schnet
**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.
| SchNet layer | Plasma-surface contract and failure prevented |
|---|---|
| target domain | Elements, surfaces/films, coverages, products, temperature, impact species/energy/angle, charge convention and decisions; prevents a molecular benchmark from becoming an etch model by name. |
| atomic graph | Periodic cell, neighbor convention, cutoff, self/duplicate edges and chemical embeddings; prevents discontinuous or double-counted neighborhoods. |
| continuous filter | Distance expansion, filter network, cutoff envelope, interaction depth and scalar feature width; prevents unreported receptive-field and smoothness limits. |
| energy/forces | Extensive atomic-energy sum, differentiable forces, optional stress and consistent units/reference zeros; prevents force-only nonconservative impact dynamics. |
| reference/training | Versioned DFT/AIMD labels, family splits, loss weights, seeds, precision and class-resolved errors; prevents leakage and equilibrium-data domination. |
| collision/OOD guard | Compressed data, smooth repulsive splice, calibrated ensemble/distance alerts and stop/fallback policy; prevents unphysical close-range attraction and silent extrapolation. |
| dynamics qualification | Symmetry/gradient, NVE/NVT, cutoff, cell/timestep, event ledgers, replicas and held-out impact tests; prevents low test MAE from substituting for stable chemistry. |
| architecture decision | Same data/splits/reference, parameter/throughput budget and process observables versus equivariant or physics-based alternatives; prevents unfair leaderboard conclusions. |
**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,
$$
\mathbf x_i^{l+1}=\mathbf x_i^l+\mathcal U^l\!\left(\sum_{j\in\mathcal N_i}\mathbf x_j^l\odot W^l(r_{ij})\right),
$$
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,
$$
E_{NN}(\mathbf R,\mathbf Z)=\sum_i\varepsilon(\mathbf x_i^L),
$$
and conservative forces follow by automatic differentiation,
$$
\mathbf F_i=-\nabla_{\mathbf r_i}E_{NN}.
$$
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:
$$
E(Q\mathbf R+\mathbf t)=E(\mathbf R),\qquad
\mathbf F(Q\mathbf R+\mathbf t)=Q\mathbf F(\mathbf R),
$$
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,
$$
E_{tot}=E_{SchNet}^{short}+E_{Coulomb}+E_{dispersion}+E_{field},
$$
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,
$$
f_c(r)=\frac12\left[\cos\left(\frac{\pi r}{r_c}\right)+1\right],\quad rSchNet for Plasma Surfaces: Continuous Filters to Qualified MD distance graph + scalar messages + conservative forces + collision/OOD protection + fair benchmarking ATOMIC GRAPH elements · distance periodic neighbors CONTINUOUS FILTER radial basis · cutoff scalar message ENERGY → FORCE atomic sum negative gradient PLASMA MD react · reflect · etch implant · damage NO UNGUARDED IMPACT STEP smooth repulsion · neighbor continuity · calibrated OOD score · save/stop/acquire before corruption MATCHED TEST same labels · splits budget · hardware SCHNET scalar invariant simple baseline EQUIVARIANT tensor features data efficiency DECISION OUTPUT stable MD · products yield · cost · confidence SCHNET RELEASE GATES label audit graph symmetry cutoff / ZBL OOD challenge MD ledgers held-out beam Choose the simplest architecture that remains physical, stable and accurate on the actual etch decision.
**A gated workflow avoids architecture theater.** Freeze domain/decision; audit DFT/AIMD references; assemble diverse family-tagged data; configure graph/filter/cutoff; train seeded models with leak-free splits; verify symmetry/gradients/cutoff; add and test repulsive/long-range physics; calibrate OOD and active learning; qualify thermal/reactive/impact MD; compare fairly to equivariant and physics-based alternatives; validate held-out experiments; then release the full artifact and conditional kernels.
Stop when reference labels conflict; trajectory leakage inflates performance; force/energy gradients disagree; neighbor/cutoff or repulsive splice is discontinuous; OOD tests fail silently; MD produces impossible species or energy drift; architecture seeds disagree beyond tolerance; or held-out products/yields/damage fail. More hidden channels cannot repair missing physics.
**Safety applies to validation and data governance.** Plasma/beam equipment involves high voltage/RF, vacuum, toxic/corrosive/pyrophoric gases, reactive residues, UV, heat and stored energy. Use trained operators, approved recipes, interlocks, monitoring, compatible materials, purge verification, ventilation, PPE and lockout/tagout. Protect licensed reference data/software, controlled process information and credentials; never embed secrets in model configs or shared logs.
**A credible Etch Plasma–Surface SchNet Model is a qualified invariant force engine.** It learns smooth continuous-filter interactions from consistent first-principles data; states its scalar/local representation limits; covers the evolving surface, products, reactions and collision manifold; preserves symmetry and energy-derived forces; joins smoothly to repulsive and long-range physics; detects OOD environments before they corrupt trajectories; remains stable under converged MD; passes atom/energy ledgers and held-out evidence; and beats alternatives on matched process accuracy, cost and uncertainty. That evidence—not a benchmark headline—earns deployment.