# SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biases

arXiv: https://arxiv.org/abs/2308.13212 · HTML: https://mlsanity.com/paper/2308.13212/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 59 references that are in the map.
- First posted on arXiv 25 Aug 2023.

## Builds on (most cited first, 30 of 43)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [All in One: Multi-task Prompting for Graph Neural Networks](https://mlsanity.com/paper/2307.01504/) (2023)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints](https://mlsanity.com/paper/2010.13581/) (2020)
- [LieTransformer: Equivariant self-attention for Lie Groups](https://mlsanity.com/paper/2012.10885/) (2020)
- [Flexible Neural Representation for Physics Prediction](https://mlsanity.com/paper/1806.08047/) (2018)
- [On Second Order Behaviour in Augmented Neural ODEs](https://mlsanity.com/paper/2006.07220/) (2020)
- [Equivariant Graph Mechanics Networks with Constraints](https://mlsanity.com/paper/2203.06442/) (2022)
- [Learning Continuous System Dynamics from Irregularly-Sampled Partial Observations](https://mlsanity.com/paper/2011.03880/) (2020)
- [GADBench: Revisiting and Benchmarking Supervised Graph Anomaly Detection](https://mlsanity.com/paper/2306.12251/) (2023)
- [Equivariant Flows: sampling configurations for multi-body systems with symmetric energies](https://mlsanity.com/paper/1910.00753/) (2019)
- [Semi-Supervised Graph Classification: A Hierarchical Graph Perspective](https://mlsanity.com/paper/1904.05003/) (2019)
- [Neural Stochastic PDEs: Resolution-Invariant Learning of Continuous Spatiotemporal Dynamics](https://mlsanity.com/paper/2110.10249/) (2021)
- [Efficient Learning of Mesh-Based Physical Simulation with BSMS-GNN](https://mlsanity.com/paper/2210.02573/) (2022)

## Built on by (most cited first, 27 of 27)

- [All in One and One for All: A Simple yet Effective Method towards Cross-domain Graph Pretraining](https://mlsanity.com/paper/2402.09834/) (2024)
- [ProbTS: Benchmarking Point and Distributional Forecasting across Diverse Prediction Horizons](https://mlsanity.com/paper/2310.07446/) (2023)
- [GLBench: A Comprehensive Benchmark for Graph with Large Language Models](https://mlsanity.com/paper/2407.07457/) (2024)
- [ProG: A Graph Prompt Learning Benchmark](https://mlsanity.com/paper/2406.05346/) (2024)
- [A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications](https://mlsanity.com/paper/2403.00485/) (2024)
- [A Survey of Graph Transformers: Architectures, Theories and Applications](https://mlsanity.com/paper/2502.16533/) (2025)
- [CirT: Global Subseasonal-to-Seasonal Forecasting with Geometry-inspired Transformer](https://mlsanity.com/paper/2502.19750/) (2025)
- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [Large Language-Geometry Model: When LLM meets Equivariance](https://mlsanity.com/paper/2502.11149/) (2025)
- [Materials Generation in the Era of Artificial Intelligence: A Comprehensive Survey](https://mlsanity.com/paper/2505.16379/) (2025)
- [Dynamic PDB: A New Dataset and a SE(3) Model Extension by Integrating Dynamic Behaviors and Physical Properties in Protein Structures](https://mlsanity.com/paper/2408.12413/) (2024)
- [GeoMFormer: A General Architecture for Geometric Molecular Representation Learning](https://mlsanity.com/paper/2406.16853/) (2024)
- [DuSEGO: Dual Second-order Equivariant Graph Ordinary Differential Equation](https://mlsanity.com/paper/2411.10000/) (2024)
- [Conservation-informed Graph Learning for Spatiotemporal Dynamics Prediction](https://mlsanity.com/paper/2412.20962/) (2024)
- [Beyond Structure: Invariant Crystal Property Prediction with Pseudo-Particle Ray Diffraction](https://mlsanity.com/paper/2509.21778/) (2025)
- [Universally Invariant Learning in Equivariant GNNs](https://mlsanity.com/paper/2510.13169/) (2025)
- [InversionGNN: A Dual Path Network for Multi-Property Molecular Optimization](https://mlsanity.com/paper/2503.01488/) (2025)
- [A Survey of Cross-domain Graph Learning: Progress and Future Directions](https://mlsanity.com/paper/2503.11086/) (2025)
- [Geometric Mixture Models for Electrolyte Conductivity Prediction](https://mlsanity.com/paper/2510.15403/) (2025)
- [Relaxing Continuous Constraints of Equivariant Graph Neural Networks for Physical Dynamics Learning](https://mlsanity.com/paper/2406.16295/) (2024)
- [Learning System Dynamics without Forgetting](https://mlsanity.com/paper/2407.00717/) (2024)
- [Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs](https://mlsanity.com/paper/2601.11259/) (2026)
- [TimeGMM: Single-Pass Probabilistic Forecasting via Adaptive Gaussian Mixture Models with Reversible Normalization](https://mlsanity.com/paper/2601.12288/) (2026)
- [Latent-Hysteresis Graph ODEs: Modeling Coupled Topology-Feature Evolution via Continuous Phase Transitions](https://mlsanity.com/paper/2604.24293/) (2026)
- [Fourier Geometric Wind Power Forecasting with Numerical Weather Prediction](https://mlsanity.com/paper/2607.17095/) (2026)
- [ExPhy: A Benchmark for Explicit Physical Property Learning in Multi-Object Trajectory Forecasting](https://mlsanity.com/paper/2608.20009/) (2026)
- [Equivariant Sheaf Neural Networks: Learning Geometric Transport on Graphs](https://mlsanity.com/paper/2608.28853/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) with equivariant properties have emerged as powerful tools for modeling complex dynamics of multi-object physical systems. However, their generalization ability is limited by the inadequate consideration of physical inductive biases: (1) Existing studies overlook the continuity of transitions among system states, opting to employ several discrete transformation layers to learn the direct mapping between two adjacent states; (2) Most models only account for first-order velocity information, despite the fact that many physical systems are governed by second-order motion laws. To incorporate these inductive biases, we propose the Second-order Equivariant Graph Neural Ordinary Differential Equation (SEGNO). Specifically, we show how the second-order continuity can be incorporated into GNNs while maintaining the equivariant property. Furthermore, we offer theoretical insights into SEGNO, highlighting that it can learn a unique trajectory between adjacent states, which is crucial for model generalization. Additionally, we prove that the discrepancy between this learned trajectory of SEGNO and the true trajectory is bounded. Extensive experiments on complex dynamical systems including molecular dynamics and motion capture demonstrate that our model yields a significant improvement over the state-of-the-art baselines.