HeLoFusion: Multi-Domain Local Interaction

• HeLoFusion is a context-dependent term defining localized interaction modeling across autonomous driving and various fusion research domains.
• In autonomous driving, it is implemented as a modular encoder using multi-scale graphs and heterogeneous message passing to predict complex agent trajectories.
• In fusion research, HeLoFusion encompasses diverse applications including hohlraum design for laser ignition, helicon current drive, and helium retention in plasma-facing materials.

HeLoFusion is a context-dependent label. In autonomous-driving literature, it denotes an encoder for multi-agent trajectory prediction that models heterogeneous and multi-scale local interactions. In fusion-related technical syntheses, the same label is applied more broadly to hohlraum-based laser fusion, helicon-wave current drive and boundary-density control, and helium loading and retention in fusion-relevant tungsten–oxide coatings. This suggests that the supplied literature does not define a single canonical HeLoFusion formalism; rather, it uses the name for several technically distinct constructs whose common thread is the explicit treatment of localized interactions, whether social, radiative, electromagnetic, or material-transport based (Wei et al., 15 Sep 2025, Lan et al., 2013, Wu et al., 2023, Zhou et al., 23 Feb 2026, Mateus et al., 2018, Thakur et al., 2020).

1. Scope and nomenclature

The supplied literature uses “HeLoFusion” in multiple, unrelated research settings. Only one of the cited papers is formally titled “HeLoFusion,” namely the trajectory-prediction encoder introduced for the Waymo Open Motion Dataset. In the fusion-related entries, the label functions as a shorthand applied to design syntheses rather than as the original title of the underlying source paper (Wei et al., 15 Sep 2025, Lan et al., 2013, Wu et al., 2023, Mateus et al., 2018).

Usage	Primary object	Source
Trajectory prediction	Efficient and scalable encoder for heterogeneous and multi-scale agent interactions	(Wei et al., 15 Sep 2025)
Inertial fusion	Octahedral 6-LEH spherical hohlraum at $R_H/R_C \approx 5.14$	(Lan et al., 2013)
Magnetic-confinement fusion	Helicon current drive and boundary-density control	(Wu et al., 2023, Zhou et al., 23 Feb 2026, Thakur et al., 2020)
Plasma-facing materials	Helium loading and retention in W–O coatings	(Mateus et al., 2018)

A common misconception is to assume that all occurrences refer to the same method or apparatus. The available record indicates otherwise. The autonomous-driving encoder is architecturally unrelated to the fusion applications, while the fusion usages themselves span inertial confinement fusion, radio-frequency plasma coupling, and plasma-facing material behavior.

2. HeLoFusion as a trajectory-prediction encoder

In motion forecasting, HeLoFusion is a modular encoder integrated into a standard trajectory-prediction pipeline. Its design target is the simultaneous treatment of two coupled difficulties: the multi-scale nature of social interaction and the heterogeneity of agent classes such as vehicles, cyclists, and pedestrians. Rather than relying on global context, the encoder constructs local multi-scale graphs centered on each agent, explicitly separating direct pairwise dependencies from group-wise interactions such as vehicle platoons or pedestrian crowds (Wei et al., 15 Sep 2025).

The architecture has three stages: motion encoding, interaction modeling with local multi-scale graphs and heterogeneous message passing, and local context fusion. Historical trajectories are vectorized and encoded with a PointNet-style polyline encoder, and learned type embeddings are added to initialize heterogeneous signals. In the WOMD configuration, the pairwise scale is a $k$-NN graph with $K=10$ nearest neighbors. Two additional group-wise scales are implemented as hypergraphs with cluster sizes $5$ and $7$. For each neighbor $j \in \mathcal{N}_1(i)$, local clusters are formed around $j$ and then treated as hyperedges connecting the target agent to pooled group representations. Pairwise edge features can include relative positions $\Delta p_{ij}$, relative velocities $\Delta v_{ij}$, and optionally derived quantities such as time-to-collision or lane/topology indicators when available by proximity to map elements. Group-wise hyperedge features summarize the relative configuration between the target and the pooled group (Wei et al., 15 Sep 2025).

The message-passing layer is scale-specific. With $h_i^{(\ell)}$ denoting the embedding of agent $k$0 at layer $k$1, attention and per-neighbor messages are defined as

$k$2

$k$3

followed by per-scale aggregation

$k$4

For group-wise interactions, each local cluster $k$5 is first pooled by a permutation-invariant operator,

$k$6

and then used to form an agent-to-group message

$k$7

This allows the encoder to represent both direct interactions and local collective structure without a dense all-to-all graph (Wei et al., 15 Sep 2025).

Heterogeneity is handled through an aggregation–decomposition scheme. Interaction signals are first aggregated into a shared summary $k$8, then decomposed into type-specific influence channels by lightweight decomposers $k$9 for $K=10$0. Beyond this, a bank of category-specific MLPs $K=10$1 is applied before local context fusion. After interaction modeling, each agent attends only to nearby neighbors and nearby map polylines within a local neighborhood of size $K=10$2, so the architecture remains localized throughout. Its computational complexity is

$K=10$3

in contrast to the $K=10$4 compute and memory of dense global interaction models (Wei et al., 15 Sep 2025).

3. Empirical performance and implementation in motion forecasting

HeLoFusion is evaluated on the Waymo Open Motion Dataset using the BeTopNet decoder unchanged, which isolates encoder effects. Following the MTR protocol, the system uses $K=10$5 predefined intention points generated via $K=10$6-means clustering on the training set, and WOMD evaluation uses $K=10$7 predicted trajectories per agent. The paper does not redefine the exact internal scoring formulas for mAP and Soft mAP, instead adhering to WOMD’s official evaluation protocol and tooling (Wei et al., 15 Sep 2025).

Among single-model, LiDAR-free methods with identical decoder settings, the reported WOMD test-set results are Soft mAP $K=10$8, mAP $K=10$9, minADE $5$0, minFDE $5$1, Miss Rate $5$2, and Overlap Rate $5$3. On the validation set, mAP-Val is $5$4. Relative to the BeTopNet backbone, replacing the encoder yields Soft mAP $5$5, mAP $5$6, minADE $5$7, minFDE $5$8, and OR $5$9 (Wei et al., 15 Sep 2025).

The training setup is reported explicitly: $7$0 epochs on $7$1 NVIDIA GeForce RTX 3090 GPUs, AdamW with initial learning rate $7$2 and weight decay $7$3, step learning-rate decay at epochs $7$4 by $7$5, batch size $7$6 with gradient accumulation, gradient clipping with max norm $7$7, and initialization from a BeTopNet model pretrained for $7$8 epochs. Runtime and parameter count are not explicitly reported, but the encoder is described as lightweight and as having linear scaling in the agent count due to the bounded local neighborhoods (Wei et al., 15 Sep 2025).

The limitations are correspondingly specific. The model is validated on WOMD, while cross-dataset generalization and rare out-of-distribution events remain open. Additional considerations noted in the source include diminished benefit from group-wise reasoning in sparse scenes, the possibility that local modeling may miss far-field cues relevant to very long-range intent, sensitivity to neighborhood hyperparameters $7$9, and the dependence of type-specific routing on correct agent typing.

4. HeLoFusion in inertial confinement fusion: octahedral spherical hohlraums

In the inertial-confinement setting, HeLoFusion denotes hohlraum-based laser fusion built around a spherical hohlraum with octahedral six laser entrance holes. A hohlraum is a high-$j \in \mathcal{N}_1(i)$0 cavity that converts laser energy into a quasi-isotropic x-ray radiation field to drive the implosion of a deuterium–tritium capsule. In this geometry there is one cone at each LEH and one laser cone per LEH, which eliminates crossed-beam energy transfer, reduces backscattering, and avoids the beam overlap characteristic of cylindrical hohlraums with multiple cone beams per LEH (Lan et al., 2013).

The principal design result is the existence of a “golden” hohlraum-to-capsule radius ratio that minimizes radiation-flux asymmetry on the capsule. The reported optimum is $j \in \mathcal{N}_1(i)$1. The source explicitly notes that this “golden ratio” is not the mathematical golden ratio $j \in \mathcal{N}_1(i)$2, but the optimal geometric ratio for this octahedral design. Example parameters are $j \in \mathcal{N}_1(i)$3, $j \in \mathcal{N}_1(i)$4 mm, $j \in \mathcal{N}_1(i)$5 mm, $j \in \mathcal{N}_1(i)$6 mm, cone opening angle $j \in \mathcal{N}_1(i)$7, and $j \in \mathcal{N}_1(i)$8 quads total, namely $j \in \mathcal{N}_1(i)$9 per LEH, with azimuthal staging $j$0 to avoid overlap (Lan et al., 2013).

Capsule irradiation symmetry is expanded in spherical harmonics,

$j$1

with normalized coefficients $j$2 used to quantify relative asymmetry and with a global measure

$j$3

The analytic negative-source model treats LEHs as the main asymmetry source and predicts that $j$4 reaches a minimum at $j$5. View-factor calculations confirm a minimum near $j$6 and show $j$7 remaining low at approximately $j$8 for $j$9, indicating robustness as the geometry evolves in time (Lan et al., 2013).

The mode structure is central to the design rationale. In conventional cylindrical hohlraums, low-order asymmetries such as $\Delta p_{ij}$0 are important and require active tuning. In the proposed octahedral spherical hohlraum, the $\Delta p_{ij}$1 modes $\Delta p_{ij}$2 are at noise level and negligible. Away from the optimum, $\Delta p_{ij}$3 modes $\Delta p_{ij}$4 dominate. Near the optimum, the residual asymmetry shifts to $\Delta p_{ij}$5 modes $\Delta p_{ij}$6, but at much smaller amplitude, below $\Delta p_{ij}$7. This shift to higher order is presented as the source of robustness against manufacturing errors, beam-pointing offsets, or capsule offsets (Lan et al., 2013).

The design trade-off is energetic rather than geometric. To produce an ignition radiation pulse of $\Delta p_{ij}$8 eV, the golden octahedral hohlraum requires approximately $\Delta p_{ij}$9 MJ absorbed laser energy, versus approximately $\Delta v_{ij}$0 MJ for a traditional cylindrical uranium hohlraum driving a similar capsule, i.e. about $\Delta v_{ij}$1 more absorbed energy. The larger spherical volume, approximately $\Delta v_{ij}$2 the capsule volume compared with approximately $\Delta v_{ij}$3–$\Delta v_{ij}$4 for typical cylinders, reduces plasma filling but increases the amount of material and area that must be heated. In the extended plasma-filling model, the normalized electron density is $\Delta v_{ij}$5 for the spherical octahedral hohlraum and $\Delta v_{ij}$6 for the cylinder, both under a plasma-filling criterion of $\Delta v_{ij}$7. The same geometry is also proposed for hybrid indirect-direct drive, where a four-step radiation pulse with fourth-step $\Delta v_{ij}$8–$\Delta v_{ij}$9 eV lasting about $h_i^{(\ell)}$0 ns can be achieved for a capsule of $h_i^{(\ell)}$1 with absorbed laser energy of approximately $h_i^{(\ell)}$2–$h_i^{(\ell)}$3 MJ while satisfying the LPI constraints used in the study (Lan et al., 2013).

5. HeLoFusion in magnetic-confinement fusion: helicon current drive, boundary-density control, and source engineering

A second fusion usage of HeLoFusion concerns helicon or whistler-wave systems for current drive and boundary-density control. In the CFETR hybrid scenario, helicon current drive is evaluated with GENRAY/CQL3D using reactor-grade profiles with $h_i^{(\ell)}$4 T, core $h_i^{(\ell)}$5, core $h_i^{(\ell)}$6 keV, baseline $h_i^{(\ell)}$7 MW, and baseline $h_i^{(\ell)}$8 GHz. The study identifies an optimal launched parallel refractive index $h_i^{(\ell)}$9, a preferred poloidal launch window of approximately $k$00–$k$01, and a narrow useful spectrum width $k$02–$k$03. At $k$04, the maximum reported current-drive efficiency is $k$05 with $k$06 kA, and deposition typically peaks at normalized poloidal flux $k$07–$k$08 (Wu et al., 2023).

The same literature base extends the idea to boundary-density control in toroidal devices through the THEMIS full-wave code. THEMIS is a three-dimensional multiphysics model of helicon/TG-wave propagation, damping, and antenna–plasma coupling in toroidal geometry, implemented in COMSOL’s RF module with a finite-temperature dielectric tensor. In Helimak-relevant conditions $k$09, the accessible heating regime is dominated by slow-wave propagation and electron Landau damping. The reported electron damping partition is approximately $k$10–$k$11 Landau damping, $k$12–$k$13 collisional damping, and about $k$14–$k$15 each for Doppler-shifted cyclotron damping and anomalous Doppler damping. Under a protruding-window launch, main-plasma absorption efficiency is poor: $k$16 for the rectangular spiral antenna, $k$17 for the spiral antenna, $k$18 for the S-bend, and $k$19 for the comb antenna. Recessing the dielectric window inside the vessel removes the external waveguide cavity and improves coupling; guided by scans of window position, antenna geometry, and orientation, the optimized open-circuit racetrack spiral antenna reaches $k$20 for the entire plasma, more than an order of magnitude above the conventional short-circuited rectangular spiral antenna at approximately $k$21 (Zhou et al., 23 Feb 2026).

The engineering feasibility of steady-state high-power helicon operation is demonstrated experimentally in PISCES-RF. That device uses a double-walled cylindrical RF-transparent window with an alumina inner cylinder of thickness about $k$22 mm, a fused-quartz outer cylinder of thickness about $k$23 mm, and a full azimuthal de-ionized-water blanket in a $k$24 mm annular channel. The source operates at $k$25 MHz and up to $k$26 kW. With the coolant present, the loaded quality factor decreases by about $k$27–$k$28, the vacuum resistance rises from approximately $k$29 to approximately $k$30, and the resistive loading in plasma increases by $k$31; nevertheless, the water blanket does not degrade helicon-mode access or peak $k$32. In hydrogen, with $k$33 sccm, $k$34 mTorr, and $k$35 T, helicon onset occurs at about $k$36 kW and the central electron density at $k$37 m downstream rises to approximately $k$38 at $k$39 kW. In helium, with $k$40 sccm, $k$41 mTorr, and $k$42 T, the helicon mode appears at about $k$43 kW and the central density rises from approximately $k$44 at $k$45 kW to approximately $k$46 at $k$47 kW (Thakur et al., 2020).

Across these studies, the implied HeLoFusion design space in magnetic-confinement fusion is coherent. Current-drive studies emphasize $k$48-spectrum control and off-axis deposition, full-wave modeling emphasizes accessible slow-wave coupling and launcher geometry, and source engineering shows that steady-state operation in light gases requires aggressive thermal management of the RF window. A plausible implication is that the three strands are complementary rather than competing: CFETR-style current-drive optimization, THEMIS-style launcher co-design, and PISCES-RF-style cooling address different layers of the same helicon deployment problem.

6. HeLoFusion in plasma-facing materials: helium loading and retention in W–O coatings

A third fusion-related usage concerns helium loading and retention in tungsten–oxide coatings relevant to redeposition on plasma-facing components. In this setting, HeLoFusion refers to the coupling between pulsed-laser-deposition-controlled morphology, oxygen uptake, helium implantation, and long-term release. W films were grown from a pure metallic tungsten target onto SS316L substrates, using a $k$49 nm crystalline W adhesion layer deposited in vacuum at approximately $k$50 Pa. Growth in Ar at $k$51 Pa produced porous, columnar “cauliflower” coatings with thickness about $k$52, nanocolumns around $k$53 nm wide, and oxygen content around $k$54 at.% by ToF-ERDA. Growth in He at $k$55 Pa produced smooth, compact amorphous-like coatings of similar thickness with very small grains and oxygen content around $k$56–$k$57 at.% (Mateus et al., 2018).

Helium loading was performed by sequential room-temperature implantation of $k$58 at $k$59 keV, $k$60 keV, and $k$61 keV with fluences $k$62, $k$63, and $k$64, respectively, for a total fluence of $k$65. RBS/EBS and ToF-ERDA show markedly different retention behavior in porous and compact films. In porous Ar-grown W–O, the as-implanted helium peak reaches about $k$66 at.% and is concentrated between roughly $k$67 and $k$68, while the film thickness decreases from $k$69 to $k$70, implying a sputtering yield of approximately $k$71 atoms per incident $k$72. After five months in ambient conditions, ToF-ERDA shows that most helium has been released, with only about $k$73 at.% remaining on average across the superficial $k$74 layer, corresponding to an approximate near-surface retention ratio $k$75 (Mateus et al., 2018).

In compact He-grown W–O, sputter erosion is minimal and long-term retention is much larger. After five months, ToF-ERDA reports about $k$76 at.% helium within approximately $k$77, corresponding to an approximate near-surface retention ratio $k$78. The depth profile shows helium smoothly increasing with depth, which is interpreted as evidence of surface degassing while deeper layers remain helium-rich (Mateus et al., 2018).

The mechanistic interpretation is morphology-driven. Porous, columnar W–O provides open percolation pathways and high surface-to-volume ratio, allowing rapid helium migration and outgassing at room temperature. Compact amorphous-like W–O has fewer open pathways, so deeper helium reservoirs persist. The transport discussion is framed by the diffusion relation

$k$79

the diffusion length $k$80, the retention ratio $k$81, and first-order desorption kinetics

$k$82

For fusion materials, the implication is specific: porous, oxygen-rich redeposits may exhibit high transient helium uptake but low long-term inventory at room temperature, whereas denser, lower-oxygen redeposits can sustain a deeper helium reservoir with possible consequences for subsequent bubble formation and blistering under thermal excursions (Mateus et al., 2018).