PaperlayerView exact revision on arXiv

Source-linked AI summary

NEMSim: Learning Control-Conditioned Multi-Event Physical Dynamics via Executable Event-Mechanism Priors

Junsong Yu, Junjie Xie, Pengwei Liu, Dong Ni

arXiv:2609.30718v1cs.LG

TL;DR

Limited trajectory coverage makes learning control-conditioned multi-event dynamics challenging, while available knowledge often takes the form of discrete event rules. NEMSim compiles those rules into an executable event-mechanism transition structure, reducing Avg. RMSE by 58.9%–81.3% across three rollout settings. The evaluation is limited to one 3D KMC-based plasma-etching benchmark.

  • Problem

    Finite trajectory coverage of control-state-event combinations makes direct transition learning data-inefficient and weakens generalization to held-out controls, while available system knowledge often consists of discrete event rules.

    Source: Introduction · p. 1

  • Method

    NEMSim compiles predefined event rules into an executable transition structure linking control-dependent event intensities, prior-guided mechanism attribution, and state-dependent responses.

    Source: Introduction · pp. 1–2

  • Results

    Avg. RMSE is reduced by 58.9%–81.3% across three 100-step rollout settings relative to the strongest baseline in each setting, and NEMSim remains superior with 10% of training data.

    Source: Conclusion and Limitations · p. 7

  • Takeaways & Limitations

    Prior-controlled comparisons, rule perturbations, ablations, and mechanism-aligned analyses support the benefit of executable rule integration beyond prior access or architectural structure alone.

    Source: Conclusion and Limitations · p. 7

    Evaluation is limited to one 3D KMC-based plasma-etching benchmark; rollouts are deterministic and assume predefined event-attribute descriptions.

    Source: Conclusion and Limitations · p. 7

Abstract

from arXiv · show

High-fidelity simulation of control-conditioned multi-event physical systems is computationally expensive, especially across broad control spaces and long trajectories. In these systems, macroscopic evolution emerges from localized discrete events whose intensities and effects depend on process controls and evolving local states, while the available system knowledge is typically expressed as event-attribute descriptions. Purely data-driven surrogates must infer these event effects from limited trajectory coverage, which can hinder generalization to unseen control regimes. Physics-guided methods instead primarily build on equation-level constraints or differentiable solvers rather than discrete event-rule priors. We therefore propose NEMSim (Neural Event-Mechanism Simulator), which compiles predefined event-attribute descriptions into an executable transition structure linking control-dependent event intensities, prior-guided mechanism attribution, and state-dependent responses. To enable evaluation of control-conditioned multi-event dynamics with explicit system knowledge, we construct a 3D KMC-based benchmark pairing high-fidelity trajectories with explicit event rules, standardized splits, and evaluation protocols. Across three settings, NEMSim reduces Avg. RMSE by 58.9%-81.3% relative to the strongest baseline in each setting. It also remains best in the data-efficiency study with training-data fractions down to 10%. Mechanism analyses further show that these gains arise from executable rule integration rather than prior access or architecture alone.

Introduction

NEMSim compiles discrete event-rule priors into an executable event-mechanism transition structure for control-conditioned multi-event dynamics. On a 3D KMC-based benchmark, it improves long-horizon rollout accuracy across control and temporal extrapolation settings.

Introduction

  • Finite trajectory coverage makes direct transition learning data-inefficient, weakens generalization to held-out controls, and amplifies error during long autoregressive rollouts.Controls and evolving local states jointly determine event intensities, while event dependencies shape how effects combine.Source: Introduction · p. 1
  • Existing physics-guided formulations primarily encode knowledge through equation-level constraints or numerical structures, unlike the discrete event rules often available for these systems.Those rules describe control dependencies, rate and yield relations, event dependencies, and event-mechanism relations.Source: Introduction · p. 1
  • NEMSim compiles event rules into an executable structure that computes control-dependent event intensities, prior-guided mechanism attribution, and state-dependent responses.Events share mechanism-family structure while retaining event-specific control dependence and local responses.Source: Introduction · pp. 1–2
  • Avg. RMSE falls by 63.3%, 58.9%, and 81.3% across control interpolation, control extrapolation, and temporal extrapolation, respectively, versus the strongest baseline in each setting.NEMSim also remains best with 10% of training data, and mechanism analyses attribute gains to executable rule integration rather than prior access or architecture alone.Source: Introduction · p. 2
  • The benchmark pairs high-fidelity 3D KMC trajectories with explicit event rules and standardized splits and evaluation protocols.It is designed to evaluate control-conditioned multi-event dynamics with explicit system knowledge.Source: Introduction · p. 2

Related Work

Prior physical-learning methods use varied representations, but commonly learn state transitions directly from observations or encode prior knowledge through equations, solvers, and constraints. Existing benchmarks primarily center on equation- or operator-specified systems rather than heterogeneous control-dependent event rules.

Purely Data-Driven Methods

  • Data-driven simulators use recurrent, graph-based, and neural-operator representations to learn mappings from observed states and controls to future states.Examples include ConvLSTM and PredRNN, GNS and MeshGraphNet, and DeepONet and FNO.Source: Related Work · p. 2

Physics-Guided Methods

  • Physics-guided methods encode prior structure through PDE residuals, equation-level constraints, differentiable solvers, kinetic laws, or regularization rather than heterogeneous event-rule libraries.The passage also describes local transition constraints and operating-condition and conservation constraints.Source: Related Work · pp. 2–3

Benchmarks for Physical Learning

  • PDEBench, APEBench, CFDBench, and phase-field benchmarks primarily specify systems through equations, boundary conditions, geometries, or numerical operators.These benchmarks differ from heterogeneous control-dependent multi-event descriptions.Source: Related Work · p. 3

Method

NEMSim learns one-step control-conditioned state transitions by compiling event-rule inputs into an event-mechanism structure. Its pipeline computes event intensities and mechanism attributions, composes state-dependent responses, and decodes the result into a next-state prediction.

Problem Setting and Notation

  • The Event Rules Library encodes control bindings, probability and yield relations, product-mediated dependencies, and event-mechanism roles as fixed system-specific priors.These priors structure the forward transition without event- or mechanism-level supervision.Source: Problem Setting and Notation · p. 3
  • NEMSim predicts a one-step transition from state and process control using fixed structural priors R and M, while learning neural parameters from state trajectories.Training uses one-step state-transition supervision, and long-horizon evaluation recursively applies the learned transition from the true initial state under the trajectory control.Source: Problem Setting and Notation · p. 3

Model Architecture

  • The Event-Mechanism Compiler uses state context, process control, and the rules library to compile event intensities and event-to-mechanism attribution.Their element-wise product forms the event-mechanism drive passed to the response compiler.Source: Model Architecture · p. 3
  • Figure 2 details the EIC, MAC, and MRC computations, with purple pentagons marking operations parameterized by event-rule attributes.Together, the stages compile event intensity, mechanism attribution, and state response.Source: Model Architecture · p. 3, Figure 2 · p. 4
  • The Event Intensity Compiler derives primary-event intensities from rule-specified control bindings and probability and yield relations, then applies a bounded correction in log-rate space.For product-mediated events, the Product Pool aggregates upstream products to determine dependency-driven intensity, which contributes to final event intensity.Source: Model Architecture · p. 4
  • The Mechanism Attribution Compiler distributes event intensities across mechanism families using rule-based preferences and bounded context corrections, with normalized nonnegative attributions.Bounding event intensities reduces scale differences before attribution; state and control can adjust the rule-defined mechanism preference.Source: Model Architecture · p. 4
  • The Mechanism Response Compiler aggregates event-mechanism drives into response modes, then combines bounded state-control-dependent amplitudes with state-dependent spatial response fields.Event descriptors retain event-specific preferences across modes within shared mechanism families.Source: Model Architecture · pp. 4–5
  • The state increment decoder maps the mechanism-induced latent response back to the state space through a residual transition.The residual formulation focuses prediction on transition-induced changes.Source: Model Architecture · p. 5

Experiments

Experiments evaluate NEMSim on 100-step rollouts across control interpolation, control and temporal extrapolation, and data-efficiency and mechanism analyses. NEMSim outperforms baselines across the reported settings, while ablations and counterfactual analyses examine the role and behavior of its event-rule mechanisms.

Experimental Setup

  • The benchmark contains 500 trajectories of 101 two-channel 3D signed-distance fields, with trajectory-level splits and 100-step autoregressive evaluation without ground-truth correction.Evaluation covers control interpolation, control extrapolation, temporal extrapolation, data efficiency, rule robustness, mechanism-aligned counterfactuals, and component ablations.Source: Experimental Setup · p. 5, Experiments · p. 5

Performance Comparison

  • 63.3%, 62.5%, and 47.4%: versus DeepONet, NEMSim reduces Avg. RMSE, Final RMSE, and CD, respectively, under unseen in-domain controls.It uses 0.253M trainable parameters; the results improve rollout-wide field prediction and final-state geometry.Source: Main Results · p. 5, Table 1 · p. 6
  • 58.9% under OOD-Joint and 81.3% under Vis-50%: NEMSim reduces Avg. RMSE relative to the strongest standard baseline in each setting.The reductions accompany consistent gains in Avg. RMSE, Final RMSE, and CD under held-out control regions and later evolution stages.Source: Experimental Setup · p. 5, Main Results · p. 6, Table 1 · p. 6

Mechanism Analysis

  • Feature-level access to the Event Rules Library does not close the gap: NEMSim reduces Avg. RMSE versus the strongest prior-augmented baseline by 56.1% under OOD-Joint and 77.8% under Vis-50%.The full model also outperforms Structure-only with the same topology and parameter capacity; perturbed rule variants retain nontrivial predictive performance.Source: Main Results · p. 6, Mechanism Analysis · p. 7, Table 2 · p. 7

Visualization

  • Under OOD-Joint and Vis-50%, NEMSim maintains lower stepwise RMSE than CNO and DeepONet and better aligns final surfaces and SDF contours with ground truth.The contrast is especially visible near trench bottoms and sidewalls, where DeepONet shows substantial deviations and contour misalignment.Source: Main Results · p. 6, Figure 3 · p. 6, Figure 4 · p. 6

Data Efficiency

  • NEMSim achieves the lowest Avg. RMSE and final-step CD at every tested training-data fraction from 10% to 100%.At 10%, its Avg. RMSE is below 0.10 and lower than both DeepONet variants trained on the complete partition.Source: Data Efficiency · pp. 6–7, Figure 5 · p. 6

Mechanism Analysis

  • Counterfactual Cl+ increases primarily strengthen physical and coupled responses, while neutral Cl increases selectively strengthen chemical responses.Cl+-related interventions link stronger coupled responses with greater material removal; removing EIC, MAC, or MRC increases Avg. RMSE by 2.4×–4.6× across the three settings.Source: Mechanism Analysis · p. 7, Figure 6 · p. 7, Ablation Studies · p. 7

Conclusion and Limitations

NEMSim compiles event-attribute descriptions into an executable event–mechanism transition structure and reduces Avg. RMSE across three 100-step rollout settings. The evaluation is limited to one 3D KMC-based plasma-etching benchmark, and the method assumes predefined event-attribute descriptions.

Conclusion

  • Avg. RMSE falls by 58.9%–81.3% across three 100-step rollout settings, and NEMSim remains superior with only 10% of the training data.Prior-controlled comparisons, rule perturbations, ablations, and mechanism-aligned analyses support executable rule integration beyond prior access or architectural structure alone.Source: Conclusion and Limitations · p. 7

Limitations

  • The current evaluation covers one 3D KMC-based plasma-etching benchmark; NEMSim also produces deterministic rollouts and assumes predefined event-attribute descriptions.Future work will broaden evaluation, develop probabilistic rollouts for uncertainty estimation, and support data-driven event discovery and rule refinement.Source: Conclusion and Limitations · p. 7

S1 Physical-System Background

Plasma etching evolves through control- and state-dependent local events whose repeated interactions produce macroscopic morphology changes. The benchmark simulates these interactions and organizes events by shared physical, chemical, and coupled mechanisms.

S1.1 Plasma Etching as a Controlled Multi-Event System

  • Plasma controls regulate particle supply, energy, and incidence, while local events depend on controls and surface state and can compete or interact through assistance and product-mediated dependencies.Repeated event occurrence, competition, and coupling accumulate into macroscopic 3D morphology evolution.Source: S1.1 Plasma Etching as a Controlled… · p. 10

S1.2 Particle-Based Monte Carlo Surface-Evolution Simulation

  • The particle-based Monte Carlo simulator updates microscopic surface configurations through stochastic interactions, then records morphology states as multi-channel 3D signed-distance fields.Learning models receive fixed event-attribute descriptions, not particle trajectories, event locations, realized event identities, microscopic states, or intermediate variables.Source: S1.2 Particle-Based Monte Carlo… · p. 10

S1.3 Localized Events and Mechanism Families

  • Event types describe possible local transitions, while physical, chemical, and coupled mechanism families describe their underlying effects; events and mechanisms have a many-to-few relationship.Fixed event–mechanism priors are constructed from predefined event attributes and encode structural support, not event-occurrence labels or dynamically observed mechanism targets.Source: S1.3 Localized Events and Mechanism… · pp. 10–11

S2 Benchmark Construction

The benchmark pairs high-fidelity 3D morphology trajectories and transitions with process controls and executable event-rule metadata, and defines shared splits, rollouts, and evaluation protocols. Its construction covers simulator scope, control-space sampling, and model-ready state and transition representations, with a planned release supporting reproduction without the proprietary simulator.

S2 Benchmark Construction

  • The benchmark contains 500 trajectories of 100 transitions on a 54×54×127 grid and evaluates Control-ID, Control-OOD, and temporal extrapolation with 100-step autoregressive rollouts.It combines transition data, process-control metadata, a machine-readable Event Rules Library, predefined splits, and standardized protocols.Source: S2 Benchmark Construction · p. 11

S2.1 High-Fidelity Simulator and Physical Configuration

  • The reference is a 3D particle-based Monte Carlo chlorine-plasma etching simulator, but it is neither experimental ground truth nor an exact continuous-time kinetic Monte Carlo solver.Its source code is confidential, and the simulator is unavailable to learning methods; fixed generated trajectories and benchmark materials are intended for release.Source: S2.1 High-Fidelity Simulator and… · pp. 11–12

S2.2 Trajectory Generation and Control-Space Sampling

  • Five hundred distinct stationary process-control configurations were generated by Latin hypercube sampling, with one independently simulated trajectory per configuration.The deterministic control design is reproducible, but particle-level random seeds were not retained; the generated trajectories and raw controls are fixed for release.Source: S2.2 Trajectory Generation and… · p. 14

S2.3 State, Control, and Transition Representation

  • Each model-ready state comprises two normalized signed-distance fields for the resist-mask and Si interfaces, and evaluation recursively feeds predicted states into subsequent transitions.Controls are normalized using fixed global bounds specified before splitting, and the two channels are stacked in a fixed order.Source: S2.3 State, Control, and Transition… · pp. 14–15
  • Methods learn coarse-grained morphology transitions from saved next-state fields under stationary controls; only NEMSim additionally receives the shared Event Rules Library.No method receives microscopic event identities, counts, reaction outcomes, or particle histories.Source: S2.3 State, Control, and Transition… · p. 15

S2.4 Dataset Statistics and Quality Control

  • The benchmark contains 500 distinct control configurations, each paired with one 101-state trajectory providing 100 consecutive transitions; Latin hypercube sampling stratifies all 14 control dimensions.All cases passed integrity checks, with no missing steps, channel-time mismatches, inconsistent dimensions, or duplicate controls.Source: S2.4 Dataset Statistics and Quality… · p. 16

S2.5 Data Splits, Rollout Protocols, and Metrics

  • Trajectory-level splits prevent trajectory sharing across train, validation, and test; Control-ID tests unseen in-domain controls, OOD settings hold out flux boundaries, and Temporal Extrapolation limits visible training prefixes while evaluating full 100-step rollouts.The OOD axes are Ar+ and Cl+ incident fluxes, selected using benchmark morphology associations rather than model results.Source: S2.5 Data Splits, Rollout Protocols,… · pp. 16–18
  • Evaluation recursively feeds each predicted state into the next transition without teacher forcing or state correction, reporting normalized-field RMSE and final-surface Chamfer Distance in voxel units.Avg. RMSE averages the 100 step-wise RMSE values; Chamfer Distance averages mask and Si channel distances across test trajectories.Source: S2.5 Data Splits, Rollout Protocols,… · p. 18

S2.6 Release Package and Reproducibility

  • The planned release includes trajectories, controls, the Event Rules Library, fixed split manifests, preprocessing and evaluation code, and model configurations, enabling benchmark reproduction without the proprietary simulator.Reproducibility is defined at the benchmark level, not as bitwise reproduction of the underlying simulator or microscopic stochastic histories.Source: S2.6 Release Package and Reproducibility · pp. 18–19

S3 Event Rules Library

The Event Rules Library and compiler turn benchmark-specific event descriptions into fixed executable structures that connect process controls and states to kinetic responses, event dependencies, and mechanism attribution. The rules define a reduced-order event catalog and shared mechanism families with fixed priors and role signals, while transition-specific quantities and latent responses are learned from state-transition data.

S3.1 Provenance and Role of the Event Rules Library

  • The compiled library fixes event structure and control bindings across runs, while event intensities vary with controls and learned state-dependent corrections and responses remain data-driven.Only state transitions are supervised; event identities, propensities, product-pool values, mechanism attributions, and response-mode targets are not provided as intermediate labels.Source: S3.1 Provenance and Role of the Event… · pp. 20–21

S3.2 Rule Schema and Executable Attributes

  • Rules encode event identity, control bindings, probability and yield models, product dependencies, and generated products, which compilation maps to fixed model buffers and semantic descriptors.The schema distinguishes control-driven primary events from product-mediated deposition events; compiled attributes include control indices, a product graph, mechanism priors, and event descriptors.Source: S3.2 Rule Schema and Executable… · pp. 21–22

S3.3 Benchmark Event Catalog and Parameterization

  • The benchmark catalog contains 37 channels: 22 control-driven primary events and 15 product-mediated deposition events formed from three products and five target classes, each with sticking coefficient 0.02.Product bookkeeping retains source–sink dependencies but is not a complete gas-phase reaction mechanism or exact microscopic stoichiometry.Source: S3.3 Benchmark Event Catalog and… · pp. 22–24

S3.4 Kinetic Probability and Angular Models

  • Differentiable kinetic forms compute each primary event’s formula-guided base intensity from particle supply, incident energy, and incidence orientation before learned state-dependent corrections.The forms adapt threshold-energy and angular models used in Monte Carlo feature-profile simulation.Source: S3.4 Kinetic Probability and Angular… · p. 24
  • Smooth threshold gates, bounded probability and angular or yield models, and normalized energy coordinates define kinetic event responses; product-mediated deposition instead uses product-pool dependencies.The safeguards preserve rule dependence while avoiding unbounded values and discontinuous gradients; learned corrections adapt magnitudes without replacing the event-rule structure.Source: S3.4 Kinetic Probability and Angular… · pp. 25–26

S3.5 Mechanism-Family Mapping and Prior Construction

  • The compiler maps event rules to physical, chemical, or coupled mechanism families, with “both” denoting an interaction rather than an average of physical and chemical effects.The families represent recurring processes: energetic impact and direct removal, reactive surface transformations, and interactions among energetic activation, surface chemistry, and product transfer.Source: S3.5 Mechanism-Family Mapping and… · p. 26
  • Each event receives a smoothed static prior assigning 0.90 mass to its rule-defined family and 0.05 to each alternative, while multi-hot role signals can represent multiple functional roles.For example, product-mediated deposition retains a chemical prior while also activating a coupled source–sink role.Source: S3.5 Mechanism-Family Mapping and… · p. 27
  • Neither the static priors nor role signals are optimized from trajectory data; learned attribution components adapt the rule-based anchor using state and control context.The mapping is a fixed executable organization of the event catalog, not intermediate supervision or a claim of uniquely identifiable microscopic mechanisms.Source: S3.5 Mechanism-Family Mapping and… · p. 28

S4 Additional Model Details

S4 details the implementation of the event-intensity, mechanism-attribution, and mechanism-response compilers and residual decoder, including how fixed event rules and learnable mappings support the final state-transition loss. It also clarifies the constrained executable roles of intermediate quantities without treating them as uniquely identifiable microscopic variables.

S4.1 Event Intensity Compiler

  • EIC combines rule-defined control-driven primary-event kinetics with a Product Pool for product-mediated events, applying bounded state-control corrections without changing rule-defined kinetic support.Product Pool values and intermediate intensities remain latent and receive no direct supervision.Source: S4.1 Event Intensity Compiler · p. 29

S4.2 Mechanism Attribution Compiler

  • MAC combines a fixed-prior, event-attribute anchor with rule-induced and state-control corrections, preserving anchor support as it composes mechanism attributions with event intensities into drivers.Its three mechanism families are physical, chemical, and coupled.Source: S4.2 Mechanism Attribution Compiler · pp. 30–31

S4.3 Mechanism Response Compiler

  • MRC aggregates event-mechanism drivers into shared mechanism-specific modes, using event signatures, state-control gates, bounded saturating amplitudes, and state-dependent spatial fields to compose latent increments.The default uses three mechanism families with four response modes per family.Source: S4.3 Mechanism Response Compiler · pp. 31–32
  • The residual decoder predicts the state-space increment, and b_t denotes the boundary feature produced by the State Encoder.Source: S4.3 Mechanism Response Compiler · p. 32
  • Intermediate quantities have constrained executable roles rather than uniquely identifiable microscopic meanings, and their contributions are examined through component ablations and mechanism-aligned counterfactuals.These roles include distributing event-mechanism drivers across response modes, aggregating contributions, controlling state-control realizability and bounded response amplitude, and providing spatial response patterns.Source: S4.3 Mechanism Response Compiler · p. 32

S5 Experiments

Across additional control and temporal-extrapolation settings, NEMSim retains strong rollout accuracy, including with limited training data. The supplementary experiments also examine inference efficiency, event-rule robustness, mechanism-aligned counterfactuals, and the contributions of structured components.

S5.2 Computational Efficiency

  • NEMSim is not the fastest for one-step inference, but has moderate latency and memory usage, fewer FLOPs than ConvLSTM, CNO, and DeepONet, and higher latency than FNO and U-NO.Its peak allocated memory is comparable to CNO and substantially lower than ConvLSTM and DeepONet; measured latency also depends on operator composition and execution overhead.Source: S5.2 Computational Efficiency · p. 32

S5.1 Additional Benchmark Results

  • 79.3%, 70.9%, and 78.7% Avg. RMSE reductions over the strongest baseline occur under OOD-Ar+, OOD-Cl+, and Vis-60%, respectively; NEMSim is best across all reported metrics in each setting.These results extend the OOD-Joint and Vis-50% evaluations to single-axis control extrapolation and a less restrictive temporal-visibility setting.Source: S5.1 Additional Benchmark Results · p. 32, Table S11 · p. 33

S5.4 Data Efficiency

  • With 10% of training trajectories, NEMSim reaches Avg. RMSE 0.0967, below DeepONet and DeepONet+Prior trained on the complete partition; it has the lowest Avg. RMSE, Final RMSE, and CD at every fraction.The fractions vary the number of trajectories, each contributing all 100 consecutive one-step transitions.Source: S5.4 Data Efficiency · pp. 34–35, Table S13 · p. 34

S5.5 Robustness to Perturbed Event Rules

  • The robustness experiment perturbs event-rule semantics, mechanism priors, event availability, or numerical rate/yield parameters while retaining model topology and parameter capacity.Each variant is retrained from scratch and evaluated against the full model on OOD-Joint.Source: S5.5 Robustness to Perturbed Event Rules · p. 35

S5.6 Mechanism-Aligned Counterfactual Analysis

  • The counterfactual analysis varies Cl+ and neutral-Cl fluxes across eight interventions, then compares mechanism-response changes with a predicted material-removal proxy.It uses a frozen Control-ID checkpoint and 100 test trajectories; the supplied passages describe the protocol, not its outcomes.Source: S5.6 Mechanism-Aligned Counterfactual… · pp. 35–36

S5.7 Ablation Studies

  • Removing any structured component degrades performance in Control-ID, OOD-Joint, and Vis-50%, with larger drops under OOD-Joint and Vis-50%.The ablated components are event-intensity compilation, event-to-mechanism attribution, and mechanism-response compilation.Source: Table S14 · p. 36, S5.7 Ablation Studies · p. 36

S6 Implementation and Reproducibility Details

The implementation details specify NEMSim’s model and training configuration, the shared inputs and adaptations used for baselines, and the rollout-based evaluation and checkpoint-selection procedure.

S6.1 Model and Training Configuration

  • NEMSim uses a three-level 3D encoder with 18 latent channels, three mechanism families, and a rank-4 mechanism-conditioned response operator; training uses AdamW and voxel-wise next-state MSE.The encoder stem width is 12, pyramid widths are (12, 18, 24), and the response readout hidden width is 24.Source: S6.1 Model and Training Configuration · p. 36

S6.2 Baseline Implementations

  • Baselines receive the same two-channel 3D state and normalized 14-dimensional control vector as NEMSim, with architecture adaptations for volumetric state-transition data.Knowledge-augmented CNO+Prior and DeepONet+Prior implementation details are provided in S5.3.Source: S6.2 Baseline Implementations · p. 36

S6.3 Evaluation and Computational Details

  • Models train with one-step supervision, while 100-step autoregressive validation rollouts select checkpoints; final evaluation uses 100-step rollouts without teacher forcing or later ground-truth correction.In Vis-50%, training exposes only the first 50 transitions, but evaluation still runs all 100 steps from the initial ground-truth state.Source: S6.3 Evaluation and Computational… · pp. 36–37

S7 Additional Qualitative Results

The additional visualizations compare NEMSim and baselines during OOD-Joint and Vis-50% autoregressive rollouts. NEMSim retains closer morphology and contours, including after Vis-50% enters the temporally extrapolative stage.

S7 Additional Qualitative Results

  • Under OOD-Joint, NEMSim maintains a coherent surface through step 100, with most remaining errors near the evolving interface, while baselines accumulate geometric deviations.The comparison shows signed surface deviations alongside SDF errors and zero-level contours at rollout steps 10, 25, 50, 75, and 100.Source: S7 Additional Qualitative Results · p. 37, Figure S1 · p. 38
  • Under Vis-50%, NEMSim remains closer to ground truth at steps 75 and 100, while several baselines develop rapid error growth after step 50.Steps 75 and 100 are beyond the temporal range exposed during training; NEMSim retains more accurate bottom and sidewall contours.Source: S7 Additional Qualitative Results · p. 37, Figure S2 · p. 39

Related papers

Loading 2609.30718v1…