient can terminate early with 'line search alpha is zero' while fire 2.0 continues to reduce the forces, making fire 2.0 a more reliable choice for such problems.
  • The time integration scheme is the dominant algorithmic choice: switching from explicit Euler to semi-implicit Euler is enough to change FIRE from a steepest-descent-like method into a robust minimizer.
  • Users should cite the exact force norm in published results, because LAMMPS's Euclidean-norm criterion is several orders of magnitude stricter than maximum-force-component criteria used in some other codes.
  • As default recommendations, alpha0 should lie in 0.10–0.25 and tmax in 2–12, with the simulation timestep set to the same value used in low-temperature MD; reducing tmax improves stability.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The half-step back correction is a generic remedy for discrete-time overshoot, so a natural (untested) extension is to apply the same correction to other damped-dynamics minimizers such as Quickmin and see whether they gain similarly.
  • Force-evaluation counts ignore communication and overhead, so on massively parallel machines the wall-clock speedup of fire 2.0 over FIRE could be smaller than the force-evaluation ratio; benchmarking wall-clock time on target hardware would settle this.
  • Since the parameter sweep was run on one system only, the recommended alpha0 and tmax ranges may need case-specific retuning for energy landscapes with very different curvature scales; this is an inference beyond the paper's own generalization.
  • The case-6 result implies that a published relaxed structure can depend on the minimizer, not just the force field and threshold; reporting the minimizer, integrator, and force norm alongside structures would make such results reproducible.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper presents FIRE 2.0, a modified version of the FIRE energy-minimization algorithm, and its implementation in LAMMPS. The main algorithmic changes are the use of semi-implicit Euler or Velocity-Verlet integration instead of the explicit Euler integrator used by the earlier LAMMPS implementation, a half-step backtracking correction after uphill motion is detected, a delay in adjusting timestep and mixing factor, and an additional stopping criterion based on repeated downhill failures. The authors benchmark FIRE 2.0 against conjugate gradient and the standard LAMMPS FIRE on eight atomistic test cases spanning EAM, MEAM, SW, and BKS force fields, including NEB path optimizations, and report speedups measured in force-evaluation counts. They recommend specific parameter ranges (alpha0 in 0.10–0.25, tmax in 2–12) and conclude that FIRE 2.0 is significantly faster than FIRE and CG and can find lower-energy structures.

Significance. If the performance claims hold, the paper has clear practical value for the atomistic simulation community: it provides a drop-in improved minimizer for LAMMPS, gives explicit guidance on time integration for FIRE-style methods, and documents the algorithm at the level needed for reproduction. The source code is made available, and the benchmark methodology using force-evaluation counts is a standard and reasonable basis for comparison. The identification of the explicit Euler integrator as a major performance bottleneck in the original LAMMPS FIRE is a concrete and useful contribution. However, the strength of the general conclusions is currently limited by the uneven benchmarking protocol and the single-case parameter study.

major comments (3)
  1. [Table 2 and Section 5.4.1] The speedup ratios versus CG in cases 3 and 4 are not measured at a common convergence threshold: the text states that CG fails to reach the 1e-8 eV/Å f2norm target, so the comparison is made at the lowest f2norm CG achieved, while FIRE 2.0 continues to the full target. Similarly, in case 2 the speedup versus FIRE is defined by matching the MAXVDOTF plateau rather than the threshold. Because the quoted ratios therefore correspond to different stopping points, the summary claim that FIRE 2.0 is 'significantly faster' than CG and FIRE is quantitatively underdetermined. Please report, for every case and every method, the final f2norm value, the number of force evaluations, and the stopping criterion used, and recompute ratios at a common target wherever possible.
  2. [Section 5.4.4 and Figure 3] The statement that 'the observed trends do not depend on the problem' is not supported by the evidence shown. The parameter sweeps for alpha0 and tmax are performed only on case 5 (vacancies in Si with the SW potential); no sweeps are shown for EAM, BKS, MEAM, or NEB cases, and no repeat runs or error bars are reported. Since this single case is used to justify the general recommendations alpha0 in 0.10–0.25 and tmax in 2–12, those recommendations are not yet established for the broader class of materials-science problems the paper targets. Please run the same sweep on at least one representative case from another force-field class, or explicitly restrict the recommendation to covalent SW-type systems.
  3. [Section 5.4.1, Figure 2(6), and Summary] The claim that FIRE 2.0 'can result in lower energy structures not found by other algorithms' is not demonstrated. In case 6, the paper reports that FIRE 2.0 produces a different dislocation position than CG and FIRE, but it does not report the final potential energies of the competing configurations. A lower final force norm does not by itself imply a lower energy, and no energy comparison is provided anywhere in the paper. Please either report the final potential energies (or energy differences) for the configurations obtained by each method in case 6, or soften the claim to state that FIRE 2.0 finds qualitatively different configurations.
minor comments (4)
  1. [Section 5.4] The text says the evolution of f2norm is shown in Fig. 1, but the convergence curves appear in Fig. 2; please correct the cross-reference.
  2. [Section 5.4.4 and Figure 3 caption] The text states the parameter study used a timestep of '1 ps' while the Figure 3 caption says '1 fs'; the later discussion of 'optimum ∆t being 1 fs' suggests the caption is correct, so please fix the text.
  3. [Data availability] The statement that raw data 'cannot be shared at this time' makes it difficult to verify the reported force-evaluation counts and convergence curves; providing at least a table of final f2norm values and force-evaluation counts for all cases and methods would improve reproducibility.
  4. [Section 3.1 and Algorithms 3–6] The terms 'Euler Implicit' and 'Euler Semi-implicit' are used interchangeably in places (e.g., Section 5.4.3 vs. Section 5.4.4); please use one consistent name to avoid confusing the semi-implicit Euler scheme with a fully implicit integrator.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the performance claims are empirical benchmark comparisons against external test cases with fixed defaults, not derivations from fitted inputs or self-citation chains.

full rationale

The paper's chain is: define the modified algorithm (Algorithm 2), implement it in LAMMPS, run it on eight independent atomistic test cases using standard literature force fields, and compare force-evaluation counts to reach a fixed f2norm threshold against baseline FIRE and conjugate gradient. No parameter is fitted to the quantity being predicted; the main Table 2 comparisons use fixed default parameters (alpha0=0.25, tmax=10.0), so fire 2.0's reported speedups are not forced by construction. The citation to the original FIRE paper (Ref. [17], with overlapping authorship) defines the baseline algorithm and is not load-bearing for the new performance claim, which is tested empirically. The parameter study in Sec. 5.4.4 draws recommended ranges for alpha0 and tmax from only case 5 and asserts 'the observed trends do not depend on the problem'; this is a robustness or generalizability weakness, not circularity, since the central benchmark is not optimized per case. Likewise, the speedup ratios in cases 2, 3, and 4 are defined at non-common stopping points (MAXVDOTF plateau or the lowest f2norm reached by CG), which is a comparability caveat but not a circular reduction. No equation or fitted value is shown to be equivalent to the claimed result by definition, so no specific circular step can legitimately be flagged.

Assumptions & free parameters 10 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities. Its central claims rest on literature force fields, standard integrators, and the representativeness of the test suite. The numeric defaults of the algorithm are hand-chosen or inherited from the original FIRE paper; the recommended ranges for alpha0 and tmax are fitted to a single benchmark case (case 5).

free parameters (10)
  • alpha0 = 0.25 (default), 0.10-0.25 (recommended)
    Mixing coefficient for velocity and force. Recommended range obtained from parameter study on case 5 (Fig. 3(1)).
  • tmax = 10.0 (default), 2-12 (recommended)
    Maximum timestep multiplier. Recommended range obtained from parameter study on case 5 (Fig. 3(2)).
  • tmin = 0.02
    Minimum timestep multiplier; hand-chosen default, not optimized in this study.
  • delaystep = 20
    Steps to wait after P<0 before increasing timestep; hand-chosen default.
  • dtgrow = 1.1
    Timestep growth factor; standard from original FIRE.
  • dtshrink = 0.5
    Timestep shrink factor; standard from original FIRE.
  • alphashrink = 0.99
    Alpha decay factor; standard from original FIRE.
  • vdfmax = 2000
    Stopping threshold for consecutive P<0 steps; hand-chosen default.
  • halfstepback = yes (default)
    Boolean switch for uphill correction; algorithmic choice evaluated in the paper.
  • initialdelay = yes (default)
    Boolean switch for delayed timestep adjustment; algorithmic choice, and the paper notes it replaces the original FIRE behavior.
assumptions (4)
  • domain assumption The interatomic potentials (EAM, MEAM, SW, BKS) used in the benchmarks accurately represent the materials studied.
    Section 5.2 relies on these literature force fields to draw conclusions about performance on typical applications in material science.
  • domain assumption The number of force evaluations is a valid proxy for minimizer performance.
    Section 5.4 states force evaluations are used for comparison because they are the computationally most expensive task; this assumes per-evaluation cost is comparable across methods, which may not hold for different integrators.
  • domain assumption The eight test cases are representative of typical materials science minimization problems, and trends observed on case 5 generalize to other problems.
    Section 5.4.4 states the observed trends do not depend on the problem without showing evidence from other cases; this generalization is load-bearing for the recommended parameter ranges.
  • standard math Euler semi-implicit and Velocity Verlet integrators are implemented correctly and have the stability properties assumed.
    The algorithms in Appendix A are standard numerical integration schemes; the paper assumes their standard properties.

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Cite this review

Pith. "Pith review of Assessment and optimization of the fast inertial relaxation engine (FIRE) for energy minimization in atomistic simulations and its implementation in LAMMPS." pith.science (2026). https://pith.science/paper/DQIZRLNJ

@misc{pith2026190802038,
  author       = {Pith},
  title        = {Pith review of: Assessment and optimization of the fast inertial relaxation engine (FIRE) for energy minimization in atomistic simulations and its implementation in LAMMPS},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DQIZRLNJ}},
  note         = {Machine review of arXiv:1908.02038}
}
read the original abstract

In atomistic simulations, pseudo-dynamics relaxation schemes often exhibit better performance and accuracy in finding local minima than line-search-based descent algorithms like steepest descent or conjugate gradient. Here, an improved version of the fast inertial relaxation engine (FIRE) and its implementation within the open-source code LAMMPS is presented. It is shown that the correct choice of time integration scheme and minimization parameters is crucial for performance.

Figures

Figures reproduced from arXiv: 1908.02038 by the authors.

Figure 1
Figure 1. Snapshots of the atomistic samples used for the test simulations [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Force f2norm as a function of the number of interatomic forces evaluation during minimization. Subfigures 1 to 6 correspond to the test cases 1 to 6, respectively. (Continue on next page.) 12 [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 2
Figure 2. (Continued) The color of curves indicates the minimization method: steepest descent ( [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figures from the paper (1 more)
Figure 3
Figure 3. Figure 3: Influence of the parameters alpha0 (1) and tmax (2) on the minimization performances, characterized by the number of force evaluations required to reach the force threshold in the case 5. (1) shows the performance as a function of alpha0 for different choice of tmax, w…

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