arXiv subjects

Yaojun Li

Publications and source records attributed to Yaojun Li.

6 recordsLinked to original sources

arXiv2026

Low-Rank Clebsch--Gordan Coupling for Equivariant Spherical Forecasting

Spherical-harmonic neural operators provide an efficient representation for global forecasting, but their discretized pointwise nonlinearities can break rotational equivariance through aliasing. Clebsch-Gordan (CG) tensor products provide exactly equivariant interactions between spherical-harmonic representations, but their computational cost grows rapidly with spectral bandwidth and has limited their use at forecasting scale. We introduce LCG-SFNO, which combines low-rank CG interactions within a controlled low-degree band with coefficient-space residual propagation and an exactly projected quadratic nonlinearity, preserving SO(3) equivariance throughout the learned operator. To make the CG interaction practical, we further develop SSHCG, a sparse GPU implementation with a factorized alternative for wider coupled bands. On spherical shallow-water dynamics and the ERA5-based WeatherBench benchmark, LCG-SFNO reduces rotational error to numerical precision (more than three orders of magnitude below SFNO on shallow water and five orders of magnitude below it on WeatherBench), while matching SFNO on shallow-water forecasting and substantially improving forecast skill relative to SFNO on WeatherBench. Matched ablations show that CG coupling accelerates convergence, while SSHCG keeps the coupling to about 10 percent of a training step at the operating bandwidth, making exact equivariant coupling practical at forecasting scale.

cs.LG↗

arXiv2026

Improving Hamiltonian Learning through Local Energy Decomposition

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.

cs.LG↗

arXiv2026

A Hypertoroidal Covering for Perfect Color Equivariance

When the color distribution of input images changes at inference, the performance of conventional neural network architectures drops considerably. A few researchers have begun to incorporate prior knowledge of color geometry in neural network design. These color equivariant architectures have modeled hue variation with 2D rotations, and saturation and luminance transformations as 1D translations. While this approach improves neural network robustness to color variations in a number of contexts, we find that approximating saturation and luminance (interval valued quantities) as 1D translations introduces appreciable artifacts. In this paper, we introduce a color equivariant architecture that is truly equivariant. Instead of approximating the interval with the real line, we lift values on the interval to values on the circle (a double-cover) and build equivariant representations there. Our approach resolves the approximation artifacts of previous methods, improves interpretability and generalizability, and achieves better predictive performance than conventional and equivariant baselines on tasks such as fine-grained classification and medical imaging tasks. Going beyond the context of color, we show that our proposed lifting can also extend to geometric transformations such as scale.

cs.CV↗

arXiv2026

Frequency-Separable Hamiltonian Neural Network for Multi-Timescale Dynamics

While Hamiltonian mechanics provides a powerful inductive bias for neural networks modeling dynamical systems, Hamiltonian Neural Networks and their variants often fail to capture complex temporal dynamics spanning multiple timescales. This limitation is commonly linked to the spectral bias of deep neural networks, which favors learning low-frequency, slow-varying dynamics. Prior approaches have sought to address this issue through symplectic integration schemes that enforce energy conservation or by incorporating geometric constraints to impose structure on the configuration-space. However, such methods either remain limited in their ability to fully capture multiscale dynamics or require substantial domain specific assumptions. In this work, we exploit the observation that Hamiltonian functions admit decompositions into explicit fast and slow modes and can be reconstructed from these components. We introduce the Frequency-Separable Hamiltonian Neural Network (FS-HNN), which parameterizes the system Hamiltonian using multiple networks, each governed by Hamiltonian dynamics and trained on data sampled at distinct timescales. We further extend this framework to partial differential equations by learning a state- and boundary-conditioned symplectic operators. Empirically, we show that FS-HNN improves long-horizon extrapolation performance on challenging dynamical systems and generalizes across a broad range of ODE and PDE problems.

cs.LG↗

arXiv2024

A Platform for All-optical Thomson/ Compton Scattering with Versatile Parameters

A dual-beam platform for all-optical electron-photon scattering, or Thomson/Compton scattering, with adjustable collision-angle and parameter tuning ability has been developed, which, in principle, can be used for the verification of strong-field quantum electrodynamics effects. Combining this platform with a 200 TW Ti:Sapphire laser system, we demonstrated the generation of inverse Compton scattering X/gamma-rays with tunable energies from tens of keV to MeV. The polarization of X/gamma radiation was manipulated by controlling the polarization of scattering laser. In the near future, by combining this experimental platform with multi-PW laser facilities, it is proposed to experimentally generate X/gamma radiation with orbital angular momentum for the nuclear isomer excitation, and more importantly, to explore the regime transition from nonlinear Thomson scattering to nonlinear Compton scattering, eventually to demonstrate the verification of theories on extremely strong field quantum electrodynamics effects.

hep-ex↗

arXiv2022

Femtosecond pumping of nuclear isomeric states by the Coulomb collision of ions with quivering electrons

Efficient production of nuclear isomers is critical for pioneering applications, like nuclear clocks, nuclear batteries, clean nuclear energy, and nuclear γ-ray lasers. However, due to small production cross sections and quick decays, it is extremely difficult to acquire a significant amount of isomers with short lifetimes via traditional accelerators or reactors because of low beam intensity. Here, for the first time, we experimentally present femtosecond pumping of nuclear isomeric states by the Coulomb excitation of ions with the quivering electrons induced by laser fields. Nuclei populated on the third excited state of 83Kr are generated with a peak efficiency of 2.34*10^15 particles=s from a tabletop hundred-TW laser system. It can be explained by the Coulomb excitation of ions with the quivering electrons during the interaction between laser pulses and clusters at nearly solid densities. This efficient and universal production method can be widely used for pumping isotopes with excited state lifetimes down to picoseconds, and could be a benefit for fields like nuclear transition mechanisms and nuclear γ-ray lasers.

nucl-ex↗