Etch Plasma–Surface Machine-Learned Interatomic Potential (MLIP) Modeling learns an approximation to first-principles potential energy and forces, then uses that model to run the larger cells, longer trajectories, and many impact replicas needed to estimate plasma–surface reaction, reflection, sputter/etch, product, implantation, damage, and heat-transfer statistics. A credible MLIP is not “DFT accuracy at force-field speed” everywhere. It is a bounded, symmetry-consistent surrogate with a deliberately constructed reference domain, collision-safe short-range physics, calibrated out-of-domain detection, stable molecular dynamics, and validation on the process decisions it will support.

This upgraded page owns the scale-up from DFT/AIMD evidence to atomistic ensemble dynamics. Static DFT owns reference states, reaction energies, and selected barriers; AIMD owns first-principles forces and short trajectories; the MLIP approximates that chosen electronic potential-energy surface; MD samples impact ensembles; surface kMC owns rare thermal time; feature Monte Carlo and profile models consume validated product/yield kernels. An MLIP does not repair errors in its electronic reference method or automatically model ion neutralization, electronic excitation, charge exchange, or long-range electrostatics.

Define the learned object. In an energy-conserving local MLIP, total potential energy is commonly decomposed into atomic contributions,

where $\mathcal N_i$ is the chemical/geometric neighborhood within cutoff $r_c$. Forces derive from the same scalar energy,

so translation invariance implies zero net internal force up to numerical precision. A direct force-only model may not conserve energy unless specifically constructed; do not use it for NVE impact dynamics without qualification.

Physical energy is invariant under translations, rotations, and permissible permutations of identical atoms. Forces rotate as vectors. E(3)-equivariant message-passing models such as NequIP propagate scalar, vector, and higher-order tensor features that transform predictably under rotations/reflections; invariant atom-centered models and body-ordered bases enforce related symmetries differently. Equivariance improves data efficiency but does not create absent chemistry.

For an orthogonal transformation $Q$ and translation $\mathbf t$,

Test these identities numerically, including periodic wrapping and mixed species. Permuting atom order must permute forces consistently. Reflection/parity handling must match the chosen physical outputs.

NequIP, MACE, Allegro, Deep Potential, GAP, ACE, SNAP, SchNet and other families differ in expressivity, locality, computational scaling and tooling. Select using process validation, not leaderboard rank. Hyperparameters—cutoff, interaction layers, angular momentum/body order, radial basis, channels, precision and neighbor implementation—define a specific model.

Locality is a physical assumption. A finite cutoff can capture screened/covalent chemistry when the local environment determines energy, but plasma-facing systems may contain ionic materials, charge transfer, dipoles, polarization, dispersion and field response. Increasing message-passing depth enlarges an effective receptive field yet may not reproduce correct asymptotic electrostatics.

If long-range terms matter, use a physically defined decomposition,

with consistent forces and no double counting. Learned charges/dipoles need reference definitions, conservation constraints and validation across composition/charge. Charge partition labels are method-dependent; matching them does not by itself validate energy/force or charge-transfer dynamics.

Ordinary fixed-electron DFT-trained MLIPs reproduce one electronic ensemble. They generally do not know whether a projectile arrived as an ion, neutralized near the surface, emitted an electron, or excited electron–hole pairs unless those degrees of freedom and labels are explicitly represented. Passing an integer “charge” feature without a validated open-system energy does not solve the problem.

Freeze the domain before generating data. List elements and isotope masses; target bulk/amorphous phases; facets/interfaces; native oxides and mask/passivation films; coverages and coadsorbates; molecules/radicals/products; defects/implantation/damage; temperature/density/strain; projectile species, energy/angle; and the charge/spin/electronic approximation.

Define required outputs: equilibrium structure, reaction ordering, product identity, adsorption/reflection probability, etch/sputter yield, outgoing energy-angle kernel, implantation depth, damaged-layer thickness, heat deposition, or training acceleration. The strictest observable determines the data and validation design.

Create a domain matrix with in-domain interpolation, challenge boundary, and explicitly unsupported regimes. For example, a Si–Cl–Ar ALE model trained through 150 eV does not silently cover fluorocarbon deposition, oxidized masks, or 1 keV bombardment. The runtime should expose this boundary.

Use multiple surface states because plasma chemistry evolves. Clean crystalline slabs alone omit halogenated, carbonized, oxidized, hydrogenated, amorphized, implanted and rough environments. Generate independent amorphous/film configurations and impact sites. A data-rich equilibrium bulk set can overwhelm the rare configurations controlling removal.

Reference consistency precedes dataset size. Use one versioned electronic-structure method where possible: code, functional, dispersion, spin, pseudopotential/basis, cutoff/k grid, smearing, SCF/force settings, charge and corrections. Mixed reference levels create a multivalued target unless a calibrated delta-learning or fidelity scheme is used.

Recompute imported structures at the production reference level. Do not concatenate databases with different elemental energy zeros or pseudopotentials. For total energy, isolated-atom or fitted elemental offsets may improve conditioning, but record the convention and preserve reaction energies.

Reference forces must be converged more tightly than the desired ML error. SCF noise becomes irreducible label noise and can destabilize derivatives. Check finite-difference energy/force consistency on representative bulk, surface, molecular, reactive and compressed frames.

Assign each frame provenance: structure generator/parent trajectory, physical state, DFT input/output hash, units, convergence status and intended split group. Reject incomplete SCF, wrong spin/root, atom overlap, corrupted cell, inconsistent species order and unintended periodic molecules.

Sample the process manifold, not a convenient trajectory. A balanced reference set can include relaxed/strained bulk and phases; liquid/amorphous/quenched states; clean/terminated surfaces; adsorbates and coverage patterns; molecules/radicals/products; reaction paths and transition neighborhoods; defects/interfaces; thermal displacements; impact snapshots; and compressed repulsive pairs/many-body collisions.

Equilibrium normal-mode or finite-temperature sampling covers wells. It does not cover bond breaking or collision cascades. Add constrained bond scans, reaction-path images, randomized surface chemistry, active-learning trajectories and purpose-built impact configurations. Avoid arbitrary random displacements that create only unphysical structures while missing real transition tubes.

Near-duplicate frames from AIMD are highly correlated. Cluster/thin by descriptor, energy/force novelty or time separation. Preserve rare high-force/product frames with appropriate weights rather than allowing millions of equilibrium atoms to dictate the loss.

Split data by entire configuration family, surface replica, trajectory, reaction, composition, and preferably process condition. A random frame split leaks neighbors from the same AIMD trajectory, producing an optimistic test error. Maintain interpolation validation, challenging in-domain test, and extrapolative stress sets separately.

Hold out scientific behaviors: one impact energy band, product family, surface coverage, amorphous replica or reaction route. A model intended to discover mechanisms must demonstrate useful behavior beyond memorized near-neighbors while still refusing true OOD input.

Train energy and forces with unit-aware weights. A representative objective is

State whether energy is total/per atom/formation; exponent $p$; force/stress units; configuration weights; normalization; regularization; and loss schedule. Weight choices encode priorities. Force-dominated training can miss relative basin energies; energy-dominated training can give poor dynamics.

Report errors by chemistry and force magnitude, not only aggregate MAE. Include energy differences within same stoichiometry, reaction/product energies, force angle/magnitude, stress, short-range forces and per-element/site regimes. Large systems can dilute a local reaction error in per-atom energy.

Train multiple random seeds or independently initialized ensemble members. Log exact data version, splits, architecture/configuration, optimizer, learning schedule, batch construction, precision, hardware/software and checkpoints. Select on a predefined validation objective, not the final process test.

Monitor learning curves versus dataset size and configuration class. If error plateaus above DFT noise, architecture/domain conflict or missing physics may dominate. More correlated frames are not a cure. Compare a simpler baseline to determine whether equivariance/complexity adds decision value.

Ion bombardment needs an explicit repulsive wall. Plasma impacts access interatomic separations rare in ordinary DFT/MD datasets. A flexible network can extrapolate to an unphysical attractive hole and accelerate atoms into it. Include compressed reference configurations, but very small core-overlap distances may exceed pseudopotential validity and DFT cost.

Blend a screened nuclear repulsion such as ZBL or a qualified all-electron/short-range reference with the ML region. A switching construction can be written

where $s=1$ at short range and $0$ in the learned region. Require continuity—preferably smooth derivatives to the order needed—of energy and force across both switch boundaries. For many atoms, define pair correction without double counting learned interactions.

Validate dimer and embedded collision scans for every relevant element pair and representative many-body compressed states. Test head-on and grazing impacts over energy range, timestep convergence, closest approach, energy transfer and scattering against DFT/AIMD or trusted collision reference.

The short-range splice does not fix reaction chemistry, electronic stopping or ion charge. Nuclear stopping emerges from repulsive forces; electronic stopping may need a separate qualified velocity/material-dependent reservoir. Do not apply it twice or to thermal atoms indiscriminately.

Uncertainty must trigger action. Common proxies include ensemble energy/force disagreement, Bayesian variance, descriptor distance, latent density, extrapolation grade and conformal/calibrated residual intervals. Neural-network confidence is not intrinsic; calibrate each score against actual errors on held-out and adversarial process configurations.

For ensemble forces $\mathbf F_i^{(m)}$, a disagreement score may be

Check calibration by chemistry, energy, force magnitude and configuration family. Ensembles trained on the same biased data can agree while jointly wrong. Combine disagreement with physical guards: minimum distance, coordination/composition range, energy floor, force cap, charge and known validity masks.

Define runtime bands before production: accept, log/acquire, stop/fallback. In an impact cascade, one OOD frame can corrupt every later outcome, so stopping must occur before integration proceeds. Save the pre-failure state and request a new DFT/AIMD label if the reference method remains valid.

Active learning cycles: seed diverse data; train ensemble; explore targeted MD/structure generators; score novelty/uncertainty; select diverse candidates; run reference calculations; validate; append a versioned dataset; retrain. Avoid selecting only highest force/uncertainty, which may concentrate on impossible structures. Balance scientific coverage and diversity.

Use independent challenge generators not used in acquisition: new surfaces, temperatures, impact sites, products, reaction scans and adversarial distortions. Stop active learning based on decision convergence and OOD frequency, not merely a target number of labels.

Static test accuracy is necessary but not sufficient. Run NVE energy conservation with timestep convergence; NVT structure/density/temperature tests; bulk/surface/molecular stability; phonons/vibrations where relevant; diffusion and reaction benchmarks; and long simulations that expose rare instabilities.

Test rotational/permutation/translation symmetry, force as energy gradient, periodic wrapping, neighbor-list continuity at cutoff, switch-region smoothness, determinism/precision and CPU/GPU parity. A discontinuous cutoff can heat long trajectories even with low test MAE.

For plasma impacts, compare individual MLIP and AIMD trajectories from identical initial states over the time where chaos permits structural comparison. Then compare ensemble observables: reflection, energy loss, product identity/multiplicity, etch/sputter yield, implantation, damage and heat. Exact late atom trajectories need not match; distributions and conserved ledgers must.

Run an atom ledger for every event,

and an energy ledger covering incident energy, potential change, outgoing kinetic/internal energy, lattice heat, thermostat, electronic stopping and residual. ML energy conservation cannot validate missing physical reservoirs, but unexplained numerical residual is still failure.

Converge MD cell/slab/vacuum, timestep, boundary/thermostat, trajectory duration, impact positions/orientations, surface replicas and histories. Check that high artificial sequential-impact flux does not create heating/composition artifacts. Use reset surfaces for conditional kernels or bridge slow time with kMC.

Event statistics require independent replicas. For history $p$ and product multiplicity $n_p^{(j)}$,

Report confidence/covariance and rare-event bounds. Multiple fragments in one cascade and timesteps in one trajectory are correlated. Include model ensemble and reference-method uncertainty, not only MD sampling noise.

Use hierarchical comparison: variation across thermal/site replicates, surfaces, ML seeds/ensembles, DFT method and experiment. If between-model variation exceeds sampling error, acquiring more impacts with one MLIP understates uncertainty.

When calibrating to beam data, retain held-out energies/angles/surface states. Do not tune a yield multiplier that hides incorrect products, reflection or damage. Validate multiple outputs to expose compensation.

Export conditional kernels and state increments. Feature transport may need

whose integral is a probability or expected multiplicity. Preserve species–energy–angle correlation, atom/energy balance, surface-state change and uncertainty. State the measure, binning/interpolation and validity range.

MLIP-driven MD can densely sample this kernel after AIMD qualification. Round-trip sample the exported representation and reproduce raw yields, distributions, tails and covariance. Positivity/normalization and multiplicity conventions must be explicit.

Surface kMC receives slow thermal barriers/rates primarily from DFT/transition-state calculations and prompt impact outcomes from MD. Define a commitment time/state map to avoid executing one event twice. Conserve atoms, coverage, damage and products across the handoff.

Level-set/feature conversion uses absolute flux and material density; the MLIP does not supply reactor time. A removal yield $Y_m$ under incident flux $\Gamma$ maps to planar speed

where $n_m$ uses the same atom/formula-unit convention. Mixed/passivated material needs state-dependent composition and density.

Universal/pretrained potentials are starting points, not automatic plasma models. Audit elements, charge/spin, training domains, electronic method, license and known exclusions. Zero-shot bulk/surface accuracy does not imply stable radicals, fluorocarbon fragments, ionic oxides or high-energy collisions.

Benchmark the frozen pretrained model on an etch-specific challenge set before fine-tuning. Fine-tune with diverse surface/reaction/collision data and retain replay data to avoid catastrophic forgetting. Compare from-scratch, frozen-feature and full fine-tuning under the same held-out tests.

Foundation models can accelerate reference selection and initialize representations, but their uncertainty may be poorly calibrated after domain shift. Add an independent OOD layer and collision guard. Never use a model beyond its licensed or documented element set by silently mapping species.

If combining models or delta learning,

ensure both energies/forces share geometries, boundary conditions and references. Validate the sum, not only correction error. The correction domain may be narrower than the baseline.

Reproducibility includes the deployment engine. Archive reference dataset and split manifests; unit/schema; DFT inputs/outputs/provenance; model code/config/checkpoint; normalization/element mapping; repulsive and long-range terms; compiler/runtime/GPU versions; training/MD seeds; validation and kernel analysis.

Hash the complete deployed artifact, not just neural weights. Neighbor-list implementation, cutoff table, precision and unit conversion can change forces. Export a small sentinel set of structures with expected energies/forces and tolerances; run it after conversion, compilation and deployment.

Benchmark throughput as qualified atom-steps or accepted impact histories per compute-hour, including OOD stops and analysis. Profile neighbor construction, equivariant tensor products, communication and precision. Validate mixed precision: small energy errors can produce force noise and long-run drift.

Parallel replicas are often more efficient than one enormous domain-decomposed trajectory. Ensure independent RNG and deterministic/reproducible claims match actual reductions. Check CPU/GPU and multi-device ensemble equivalence.

Verification and validation are staged. Verify schema/units, symmetry, energy gradients, neighbor/cutoff continuity and model conversion. Reproduce DFT energies/forces for exact frozen configurations. Test analytic repulsive limits and known isolated/bulk/molecular cases. Qualify stable MD and then reactive/impact ensembles.

Validate against evidence not used in fitting: higher-level electronic calculations for decisive chemistry; AIMD trajectories and transition regions; molecular-beam/ion-beam yields, products, reflection, implantation and damage; plasma-conditioned composition and etch-per-cycle; and downstream profile trends under independently supplied flux.

Forward-model measurement effects where possible: beam energy/angle spread, mass-spectrometer fragmentation/transmission, XPS depth/charging, ellipsometric density and microscopy threshold. Align initial material, coverage, temperature, dose and analysis definitions.

Maintain uncertainty components for electronic reference method, dataset coverage, ML architecture/seed, OOD calibration, repulsive/long-range splice, MD finite cell/time/sampling, event classifier, incident distribution, experiment and scale mapping. Shared reference errors correlate many products and rates.

Calibration may update a small discrepancy model or selected physical terms with held-out validation. Do not retrain repeatedly on the final profile until it matches; that conflates plasma transport, surface chemistry and geometry errors and destroys out-of-sample evidence.