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# Equivariant Graph Neural Network

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  1. arXiv

    Interatomic potentials drop the single cutoff: MCSA stacks three radial scales and cuts thermal-conductivity error by 13.7%

    SO(3)-equivariant graph-neural-network interatomic potentials usually use one cutoff radius, so radial interactions carry a single characteristic spatial-frequency scale. MCSA fuses radial kernels with different cutoff radii before the angular tensor product, covering several scales with one angular computation. Across the Nequix, Eqnorm and EquiformerV3 backbones, energy, force and stress errors fall on both in-distribution and out-of-distribution tests; Nequix+MCSA lowers the symmetric relative mean error of lattice thermal conductivity from 0.487 to 0.420, with per-material time rising from 1.107 to 1.136 minutes.

    Junfu Tan（First author）
    Multi-Cutoff Spectral AggregationMachine Learning Interatomic PotentialsEquivariant Graph Neural Network
  2. bioRxiv

    CytoBridge turns sparse spatial transcriptomics snapshots into virtual tissues, writing cell–cell interaction into the dynamics

    Time-series spatial transcriptomics measures each tissue section once, so how cells migrate, proliferate and influence one another can only be inferred indirectly. CytoBridge learns continuous population evolution in a joint space of transcriptomic state and spatial coordinates, splitting velocity into an interaction term estimated from spatial neighborhoods and ligand–receptor priors and an intrinsic-context term, while allowing cell numbers to grow or shrink. Across five datasets on three spatial transcriptomics platforms it generates unmeasured intermediate stages; in a leave-one-stage-out benchmark it had the lowest Sliced-W2 in 12 of 33 combinations, more than any other method or control.

    Peking UniversityUniversity of California, Irvine
    Zhenyi Zhang（First author）Tiejun Li（Corresponding author）Peijie Zhou（Corresponding author）
    CytoBridgeUnbalanced Mean-Field Schrödinger BridgeEquivariant Graph Neural NetworkSpatial transcriptomicsIn Silico Perturbation
  3. arXiv

    Plane-wave DFT Hamiltonians become learnable: projectability-selected eigenstates cut sodium band errors to 1–3 meV

    Converting plane-wave DFT Hamiltonians into atomic-orbital form now uses projectability-selected eigenstates to complete the subspace instead of an empirical shift, giving 1–3 meV band errors for five sodium phases with 13 orbitals per atom where real-space reconstruction needs 23 orbitals and still errs by 12–28 meV.

    Zhejiang UniversityJilin UniversityChinese Academy of Sciences
    Chuntian Wu（First author）
    Projectability-guided AO Hamiltonian constructionPlane-Wave Density Functional TheoryEquivariant Graph Neural NetworkDensity Functional Theory
  4. researchsquare.com

    A million asteroids no longer lean on soft constraints: symplectic graph neural ODEs cut position error to 1.8×10⁻⁴ AU

    For large asteroid swarms whose orbits must be reconstructed across observation gaps, a graph neural ODE was built with symplectic structure inside the network: instead of approximating conservation laws with soft penalty terms, a Hamiltonian generates the equations of motion directly, and planetary sphere-of-influence radii modulate message passing between bodies. On a one-million-body simulation spanning the Main Belt, Jupiter Trojans, near-Earth asteroids and Centaurs, mean position error is 1.8005×10⁻⁴ AU with energy drift of 8.42×10⁻⁵; on NASA JPL Horizons ephemerides for 99942 Apophis, mean position error across a 60-day blackout is 1.7983×10⁻⁴ AU.

    HUTECH University
    Quan Van Le（First author, Corresponding author）
    SympG-NODESymplectic Graph-Hamiltonian Neural ODETrajectory ReconstructionEquivariant Graph Neural NetworkCelestial Mechanics

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