V&V Campaign 2: Cross-Validating pyFrost-GM with MultiBolt

Why Cross-Validate Against a Second Solver?

A global model's answer is only as good as its electron energy distribution function (EEDF), and the EEDF comes from a Boltzmann solver. Every Boltzmann solver makes choices: two-term or multi-term expansion, how ionization growth is renormalised, how "effective" cross sections are reduced to elastic ones. With a single solver, those choices are invisible. A residual against Dias et al. (2023) could come from the global-model kinetics or from the EEDF, and there is no way to tell which.

Campaign 2 therefore put a second, independently developed solver, MultiBolt (Texas Tech, multi-term), behind the same interface as LoKI-B (IST Lisbon, two-term). Where the two agree, confidence goes up. Where they disagree, there is a precise question to chase.

Verification: Adding MultiBolt as a Second EEDF Ground Truth

MultiBolt was added as an alternative EEDF backend: the global-model solver stays backend-agnostic, and all backend-specific logic lives in one wrapper that translates the setup, runs the solver and parses its output. Verification then went from easy cases to hard ones:

• Argon (single ground state, no vibrational manifold) — 0.1–2 % agreement with LoKI-B on the swarm parameters from 50 to 2000 Td, after fixing a units bug in the output parser.
• O$_2$ at fixed E/N (molecular, vibrationally active, attaching) — started at 2.6× on electron temperature. After the "effective" cross-section defect was found and fixed, $T_e$ agreed to 1–3 %, mobility to < 0.5 %, and the main inelastic rate coefficients to ~1 % at 40–300 Td.
• Coupled O$_2$ discharge — the full 12-point sweep with LoKI-B, MultiBolt N=2 and MultiBolt N=10.

Each defect was chased the same way: change one input at a time until the discrepancy moves, then read the few lines of solver source that change points to. For example, swapping only the O$_2$ momentum-transfer cross section from EFFECTIVE to ELASTIC collapsed a 2.7× discrepancy to 1.00×.

Validation: What the Cross-Solver Comparison Shows

The coupled sweeps are where the two solvers earned their keep. Early sweeps had MultiBolt N=10 needing 10–23 % more field than LoKI-B and both solvers overpopulating O$_2$(X, v=1) by up to 8.7×. Each was traced to the coupling, not the solvers: O$_2$(X) was counted twice, the vibrational rates were frozen at the wrong temperature, MultiBolt was solving a different Boltzmann problem from LoKI-B, and three reactions silently got no rate on the MultiBolt path. With these fixed, all 36 pressure points were run again for the results below.

With LoKI-B, pyFrost-GM now reproduces Dias et al. (2023) to a mean of 0.9 % in E/N, 0.3 % in gas temperature and 1.8 % in O($^3$P) and O$_2(a^1\Delta_g)$, and the v=1/v=0 ratio is within 12 % of the paper's Fig. 15. MultiBolt N=2, given the same Boltzmann problem, agrees with LoKI-B to within 0.5 % at every pressure. MultiBolt N=10 then isolates the multi-term effect: 1.7–4.3 % less field and 2–4 % less O($^3$P) than N=2.

One residual is common to all three solvers: at 0.19 Torr, O$_2(a^1\Delta_g)$ is 14 % low and E/N 3.8 % high. Because it does not depend on the solver, it points at the chemistry and is carried into Campaign 3. The O($^3$P) pathway plots now count O atoms (O($^3$P) + O($^1$D)) and normalise over all sources, as the paper's Fig. 14a does.

Figure 1: O₂($X, v$) vibrational distribution at 0.2, 1 and 10 Torr: Dias et al. 2023 (circles), pyFrost-GM with LoKI-B (solid) and MultiBolt N=10 (dotted).

Coverage: Before vs. After This Iteration

The validation targets are unchanged: 2 publications and 7 reproduced figures (6 from Dias et al. 2023, plus electron density from Alves et al. 2026). What grew is the depth. Every figure is now produced by three EEDF configurations (LoKI-B, MultiBolt N=2, MultiBolt N=10), and with excited-state populations fed back into the EEDF.

Iteration Timeline

Campaign 2 ran from 2 to 29 September 2026: the integration work from 2 to 20 September, the first sweeps up to 23 September, and on 28–29 September the coupling fixes, the speed-up and the final sweeps.

The AI-Agentic Workflow, Campaign 2

The workflow from Campaign 1 carried over, with two changes. Integration rules and findings were written into the repository (a MultiBolt ruleset, an integration case study and a discrepancy investigation plan), so every new session starts from what is already known instead of from memory. And investigation tasks were matched to model capability: mechanical extraction to smaller models, cross-language semantics and physics causality to the strongest one.

Where AI Helped

• Adapter and preprocessing code: translating the setup into MultiBolt's inputs, parsing its outputs, and rewriting LXCat files (retagging, EFFECTIVE→ELASTIC).
• Bisection experiments: running the one-variable-at-a-time comparisons that localised each defect.
• Evidence extraction: pulling every quoted number from output files, including the check that showed the N=2 and N=10 sweeps ran on different code versions.

Where Physics Expertise Was Essential

• Choosing falsifying tests: ruling out dissociative attachment (0.2 % of the power balance) and continuous rotational cooling (T_e 2.148 → 2.149 eV) before suspecting the cross sections.
• Reading the coupled result: at fixed current, $n_e \propto 1/v_{drift}$, so an electron-density excess and a reduced-field deficit are the same error, not two.
• Deciding what counts as evidence: one AI-reported "improvement" in $n_e$ turned out to be an artifact. The "before" run already contained the fix, as byte-identical output files showed. The rules that followed: verify that a "before" really is before, change one variable at a time, and quote numbers from files on disk.

What This Unlocks

A second, independent EEDF solver behind the same interface turns solver choice into a variable that can be tested:

• Solver-independent conclusions — a result that holds with both LoKI-B and MultiBolt does not depend on one code's assumptions.
• Multi-term physics where it matters — above ~250 Td the two-term and multi-term mobilities begin to diverge (−6 % at 700 Td, −9 % at 2000 Td), the regime of nanosecond-pulsed discharges.
• A regression net for the whole model — the parity tests caught an N$_2$ rate-binding regression that had nothing to do with MultiBolt.
• Risk mitigation — the model is no longer locked to a single solver's choices or maintenance.

Bibliography