Etch Plasma–Surface SchNet and Invariant Neural Interatomic Potential Modeling uses continuous-filter atomistic neural networks to learn a smooth, energy-conserving approximation to first-principles potential energy, then evaluates that approximation rapidly in molecular-dynamics ensembles of adsorption, reaction, bombardment, reflection, removal, product formation, implantation, and damage. SchNet is best treated as a transparent scalar-message baseline and deployable model only inside a qualified domain—not as proof that a molecule benchmark transfers to reactive plasma surfaces.

This upgraded page owns the invariant continuous-filter architecture, its process-specific design and fair comparison with equivariant MLIPs. The broader MLIP page owns architecture-agnostic dataset/OOD governance; DFT/AIMD own reference labels; SchNet learns those labels with radial scalar messages; classical MD generates ensembles; kMC owns slow activated time; feature/profile models consume validated outcomes. The page does not claim that a SchNet checkpoint automatically represents ions, excited electrons, long-range charge transfer, or unseen chemistry.

Represent atoms without a grid. Each atom $i$ begins with an embedding $\mathbf x_i^0=\mathbf A_{Z_i}$ determined by element $Z_i$. For neighbors $j$ within cutoff, a SchNet-style interaction updates features through continuous-filter convolution,

where $r_{ij}=|\mathbf r_j-\mathbf r_i|$, $W^l$ is a learned radial filter, $\odot$ denotes channelwise multiplication, and $\mathcal U^l$ is an atomwise update network. Residual interaction blocks successively encode a larger chemical neighborhood.

An atomic readout gives an extensive energy,

and conservative forces follow by automatic differentiation,

Training energy and forces from the same scalar surface couples their consistency. Verify the deployed implementation’s forces with finite differences; a conversion, neighbor list, precision, or custom force head can break the mathematical guarantee.

Because standard SchNet filters use distances, predicted scalar energy is invariant to global translation, rotation, reflection and permutation of identical atoms; differentiated forces rotate covariantly. This is physically appropriate for ordinary nonchiral potential energy without external vector fields. It does not explicitly propagate oriented vector/tensor features as NequIP/MACE-type equivariant networks do.

Test symmetry numerically:

for rotations/reflections $Q$, translations $\mathbf t$, atom permutations, and periodic wraps. Use tolerances appropriate to floating precision. Symmetry failures indicate implementation/data plumbing bugs, not a need for more training.

Radial scalar messages are both strength and limitation. Distance-only filters provide simple smooth invariance and can learn angular/many-body dependence indirectly through multiple message-passing layers and neighbor interactions. However, explicit equivariant tensor features or body-ordered bases may represent directionally complex environments more efficiently.

Plasma surfaces are anisotropic: vacuum and solid differ; bonds have orientations; incidence angle matters; local coordination and product geometry are directional. SchNet can still learn scalar energy and vector forces because geometry enters through the graph, but it may require more layers/data/channels than an equivariant architecture. Determine this empirically with matched splits and process tests.

Interaction depth $L$ creates an effective graph receptive field, but information travels only through existing edges and nonlinear bottlenecks. It is not equivalent to a physically exact cutoff $Lr_c$. Sparse gas fragments, voids, separated products and long-range electrostatics remain challenging.

Use an explicit long-range decomposition when necessary,

with consistent forces and no double counting. If charges/dipoles are learned, enforce total-charge/physical constraints and validate response across composition, surface state and cell size. Charge-partition labels are method-dependent and not themselves an open-electron model.

Continuous filters require a smooth distance basis and cutoff. Expand distance using Gaussian, Bessel or other radial functions before the filter network. Record number, centers, widths, scaling and units. The basis must resolve both equilibrium bonds and the changing distances along reactions/collisions.

A cutoff envelope $f_c(r)$ should smoothly approach zero at $r_c$. For example,

and zero otherwise. Energy continuity alone is insufficient if force jumps when a neighbor crosses the cutoff. Test energy, force and, if needed, higher derivative across the boundary with neighbor-list rebuilds.

The neighbor-list skin and rebuild cadence are deployment physics. A fast projectile can move farther than the skin before an update and miss a collision. Bound maximum displacement or rebuild each collision step. Verify periodic minimum-image handling and no duplicate/self edges.

Converge cutoff against adsorption/reaction energy, surface force, scattering, product distribution and computational cost. A larger cutoff increases neighbors roughly with volume and may reduce data efficiency. A smaller cutoff can create identical local descriptors for physically different polar environments.

Freeze a plasma-etch domain before assembling labels. Specify element combinations, bulk/amorphous phases, facets/interfaces, native oxide and mask/passivation film, adsorbates/coverage, radicals/molecules/products, defects/damage, strain/density/temperature, projectile energy/angle and assumed charge/spin/electron state.

State excluded regimes. A neutral Si–Cl–Ar SchNet trained through 100 eV is not automatically valid for fluorocarbon polymer, oxygen-rich mask, charged fragments, or 1 keV impacts. Runtime queries outside composition, distance, coordination, energy and uncertainty limits must stop or fall back.

Design around decisions: product identity, reflection energy/angle, sticking, removal yield, damaged depth, ALE etch-per-cycle, or training benchmark. Required error tolerance follows sensitivity of that observable, not an arbitrary “chemical accuracy” slogan.

Represent evolving surface states. Include clean and halogenated/oxidized/hydrogenated/carbonized structures, coverage patterns, vacancies, implanted species, reconstructed/amorphized layers, molecular fragments and volatile products. For amorphous materials use independent cells and local motifs.

Reference labels define the highest fidelity available. Record exact DFT/AIMD code, functional, dispersion, spin, pseudopotential/basis, cutoff/k sampling, smearing, SCF/force convergence, charge/corrections and hashes. Recompute mixed-source structures at one target level or use a documented multi-fidelity/delta construction.

Force noise from incomplete SCF becomes learned noise. Verify energy-force consistency on representative equilibrium, reactive, molecular, surface and compressed configurations. Remove failed electronic roots, wrong spins, atom overlaps and corrupted periodic cells with auditable reasons.

Maintain elemental energy/reference conventions. Total-energy offsets do not affect forces but do affect formation/reaction comparisons and learning across stoichiometry. Store raw and transformed targets so exported predictions can be reversed exactly.

Every configuration should carry a group ID (trajectory/reaction/surface replica), physical class, generator, state variables, DFT provenance and intended split. Without group identity, leakage is difficult to detect later.

Build a diverse configuration curriculum. Include strained/equilibrium bulk; liquid and amorphous snapshots; clean/covered surfaces; interfaces; adsorbates, radicals and gas products; reaction-path and transition-neighborhood frames; defects/implantation/damage; thermal displacements; impact/cascade frames; and controlled short-range compression.

Ordinary equilibrium AIMD samples wells, not dissociation, volatile product escape, sputtering, or head-on collision. Add reaction scans/NEB neighborhoods, randomized but physically filtered chemistry, beam trajectories and active-learning candidates. Avoid flooding with nonsensical random structures that crowd out decision regions.

Adjacent AIMD frames are correlated. Cluster or thin them by time/descriptor/novelty. Split by entire trajectories, surfaces, reactions and conditions. Random frame splitting can place nearly identical structures in train and test and drastically understate error.

Keep three types of test evidence: interpolative validation for training control; challenging in-domain test families unseen during fitting; and deliberately OOD stress tests expected to trigger rejection. Do not optimize hyperparameters on the final process holdout.

Train with an interpretable joint loss. One form is

Specify total/per-atom energy, exponent $p$, units, class/configuration weights, force clipping, normalization, stress convention, optimizer/schedule, batch construction, precision, regularization, seed and stopping criterion.

Energy-heavy loss can produce poor forces; force-heavy loss can misorder basins/products. Tune against validation observables and long-run stability, not only a combined scalar loss. Retain rare reaction/product/collision classes with sampling or weights.

Report MAE/RMSE and error distributions by configuration class, element, coordination, energy/force magnitude and stoichiometric energy differences. Per-atom energy error in a large slab can hide a decisive local reaction error. Plot signed bias and worst cases.

Train multiple seeds and record prediction dispersion. Compare learning curves with data size, feature width, interaction depth, cutoff and basis. If additional correlated data no longer reduces challenge error, address representation or missing physics.

Short-range collision behavior needs a physics guard. A SchNet trained on normal bonds has no reason to become strongly repulsive at unseen core-overlap distances. An unphysical attractive pocket can capture an ion and destroy the trajectory.

Include compressed DFT configurations within pseudopotential validity, plus a screened nuclear repulsion such as ZBL at shorter distances. A smooth splice can use

with $s=1$ at small $r$ and $0$ in the ML region. Ensure energy and force continuity at both switch boundaries and prevent pair correction from double counting the learned contribution.

Validate every relevant elemental pair with dimer scans and embedded many-body compression. Test head-on/grazing scattering, closest approach, energy transfer and timestep convergence across intended energies against AIMD or a trusted collision reference.

The repulsive splice models nuclear stopping only. Electronic stopping, charge transfer, electron emission and excitation require separate qualified physics. If an electronic friction term is used, define its velocity/material domain and ledger removed work.

Out-of-domain protection cannot be an afterthought. Train an ensemble of independently seeded/sampled SchNet models and compute force disagreement, such as

Calibrate $u_F$ against actual DFT force/energy error by physical class. Ensemble members sharing the same data/architecture can agree while wrong, so add descriptor-distance and physical guards for minimum separation, coordination, composition, energy and force.

Predefine accept, acquire, and stop/fallback bands. Evaluate before advancing each MD step during impacts. Save the last valid configuration and metadata. Continuing after one OOD collision corrupts every descendant configuration and product.

Active learning iterates: train ensemble, explore targeted structures/MD, detect novelty, select diverse physical frames, compute DFT/AIMD, append a versioned dataset, retrain and challenge. Balance uncertainty with coverage so acquisition does not select only extreme/unphysical overlaps.

Validate uncertainty on independent generators and unseen surfaces/products/energies. Measure recall of high-error cases, false stops and calibration—not visual correlation alone. A low average OOD score does not certify a long trajectory if one rare step fails.

Qualify molecular dynamics separately from the regression. Verify forces equal energy gradients, translations/rotations/permutations, cutoff/neighbor continuity, periodic wrapping, atomic energy summation, unit conversion, and exported-checkpoint parity.

Run NVE tests with timestep convergence across equilibrium and high-force states; NVT structure/density/temperature; surface and molecule stability; vibrational/phonon or diffusion benchmarks where relevant; and long trajectories searching for unphysical fragmentation or energy sinks.

For impact cases, replay identical AIMD and SchNet initial conditions over short times and compare forces/mechanisms. Chaotic divergence makes atom-by-atom long-time equality inappropriate; compare ensembles of reflection, energy loss, products, removal, implantation, damage and heat.

Track element balance,

and energy reservoirs: incident kinetic/internal, potential change, outgoing energy, lattice heat, thermostat/boundary, stopping and numerical residual. Energy-conserving ML does not excuse missing physical reservoirs.

Converge cell/slab/vacuum, timestep, neighbor rebuild, thermostat/boundary, trajectory duration, surface replicas, impact positions/orientations and histories. A high artificial sequential-impact flux can heat/deplete the slab; use reset ensembles or a kMC/reservoir bridge.

Compare architectures fairly. SchNet’s scalar continuous filters are a strong baseline; NequIP/MACE propagate equivariant tensor features; other models use explicit angles/body order or different locality. Use identical reference labels, family splits, domain, training budget where possible, and deployment conditions.

Compare parameter count, label count, training cost, inference throughput/memory, test error by class, OOD calibration, energy drift, stability, short-range behavior and final process observables. A lower aggregate force MAE is not necessarily a better etch kernel.

Test data efficiency with learning curves. If an equivariant model reaches decision tolerance with fewer labels but is slower, quantify total DFT-label plus MD-inference cost at the required ensemble size. If SchNet meets all gates faster, its simpler scalar representation may be preferable.

Use multiple architecture seeds and avoid using the test set to select the winner. Report negative results and failure domains. Universal/pretrained models must be audited on the same plasma-specific challenge set before fine-tuning or zero-shot use.

Architecture ensembles can expose representation uncertainty, but their outputs should not be averaged blindly when one violates physics. Qualification is a gate; model averaging is not a repair for an unstable member.

Estimate physical outcomes with independent histories. For product/removal multiplicity $n_p^{(j)}$ and weight $w_p$,

Report confidence/covariance, surface/configuration hierarchy and model-seed variation. Timesteps and fragments from one impact are correlated. Zero observed rare events gives an upper confidence bound, not zero probability.

Separate reset-surface conditional responses from cumulative dose. Reset trajectories sample fixed state $\chi$; cumulative bombardment changes coverage, damage, roughness and composition under unrealistically compressed time. State the relaxation/slow-event policy and maintain material inventory.

Validate multiple observables against held-out AIMD and beam/plasma data: yields, products, outgoing energy/angle, sticking/reflection, implantation and damaged-layer thickness. Tuning only total yield can hide wrong channels.

Maintain uncertainty contributions from DFT reference method, training coverage, architecture/seed, OOD calibration, repulsive/long-range terms, finite cell/time, sampling, event classification, incident distributions and experiments. Propagate decision-sensitive components downstream.

Export a scale-aware event kernel. Feature Monte Carlo may consume

with a declared probability or multiplicity normalization. Preserve product–energy–angle correlation, retained-state change, uncertainty, frame/measure and validity range. Round-trip sample the exported representation and reproduce raw MD distributions and ledgers.

Surface kMC owns slow diffusion/desorption/reaction waiting time. Define a commitment state/time separating prompt SchNet-MD outcomes from thermal events so chemistry is not counted twice. Static DFT provides more efficient rare-event barriers than waiting in MD.

The ML force field supplies outcome statistics, not reactor flux/time. With removal yield $Y_m$, absolute incident flux $\Gamma$ and matching target-unit density $n_m$,

Feature/profile models own transport and geometry. Mixed/passivated layers require state-dependent composition/density. Never convert silicon-atom yield using oxide formula-unit density.

Deployment identity is larger than a checkpoint. Archive dataset/split manifests, units/element map, DFT provenance, architecture/config, normalization, checkpoint, cutoff/neighbor implementation, repulsive/long-range terms, software/compiler/device versions, seeds, validation and event-analysis code.

Hash the complete artifact. Provide frozen sentinel structures with expected energies/forces and tolerances; run them after export, compilation and every deployment. Compare CPU/GPU and precision. Mixed precision may preserve average error while adding force noise and energy drift.

Checkpoint MD atom state, velocities, cell, integrator/thermostat, RNG, physical exposure, unfinished products, ledgers and model identity. A restart under different weights or neighbor code is a new simulation.

Measure qualified atom-steps or impact histories per compute-hour, including OOD stops and analysis. Profile filter generation, neighbor building, communication and autodiff. Parallel independent histories often scale better than a single huge domain-decomposed collision.

Verification proceeds from code to process. Test graph construction, symmetry, force gradients, cutoff crossing, periodic wrapping, unit/reference conversions and checkpoint export. Reproduce frozen DFT labels and analytic repulsion. Then qualify equilibrium/thermal dynamics, reaction paths, surfaces and individual impacts before large ensembles.

Use fault injection: wrong unit, atom order, element map, neighbor skin, cutoff, charge, energy offset, missing repulsive term and out-of-domain species. Automation must fail loudly rather than return plausible forces.

Validation uses held-out surfaces, coverages, reactions, products and impact conditions. Compare higher-level/AIMD evidence and controlled beam/plasma experiments with aligned initial state, energy/angle distribution, temperature, dose and measurement definition.

Forward-model beam spread, product fragmentation/transmission, XPS depth/charging, film density and microscopy threshold where relevant. Disagreement can originate in incoming flux, electronic reference, ML domain, dynamics, event classifier or instrument model; isolate rather than refit everything.