Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Neural Hamiltonian Diffusions for Modeling Structured Geometric Dynamics
Authors: Sungwoo Park
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We establish generalization guarantees under curvature-dependent complexity and demonstrate applications across diverse scientific domains, including toroidal molecular dynamics, quantum spin systems, and relativistic n-body problems in Schwarzschild spacetime. In this section, we validate our proposed framework across three distinct physical scenarios that reflect a diverse range of geometric structures: (i) an interacting spin system evolving on the compact Lie group manifold SU(2) = S3, (ii) relativistic N-body dynamics formulated on Lorentzian spacetimes such as the Schwarzschild manifolds and (iii) molecular dynamics of protein backbones represented on high-dimensional toroidal configuration spaces TN. |
| Researcher Affiliation | Academia | Sungwoo Park Department of Computer Science and Engineering Korea University EMAIL |
| Pseudocode | Yes | In Appendix, we provide the algorithm and pseudo-code for sampling frame-equivariant and neural network architectures. Algorithm 1 GAUGE EQUIVARIANT TRANSFORMER UNET Algorithm 2 SIMULATE NEURAL HAMILTONIAN DIFFUSION(q0, p0, t0, T, nf; Hθ) |
| Open Source Code | No | The codebase and configuration files will be made publicly available at https://github.com/Anonymous/HDM. |
| Open Datasets | Yes | To extract geometric Hamiltonian states, we post-process time-aligned atomic trajectories from the Timewarp Klein et al. [2023] to compute angles (ϕ, ψ, ω, χi) as generalized coordinates... |
| Dataset Splits | Yes | All experiments were conducted on a single NVIDIA RTX 5090 GPU...We use an 80%/20% temporal split for training and testing. Each sub-trajectory consists of 0.8T frames: the initial frame t0 serves as the input, and the following 0.8T frames (t1:0.8T ) are used for supervision. |
| Hardware Specification | Yes | All experiments were conducted on a single NVIDIA RTX 5090 GPU using Python 3.11 and Py Torch 2.1.0 with CUDA 11.8 support. |
| Software Dependencies | Yes | All experiments were conducted on a single NVIDIA RTX 5090 GPU using Python 3.11 and Py Torch 2.1.0 with CUDA 11.8 support. |
| Experiment Setup | Yes | The network uses a hidden size of 128 and contains approximately 3M parameters. Training is performed for 105 epochs using the Adam optimizer with learning rate 10 4 and batch size 128. The loss combines a local alignment term and a long-range reconstruction objective. The numerical integrator uses a fixed step size t = 2.0 fs and isotropic Gaussian noise of magnitude 10 2 t. |