Hamiltonian Learning

Follow this topic Ask about this topic

Latest papers

8 papers1 paper in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

Improving Hamiltonian Learning through Local Energy Decomposition
Nov 2, 2026Yaojun Li, Yulong Yang, Christine Allen-BlanchetteHamiltonian Learning Hamiltonian Neural Networks
Princeton University
Integrable building blocks for symplectic neural networks: learned-type layers, fiber-preserving layers, and what a single layer can do
Oct 18, 2026Andrew Qing HeHamiltonian Learning Structure-Preserving Neural Networks
Duke University
Classical Hardness of Learning Functions of Hamiltonians
Oct 1, 2026Sota Hashimoto, Akinori KawachiQuantum Machine Learning Hamiltonian Learning
Graduate School of Engineering, Mie University
Simulation-Based Quantum System Inference with Neural Posterior Estimation
Sep 28, 2026Hang Zou, Anton Frisk Kockum, Martin Rahm +1Simulation-Based Inference Neural Posterior Estimation
Department of Computer Science and Engineering, Chalmers University of Technology and University of Gothenburg, 41296 Gothenburg, Sweden · Department of Microtechnology and Nanoscience, Chalmers University of Technology, 41296 Gothenburg, Sweden · Department of Chemistry and Chemical Engineering, Chalmers University of Technology, 41296 Gothenburg, Sweden
Coupled-cluster molecular properties across the main group that extrapolate beyond training size
Aug 18, 2026Wenhao He, Xu Chen, Noah Song +10Hamiltonian Learning Quantum Chemistry
Center for Computational Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA · Department of Chemistry, Emory University, Atlanta, GA 30322, USA · Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA +2
Optimal Ansatz-free Hamiltonian Learning In Situ
Jun 17, 2026Taiqi Zhou, Weiyuan GongQuantum System Identification Hamiltonian Learning
Department of Information Engineering, The Chinese University of Hong Kong. · John A. Paulson School of Engineering and Applied Sciences, Harvard University. · California Institute of Technology
SymQNet: Amortized Acquisition for Low-Latency Adaptive Hamiltonian Learning
Jun 11, 2026Yash Vardhan Tomar, Dheeraj PeddireddyReinforcement Learning Quantum System Identification
Purdue University West Lafayette, United States
Accelerating Quantum Materials Characterization: Hybrid Active Learning for Autonomous Spin Wave Spectroscopy
Apr 26, 2026William RatcliffActive Learning Hamiltonian Learning
NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA

Nov 2, 2026J/K move · Enter open · S save

Improving Hamiltonian Learning through Local Energy Decomposition

Yaojun Li, Yulong Yang, Christine Allen-Blanchette

Princeton University

Hamiltonian Learning Hamiltonian Neural Networks Spectral Bias

Open paper AskPDF arXiv

Hamiltonian neural networks provide a principled framework for learning conservative dynamics. A scalar Hamiltonian is parameterized by a neural network and the vector field is derived using Hamilton's equations. However, preserving Hamiltonian structure does not guarantee that the energy function itself is represented accurately. When modeled by a conventional multilayer perceptron, the Hamiltonian inherits the spectral bias of coordinate-based neural representations, favoring smooth over fine-scale structure. These fine-scale errors can be amplified by differentiation when computing the dynamics. To address this limitation, we introduce Local Multiscale Hamiltonian Neural Network (LM-HNN), which restructures the Hamiltonian according to its physical interaction structure. LM-HNN decomposes the energy into kinetic and potential components and represents them as sums of shared local functions over multiple interaction neighborhoods. This replaces a single high-dimensional approximation problem with lower-dimensional, reusable interaction laws, making fine-scale energy structure easier to resolve while preserving Hamiltonian dynamics. Across low-dimensional, interacting, and fast--slow systems, LM-HNN consistently achieves more accurate Hamiltonian derivatives and long-horizon rollouts than competing structure-preserving models, while substantially extending the effective spectral range of the learned energy. The same structured representation also generalizes more reliably to energy levels not observed during training. These results show that accuracy depends on the Hamiltonian representation as well as its structure, and that incorporating locality, decomposition, and shared interaction laws provides a simple and effective route to more accurate and generalizable Hamiltonian learning.