arXiv subjects

Zhonghao Sun

Publications and source records attributed to Zhonghao Sun.

8 recordsLinked to original sources

arXiv2025

Derivation of Runge--Kutta Order Conditions via Functional Tree Tensor Networks

Tree tensor networks (TTNs) provide a compact and structured representation of high-dimensional data, making them valuable in various areas of computational mathematics and physics. In this paper, we present a rigorous mathematical framework for expressing high-order derivatives of functional TTNs, both with or without constraints. Our framework decomposes the total derivative of a given TTN into a summation of TTNs, each corresponding to the partial derivatives of the original TTN. Using this decomposition, we derive the Taylor expansion of vector-valued functions subject to ordinary differential equation constraints or algebraic constraints imposed by Runge--Kutta (RK) methods. As a concrete application, we employ this framework to construct order conditions for RK methods. Due to the intrinsic tensor properties of partial derivatives and the separable tensor structure in RK methods, the Taylor expansion of numerical solutions can be obtained in a manner analogous to that of exact solutions using tensor operators. This enables the order conditions of RK methods to be established by directly comparing the Taylor expansions of the exact and numerical solutions, eliminating the need for mathematical induction. For a given function $\vector{f}$, we derive sharper order conditions that go beyond the classical ones, enabling the identification of situations where a standard RK scheme of order $p$ achieves unexpectedly higher convergence order for the particular function. These results establish new connections between tensor network theory and classical numerical methods, potentially opening new avenues for both analytical exploration and practical computation.

math.NA↗

arXiv2024

Efficacious qubit mappings for quantum simulations of the $^{12}$C rotational band

Solving atomic nuclei from first principles places enormous demands on computational resources, which grow exponentially with increasing number of particles and the size of the space they occupy. We present first quantum simulations based on the variational quantum eigensolver for the low-lying structure of the $^{12}$C nucleus that provide acceptable bound-state energies even in the presence of noise. We achieve this by taking advantage of two critical developments. First, we utilize an almost perfect symmetry of atomic nuclei that, in a complete symmetry-adapted basis, drastically reduces the size of the model space. Second, we use the efficacious Gray encoding, for which it has been recently shown that it is resource efficient, especially when coupled with a near band-diagonal structure of the nuclear Hamiltonian.

quant-ph↗

arXiv2024

HaTT: Hadamard avoiding TT recompression

The Hadamard product of tensor train (TT) tensors is a fundamental nonlinear operation in scientific computing and data analysis. However, due to its tendency to significantly increase TT ranks, the Hadamard product poses a major computational challenge in TT tensor-based algorithms. To address this, it is crucial to develop recompression algorithms that mitigate the effects of this rank increase. Existing recompression algorithms require an explicit representation of the Hadamard product, resulting in high computational and storage costs. In this work, we propose a Hadamard avoiding TT recompression (HaTT) algorithm, which reduces both computational complexity and storage requirements. By leveraging the structure of the Hadamard product in TT tensors and exploiting its Hadamard product-free property, the HaTT algorithm achieves significantly lower complexity compared to existing TT recompression methods. This is confirmed through both complexity analysis and numerical experiments. Furthermore, the HaTT algorithm is applied to solve the Allen--Cahn equation, achieving substantial speedup over existing TT recompression algorithms without sacrificing accuracy.

math.NA↗

arXiv2021

Ab initio predictions link the neutron skin of ${}^{208}$Pb to nuclear forces

Heavy atomic nuclei have an excess of neutrons over protons, which leads to the formation of a neutron skin whose thickness is sensitive to details of the nuclear force. This links atomic nuclei to properties of neutron stars, thereby relating objects that differ in size by orders of magnitude. The nucleus ${}^{208}$Pb is of particular interest because it exhibits a simple structure and is experimentally accessible. However, computing such a heavy nucleus has been out of reach for ab initio theory. By combining advances in quantum many-body methods, statistical tools, and emulator technology, we make quantitative predictions for the properties of ${}^{208}$Pb starting from nuclear forces that are consistent with symmetries of low-energy quantum chromodynamics. We explore $10^9$ different nuclear-force parameterisations via history matching, confront them with data in select light nuclei, and arrive at an importance-weighted ensemble of interactions. We accurately reproduce bulk properties of ${}^{208}$Pb and determine the neutron skin thickness, which is smaller and more precise than a recent extraction from parity-violating electron scattering but in agreement with other experimental probes. This work demonstrates how realistic two- and three-nucleon forces act in a heavy nucleus and allows us to make quantitative predictions across the nuclear landscape.

nucl-th↗

arXiv2021

Universal trend of charge radii of even-even Ca-Zn nuclei

Radii of nuclear charge distributions carry information about the strong and electromagnetic forces acting inside the atomic nucleus. While the global behavior of nuclear charge radii is governed by the bulk properties of nuclear matter, their local trends are affected by quantum motion of proton and neutron nuclear constituents. The measured differential charge radii $\delta\langle r^2_c\rangle$ between neutron numbers $N=28$ and $N=40$ exhibit a universal pattern as a function of $n=N-28$ that is independent of the atomic number. Here we analyze this remarkable behavior in even-even nuclei from calcium to zinc using two state-of-the-art theories based on quantified nuclear interactions: the ab-initio coupled cluster theory and nuclear density functional theory. Both theories reproduce the smooth rise of differential charge radii and their weak dependence on the atomic number. By considering a large set of isotopic chains, we show that this trend can be captured by just two parameters: the slope and curvature of ${\delta\langle r^2_c\rangle(n)}$. We demonstrate that these parameters show appreciable model dependence, and the statistical analysis indicates that they are not correlated with any single model property, i.e., they are impacted by both bulk nuclear properties as well as shell structure.

nucl-th↗

arXiv2018

Gogny-force derived effective shell-model Hamiltonian

The density-dependent finite-range Gogny force has been used to derive the effective Hamiltonian for the shell-model calculations of nuclei. The density dependence simulates an equivalent three-body force, while the finite range gives a Gaussian distribution of the interaction in the momentum space and hence leads to an automatic smooth decoupling between low-momentum and high-momentum components of the interaction, which is important for finite-space shell-model calculations. Two-body interaction matrix elements, single-particle energies and the core energy of the shell model can be determined by the unified Gogny force. The analytical form of the Gogny force is advantageous to treat cross-shell cases, while it is difficult to determine the cross-shell matrix elements and single-particle energies using an empirical Hamiltonian by fitting experimental data with a large number of matrix elements. In this paper, we have applied the Gogny-force effective shell-model Hamiltonian to the ${\it p}$- and ${\it sd}$-shell nuclei. The results show good agreements with experimental data and other calculations using empirical Hamiltonians. The experimentally-known neutron drip line of oxygen isotopes and the ground states of typical nuclei $^{10}$B and $^{18}$N can be reproduced, in which the role of three-body force is non-negligible. The Gogny-force derived effective Hamiltonian has also been applied to the cross-shell calculations of the ${\it sd}$-${\it pf}$ shell.

nucl-th↗

arXiv2018

When Renewable Energy Meets Building Thermal Mass: A Real-time Load Management Scheme

We consider the optimal power management in renewable driven smart building MicroGrid under noise corrupted conditions as a stochastic optimization problem. We first propose our user satisfaction and electricity consumption balanced (USECB) profit model as the objective for optimal power management. We then cast the problem in noise corrupted conditions into the class of expectation maximizing in stochastic optimization problem with convex constraints. For this task, we design a Bregemen projection based mirror decent algorithm as an approximation solution to our stochastic optimization problem. Convergence and upper-bound of our algorithm with proof are also provided in our paper. We then conduct a broad type of experiment in our simulation to test the justification of our model as well as the effectiveness of our algorithm.

eess.SY↗

arXiv2016

$\it{Ab}$ $\it{initio}$ nuclear many-body perturbation calculations in the Hartree-Fock basis

Starting from realistic nuclear forces, the chiral N$^3$LO and JISP16, we have applied many-body perturbation theory (MBPT) to the structure of closed-shell nuclei, $^4$He and $^{16}$O. The two-body N$^3$LO interaction is softened by a similarity renormalization group transformation while JISP16 is adopted without renormalization. The MBPT calculations are performed within the Hartree-Fock (HF) bases. The angular momentum coupled scheme is used, which can reduce the computational task. Corrections up to the third order in energy and up to the second order in radius are evaluated. Higher-order corrections in the HF basis are small relative to the leading-order perturbative result. Using the anti-symmetrized Goldstone diagram expansions of the wave function, we directly correct the one-body density for the calculation of the radius, rather than calculate corrections to the occupation propabilities of single-particle orbits as found in other treatments. We compare our results with other methods where available and find good agreement. This supports the conclusion that our methods produce reasonably converged results with these interactions. We also compare our results with experimental data.

nucl-th↗