Structure-Preserving Neural Networks

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14 papers3 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

Integrable building blocks for symplectic neural networks: learned-type layers, fiber-preserving layers, and what a single layer can do
Oct 18, 2026Andrew Qing HeStructure-Preserving Neural Networks Hamiltonian Neural Networks
Duke University
Do Neural Networks Learn Structure-Preserving Maps? A Case Study in Latent-to-Hilbert Embeddings
Oct 4, 2026Muhammad Adnan ShahzadRepresentation Learning Latent Space Alignment
Department of Computer Science and Software Engineering (CSSE) Montreal, QC, Canada
LLN: Learnable Lens Networks for Parameter-Efficient Long-Horizon Dynamical Prediction
Sep 28, 2026Binbin Yong, Zhao Su, Lan Guo +3Invertible Neural Networks Residual Learning
Lanzhou University · Monash University · University of Wollongong
Conservation Buys Stability and Factoring Buys Counterfactuals in Physical World Models
Sep 17, 2026Yufeng Wang, Parivesh Priye, Lu Wei +1Neural Surrogate Modeling Dynamical Systems
Stony Brook University · Georgia Institute of Technology · Westlake University
Learning Deterministic and Stochastic Forced Hamiltonian Systems
Aug 20, 2026Benedikt Brantner, Tomasz TyranowskiStructure-Preserving Neural Networks Hamiltonian Neural Networks
Max-Planck-Institut für Plasmaphysik Boltzmannstraße 2, 85748 Garching, Germany · Technische Universität München, Zentrum Mathematik Boltzmannstraße 3, 85748 Garching, Germany · University of Twente, Department of Applied Mathematics PO Box 217, 7500AE Enschede, The Netherlands
Subgrid-Scale Parameterization in Burgers' Equation Using Structure-Preserving Neural Networks and Entropy Variables
Jul 16, 2026Aijaz Nazir, Ilya TimofeyevNeural Surrogate Modeling PDE Solving
Dept. of Mathematics, University of Houston, Houston, TX 77204
Structure-Oriented Randomized Neural Networks for Poisson-Nernst-Planck and Poisson-Nernst-Planck-Navier-Stokes Systems
Jun 18, 2026Yunlong Li, Fei WangNeural PDE Solvers Structure-Preserving Neural Networks
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, P.R. China. · School of Mathematics and Statistics & State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China.
Exact equivariance, kept through training, buys zero-shot generalisation across the symmetry group
Jun 2, 2026Hongbo WangWorld Models for Robotics World Models
Department of Mathematics, Stony Brook University, Stony Brook, NY 11794, USA
A Structure-Preserving Graph Neural Solver for Parametric Hyperbolic Conservation Laws
Apr 17, 2026Jiamin Jiang, Shanglin Lv, Jingrun ChenGraph Neural Networks Neural PDE Solvers
School of Artificial Intelligence and Data Science and Suzhou Institute for Advanced Research, University of Science and Technology of China, and Suzhou Big Data & AI Research and Engineering Center, China · School of Mathematical Sciences, University of Science and Technology of China, China · School of Mathematical Sciences and Suzhou Institute for Advanced Research, University of Science and Technology of China, and Suzhou Big Data & AI Research and Engineering Center, China
Interpretable Physics Extraction from Data for Linear Dynamical Systems using Lie Generator Networks
Mar 28, 2026Shafayeth Jamil, Rehan KapadiaStructure-Preserving Neural Networks Dynamical Systems
Department of Electrical and Computer Engineering, University of Southern California
Hyperelastic constitutive model discovery with differentiable finite elements and structure-preserving neural networks
Mar 27, 2026Francesco RegazzoniStructure-Preserving Neural Networks Hyperelasticity
MOX, Department of Mathematics, Politecnico di Milano, Milan, Italy
An Invariant Compiler for Neural ODEs in AI-Accelerated Scientific Simulation
Mar 25, 2026Fangzhou Yu, Yiqi Su, Ray Lee +2Structure-Preserving Neural Networks Neural ODEs
Virginia Tech, VA, USA
NN-OpInf: an operator inference approach using structure-preserving composable neural networks
Mar 9, 2026Eric Parish, Anthony Gruber, Patrick Blonigan +1Structure-Preserving Neural Networks Reduced-Order Modeling
Sandia National Laboratories, Livermore, CA, USA · Sandia National Laboratories, Albuquerque, NM, USA
Structure-preserving Randomized Neural Networks for Incompressible Magnetohydrodynamics Equations
Mar 1, 2026Yunlong Li, Fei Wang, Lingxiao LiStructure-Preserving Neural Networks Magnetohydrodynamics
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, P.R. China. · School of Mathematics and Statistics & State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China. · School of Mathematics and Statistics, Henan University, Kaifeng, Henan 475004, China. +1

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Integrable building blocks for symplectic neural networks: learned-type layers, fiber-preserving layers, and what a single layer can do

Andrew Qing He

Duke University

Structure-Preserving Neural Networks Hamiltonian Neural Networks Dynamical Systems

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Exactly symplectic neural networks are built almost exclusively from shear maps and gain expressivity only through depth. We ask what else a single explicit symplectic layer can be. Observing that every layer in use is the exact flow of a Hamiltonian that is a function of commuting integrals, we obtain three families of layers: a learned-type layer, in which every conjugate pair is rotated, squeezed or sheared by a state-dependent amount and the type is found by training; moving-plane shears, residual symplectic maps outside the known ridge-function class; and fiber-preserving layers, which combine an unconstrained point transformation with a fiber translation at the cost of one linear solve. We characterize residual symplectic layers

x \mapsto x + J\nabla H(x)

: in one degree of freedom they are exactly the shears along a line, while from two degrees of freedom on a strictly larger class exists. Conjugating a learned-type layer by a symplectic network yields an exact one-parameter group with an exactly conserved learned Hamiltonian. In experiments on sixteen systems with one to forty degrees of freedom, against SympNets, HénonNets and learned-plane shear networks, layers built on nonlinear integrals are far more accurate when the Hamiltonian contains functions of those integrals. On nonlinear Schrödinger lattices with six to forty sites, twist layers alternating with linear symplectic maps are over a hundred times more accurate than every shear-based network, and with an on-site potential of learned form three to four orders of magnitude more accurate. On chains of Tao oscillators with the step size as an input, stretch layers are 45 to 70 times more accurate than learned-plane shears and recover the Hamiltonian to 1%. On generic non-separable systems, fiber layers improve on learned-plane shears by at most a factor of two, and widening the networks does not help any architecture.