Awesome Machine Learning Interatomic Potentials (MLIPs)

```mermaid %% Mermaid v10+ optimized vertical timeline %% Enable in compatible Mermaid live editors: https://mermaid-js.github.io/mermaid-live-editor

flowchart LR

subgraph "2007"
    BP["Behler-Parrinello NN<br/>(Atomized Energy)"]
end

subgraph "2010 - 2019"
    SOAP[SOAP]
    SchNet["SchNet<br/>(Filter, RBF)"]
    TFN["TFN<br/>(e3nn)"]
    ACE["ACE<br/>(Many-body Expansion)"]
    GDML[GDML]
    GAP[GAP]
    SNAP[SNAP]
    MTP[MTP]
    HDNNP[HDNNPs]
    ANI[ANI]
    DeepMD[DeepMD]
    sGDML[sGDML]
end

subgraph "2020 - 2023"
    M3GNet[M3GNet]
    CHGNet[CHGNet]
    SCN[SCN]
    eSCN[eSCN]
    Equiformer[Equiformer]
    NequIP[NequIP]
    MACE[MACE]
    MACE-MP["MACE-MP"]
    MACE-OFF["MACE-OFF"] 
    ANI2x[ANI2x]
    AIMNet2[AIMNet2]
    GNoME[GNoME]
    DPA1["DPA-1"]
    So3krates
end

subgraph "2024 - "
    GRACE[GRACE]
    eqV2["eqV2<br/>(OMat)"]
    MatterSim[MatterSim]
    SevenNet[SevenNet]
    ORBs[ORBs]
    DPA3["DPA-3"]
    CACE
    eSEN["eSEN<br/>(OMat, OMol)"]
    ESCalP[ESCalP]
    EFA
end

%% Edges
BP --> ANI --> ANI2x --> AIMNet2
BP --> HDNNP
BP --> GAP --> SNAP
BP --> SchNet --> TFN
BP --> M3GNet
Kernel --> GDML --> sGDML

GAP --> MTP
GAP --> SOAP --> ACE --> MACE 
M3GNet --> MatterSim
TFN --> SCN --> eSCN
TFN --> NequIP 
TFN --> MACE
TFN --> So3krates
MACE --> MACE-MP --> GRACE
MACE --> MACE-OFF
MACE --> CACE
NequIP --> GNoME
NequIP --> SevenNet
NequIP --> eSEN
MEGNet --> M3GNet --> CHGNet 

G-CNNs["G-CNNs<br/>Equivariance"] --> TFN
DeepMD --> DPA1
Attention --> DPA1 --> DPA3
Attention --> ESCalP
Attention --> Equiformer --> eqV2
Attention --> EFA
SchNet --> EFA
SCN --> Equiformer
GNS --> ORBs

%% Styling
classDef architecture fill:#1e3a8a,stroke:#1e40af,stroke-width:3px,color:#fff,font-weight:bold
classDef organic fill:#059669,stroke:#10b981,stroke-width:2px,color:#fff,font-weight:bold
classDef attention fill:#7c3aed,stroke:#8b5cf6,stroke-width:2px,color:#fff,font-weight:bold
classDef equivariance fill:#ea580c,stroke:#f97316,stroke-width:2px,color:#fff,font-weight:bold
classDef universal fill:#be185d,stroke:#ec4899,stroke-width:2px,color:#fff,font-weight:bold

class BP,ANI,HDNNP,GAP,SNAP,MTP,SchNet,DeepMD,GDML,sGDML architecture
class SOAP,TFN,ACE,MACE,NequIP,Equiformer,eqV2,eSCN,eSEN,SCN,CACE,So3krates equivariance
class ANI2x,AIMNet2,MACE-OFF organic
class GNoME,MACE-MP,CHGNet,M3GNet,MatterSim,GRACE,SevenNet,eqV2,eSEN,ORBs universal
class DPA1,DPA3,ESCalP,EFA attention

%% Click links
click BP "https://doi.org/10.1103/PhysRevLett.98.146401"
click HDNNP "https://onlinelibrary.wiley.com/doi/full/10.1002/qua.24890"
click GDML "https://doi.org/10.1126/sciadv.1603015"
click SOAP "https://doi.org/10.1039/C6CP00415F"
click SchNet "https://doi.org/10.48550/arXiv.1706.08566"
click TFN "https://arxiv.org/abs/1802.08219"
click ACE "https://doi.org/10.1103/PhysRevB.99.014104"
click SCN "https://doi.org/10.48550/arXiv.2206.14331"
click Equiformer "https://doi.org/10.48550/arXiv.2206.11990"
click NequIP "https://doi.org/10.1038/s41467-022-29939-5"
click MACE "https://arxiv.org/abs/2206.07697"
click MACE-MP "https://arxiv.org/abs/2401.00096"
click MACE-OFF "https://arxiv.org/abs/2312.15211"
click CACE "https://doi.org/10.1038/s41524-024-01332-4"
click DeepMD "https://doi.org/10.1103/PhysRevLett.120.143001"
click GAP "https://doi.org/10.1103/PhysRevLett.104.136403"
click ANI "https://doi.org/10.1039/C6SC05720A"
click NEP89 "https://arxiv.org/abs/2504.21286"
click EFA "https://arxiv.org/abs/2412.08541"
click M3GNet "https://doi.org/10.1038/s43588-022-00349-3"
click CHGNet "https://doi.org/10.1038/s42256-023-00716-3"
click GRACE "https://doi.org/10.48550/arXiv.2311.16326"
click So3krates "https://doi.org/10.48550/arXiv.2205.14276"
click GNoME "https://doi.org/10.1038/s41586-023-06735-9"
click SevenNet "https://pubs.acs.org/doi/10.1021/acs.jctc.4c00190"
click MatterSim "https://doi.org/10.48550/arXiv.2405.04967"
click GNS "https://doi.org/10.48550/arXiv.2002.09405"

```