OpenNovelty.org

Rapid Training of Hamiltonian Graph Networks Using Random Features

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 5.5Download Report PDF
Graph neural networksphysics-informed machine learningrandom feature methodsgradient-descent-free trainingHamiltonian neural network
Abstract:

Learning dynamical systems that respect physical symmetries and constraints remains a fundamental challenge in data-driven modeling. Integrating physical laws with graph neural networks facilitates principled modeling of complex N-body dynamics and yields accurate and permutation-invariant models. However, training graph neural networks with iterative, gradient-descent-based optimization algorithms (e.g., Adam, RMSProp, LBFGS) often leads to slow training, especially for large, complex systems. In comparison to 15 different optimizers, we demonstrate that Hamiltonian Graph Networks (HGN) can be trained 150-600× faster - but with comparable accuracy - by replacing iterative optimization with random feature-based parameter construction. We show robust performance in diverse simulations, including N-body mass-spring and molecular dynamics systems in up to 33 dimensions and 10,000 particles with different geometries, while retaining essential physical invariances with respect to permutation, rotation, and translation. Our proposed approach is benchmarked using a NeurIPS 2022 Datasets and Benchmarks Track publication to further demonstrate its versatility. We reveal that even when trained on minimal 8-node systems, the model can generalize in a zero-shot manner to systems as large as 4096 nodes without retraining. Our work challenges the dominance of iterative gradient-descent-based optimization algorithms for training neural network models for physical systems.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper proposes Random Feature Hamiltonian Graph Networks (RF-HGN), which replace iterative gradient-based optimization with random feature-based parameter construction for training Hamiltonian Graph Networks. It sits within the Direct Hamiltonian Function Learning leaf of the taxonomy, which contains four papers including this one. This leaf focuses on GNNs that parametrize the Hamiltonian function directly and derive dynamics through Hamilton's equations. The presence of only four papers in this specific leaf suggests a moderately sparse research direction within the broader field of Hamiltonian-informed GNN architectures.

The taxonomy reveals several neighboring research directions. The sibling leaves include Hamiltonian-Constrained Neural ODEs (three papers) and Variational and Symplectic Integrator Networks (one paper), both emphasizing geometric structure preservation through different mechanisms. The broader Electronic Structure and Quantum Hamiltonian Prediction branch addresses quantum chemistry applications, while Domain Generalization and Transfer Learning explores cross-system adaptation. The paper's focus on computational efficiency through random features distinguishes it from these neighboring areas, which prioritize either quantum-scale phenomena or explicit geometric integrators rather than training acceleration.

Among twenty-four candidates examined, the contribution-level analysis reveals mixed novelty signals. The core RF-HGN architecture (Contribution A) examined five candidates with zero refutations, suggesting relative novelty in combining random features with Hamiltonian GNNs. However, the gradient-descent-free training approach (Contribution B) examined nine candidates with two refutations, indicating existing work on alternative training strategies. Similarly, the zero-shot generalization claim (Contribution C) examined ten candidates with two refutations, suggesting prior demonstrations of generalization capabilities. The limited search scope means these findings reflect top-K semantic matches rather than exhaustive coverage.

Based on the limited literature search, the work appears to occupy a niche intersection between Hamiltonian learning and computational efficiency. The random feature approach for accelerating Hamiltonian GNN training shows some novelty, though individual components (gradient-free methods, generalization) have precedents among the examined candidates. The analysis covers top-24 semantic matches and does not claim comprehensive field coverage, leaving open the possibility of additional relevant prior work outside this scope.

Taxonomy

Core-task Taxonomy Papers
25
3
Claimed Contributions
24
Contribution Candidate Papers Compared
4
Refutable Paper

Research Landscape Overview

Core task: learning Hamiltonian dynamics of N-body systems using graph neural networks. The field organizes around several complementary directions. Hamiltonian-Informed Graph Neural Network Architectures develop specialized GNN designs that directly encode symplectic structure or learn Hamiltonian functions, with works like Hamiltonian Graph Dynamics[14] and Symbolic Hamiltonian Laws[12] exemplifying direct function learning approaches. Electronic Structure and Quantum Hamiltonian Prediction focuses on quantum chemistry applications, where methods such as Equivariant Electronic Hamiltonian[2] and Unified Quantum Chemistry[4] predict molecular properties and electronic Hamiltonians. Domain Generalization and Transfer Learning for Physical Systems addresses cross-domain challenges, as seen in Cross Domain Hamiltonian[9], while Specialized Physical System Applications target specific domains like Rydberg atom arrays in Learning Rydberg Interactions[3]. Theoretical Foundations and Comparative Analysis examines inductive biases and representational capacity, with studies like Graph Neural ODE Biases[8] and GNN Classical Methods[13] comparing neural approaches to classical techniques. A particularly active line of work explores how to efficiently parameterize and learn Hamiltonian functions within GNN frameworks, balancing expressiveness with computational cost and physical consistency. Rapid Hamiltonian Random Features[0] sits within the Direct Hamiltonian Function Learning cluster, emphasizing scalable approximation strategies that accelerate training while preserving Hamiltonian structure. This contrasts with Hamiltonian Without Gradient[1], which avoids gradient computation entirely, and differs from symbolic approaches like Symbolic Hamiltonian Laws[12] that recover interpretable closed-form expressions. Compared to Neural Differential Hamiltonian[5], which integrates differential equation solvers, Rapid Hamiltonian Random Features[0] prioritizes computational efficiency through random feature expansions. These methodological trade-offs reflect broader tensions in the field between accuracy, interpretability, generalization across system sizes, and the practical demands of training on large-scale N-body datasets.

Claimed Contributions

Random Feature Hamiltonian Graph Networks (RF-HGN)

The authors propose a novel architecture that combines random feature sampling techniques with Hamiltonian graph networks for modeling physical N-body systems. This approach incorporates translation, rotation, and permutation invariance while leveraging graph structure to capture physical dynamics.

5 retrieved papers
Gradient-descent-free training via random features and linear solvers

The authors develop a training method that replaces iterative gradient-descent optimization with random feature-based parameter construction and least-squares solvers. This approach avoids the computational bottlenecks and convergence challenges of traditional iterative optimization while achieving 150-600× speedups.

9 retrieved papers
Can Refute
Strong zero-shot generalization capability

The authors show that their RF-HGN models trained on small systems (e.g., 8-node or 3×3 systems) can accurately predict dynamics on much larger systems (up to 4096 nodes or 100×100 lattices) without retraining, demonstrating robust generalization across system sizes.

10 retrieved papers
Can Refute

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Random Feature Hamiltonian Graph Networks (RF-HGN)

The authors propose a novel architecture that combines random feature sampling techniques with Hamiltonian graph networks for modeling physical N-body systems. This approach incorporates translation, rotation, and permutation invariance while leveraging graph structure to capture physical dynamics.

Contribution

Gradient-descent-free training via random features and linear solvers

The authors develop a training method that replaces iterative gradient-descent optimization with random feature-based parameter construction and least-squares solvers. This approach avoids the computational bottlenecks and convergence challenges of traditional iterative optimization while achieving 150-600× speedups.

Contribution

Strong zero-shot generalization capability

The authors show that their RF-HGN models trained on small systems (e.g., 8-node or 3×3 systems) can accurately predict dynamics on much larger systems (up to 4096 nodes or 100×100 lattices) without retraining, demonstrating robust generalization across system sizes.

Table of Contents

Rapid Training of Hamiltonian Graph Networks Using Random Features | Novelty Validation