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Related Articles from SNS
A geometric $q$-analogue of Hamiltonian Monte Carlo
arXiv:2512.13246v3 Announce Type: replace Abstract: Hamiltonian Monte Carlo (HMC) generates efficient Markov transitions by combining Hamiltonian dynamics with a Metropolis correction. This paper develops a geometric \(q\)-analogue of HMC by replacing classical Hamiltonian dynamics with a \(q\)-deformed Hamiltonian system arising from \(q\)-calculus. Starting from a Lagrangian formulation, we derive the corresponding \(q\)-Hamiltonian equations and prove the formal invariance of the...
Efficient Hamiltonian, structure and trace distance learning of Gaussian states
Announce Type: replace-cross Abstract: In this work, we initiate the study of Hamiltonian learning for positive temperature bosonic Gaussian states, the quantum generalization of the widely studied problem of learning Gaussian graphical models. We obtain efficient protocols, both in sample and computational complexity, for the task of inferring the parameters of their underlying quadratic Hamiltonian under the assumption of bounded temperature, squeezing, displacement and maximal degree of...
ATLAS-NN: Adaptive Transfer Learnable Symplectic-aware Neural Network for Long-Time Hamiltonian Dynamics
Announce Type: new Abstract: Modeling Hamiltonian systems over long temporal intervals remains a significant challenge due to intrinsic multiscale structures and rapid nonlinear transitions. While Hamiltonian Neural Networks (HNNs) incorporate geometric invariants to improve stability, they typically rely on a fixed, externally prescribed temporal structure. This lack of adaptability often leads to accumulated phase errors and degraded accuracy in systems with heterogeneous temporal scales.
Static Effective Hamiltonians for Molecular Systems through RPA-based downfolding
arXiv:2606.07287v1 Announce Type: new Abstract: Green's function-based downfolding methods construct effective Hamiltonians of reduced dimension that capture dynamical correlations of an electronic environment through effective potentials acting on the active space only. Using methods based on the constrained random phase approximation (cRPA) and moment RPA (mRPA), we construct static effective Hamiltonians that include screening through the environment.
Counting Hamiltonian Paths in 3-Regular Planar Graphs
Combinatorics [Submitted on 5 Jun 2026] Title:Counting Hamiltonian Paths in 3-Regular Planar Graphs View PDF HTML (experimental)Abstract:We introduce two infinite families of 3-regular planar graphs. Both families are conceptual adversaries to the Pohl-Warnsdorf algorithm for finding Hamiltonians.
Efficient Prediction of SO(3)-Equivariant Hamiltonian Matrices via SO(2) Local Frames
Announce Type: replace Abstract: We consider the task of predicting Hamiltonian matrices to accelerate electronic structure calculations, which plays an important role in physics, chemistry, and materials science. Motivated by the inherent relationship between the off-diagonal blocks of the Hamiltonian matrix and the SO(2) local frame, we propose a novel and efficient network, called QHNetV2, that achieves global SO(3) equivariance without the costly SO(3) Clebsch-Gordan tensor products....
Efficient Prediction of SO(3)-Equivariant Hamiltonian Matrices via SO(2) Local Frames
Announce Type: replace-cross Abstract: We consider the task of predicting Hamiltonian matrices to accelerate electronic structure calculations, which plays an important role in physics, chemistry, and materials science. Motivated by the inherent relationship between the off-diagonal blocks of the Hamiltonian matrix and the SO(2) local frame, we propose a novel and efficient network, called QHNetV2, that achieves global SO(3) equivariance without the costly SO(3) Clebsch-Gordan tensor...
Reconciling Causality and Non-Equilibrium Thermodynamics with Hamiltonian Causal Models
arXiv:2606.04822v1 Announce Type: new Abstract: Causal modeling of physical temporal phenomena must handle interventions that act along trajectories, nonstationary induced laws, path-dependent effects, and feedback mediated by dynamics, all challenging in standard causal models. We introduce Hamiltonian Causal Models (HCMs), a trajectory-level framework in which observed variables interact with local environments and interventions act as controls of Hamiltonian mechanisms. HCMs separate...
Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach
arXiv:2509.24627v2 Announce Type: replace Abstract: Embedding physical intuition into network architectures allows the learning of dynamics that enforce fundamental properties, such as energy conservation laws, thereby leading to physically-plausible predictions. Yet, scaling these models to high-dimensional dynamical systems remains a significant challenge. This paper introduces Reduced-order Hamiltonian Neural Network (RO-HNN), a novel physics-inspired neural network that combines the...
Reduced-order modeling of Hamiltonian dynamics based on symplectic neural networks
arXiv:2508.11911v2 Announce Type: replace Abstract: We introduce a novel data-driven symplectic induced-order modeling (ROM) framework for high-dimensional Hamiltonian systems that unifies latent-space discovery and dynamics learning within a single, end-to-end neural architecture. The encoder-decoder is built from Henon neural networks (HenonNets) and may be augmented with linear SGS-reflector layers. This yields an exact symplectic map between full and latent phase spaces.