arXiv subjects

Fumihiro Imoto

Publications and source records attributed to Fumihiro Imoto.

7 recordsLinked to original sources

arXiv2026

Computing high-order mixed derivatives in physics-informed neural networks using multi-index Bell polynomials

Physics-informed neural networks for high-order partial differential equations require mixed input derivatives and their gradients with respect to the network parameters. Standard implementations obtain an order-$K$ derivative by repeated automatic differentiation. We instead organize the forward recursion of the multivariate Faà di Bruno formula and its explicit backpropagation over a prescribed downward-closed set of multi-indices, with the Bell-polynomial convolutions tabulated once. The forward pass carries only the derivatives the differential operator requires. The backward pass propagates gradients from losses formed from any subset of them, including nonlinear products and coupled fields. Both recursions are exact up to roundoff and avoid nested computational graphs. An independent Taylor-jet implementation, symbolic checks of the test problems, and finite differences verify derivatives and loss gradients through order seven. On one CPU core, the method evaluates 330 mixed derivatives with respect to four inputs through order seven and the corresponding loss gradient without the memory failures observed for several nested implementations. Numerical tests include third-, fifth-, and seventh-order dispersive equations, incompressible flow, and a manufactured five-field electrohydrodynamic system. The seventh-order Zakharov-Kuznetsov test in $3+1$ dimensions has a relative solution error of $6\times10^{-4}$.

physics.comp-ph↗

arXiv2026

Self-consistent orbital-free nuclear density functional theory with a physics-constrained learned nonlocal kinetic energy functional

Nonlocal kinetic-energy density functionals (KEDFs) can encode nuclear shell structure in orbital-free density functional theory (OFDFT), but self-consistency requires accurate functional derivatives and a stable solution of the Euler equation. We construct a density-dependent-kernel KEDF whose correction is learned from Kohn-Sham (KS) reference data. Linearity in the kernel shape yields analytic Euler--Lagrange (EL) responses. The fit uses exact energy-matching equalities and soft quadratic inequality penalties for violations of prescribed tail-response and selected-path energy-rise margins, evaluated by an active-set repeated penalized least-squares iteration. We formulate the radial EL equation as the rearranged one-orbital eigenproblem. In a constant-$k_F$ $^{16}$O benchmark it converges without density mixing and agrees with imaginary-time evolution (ITE) to sub-keV energy. Adaptive-step ITE gives final species EL residuals of at most 0.07 MeV in the reported calculations, and rearranged diagonalization reaches the same stationary densities. For spherical $N=Z$ systems without spin--orbit or Coulomb terms, nucleus-specific fits for $A=16$ to $140$ reproduce shell patterns and radii. A correction trained on three nuclei transfers the shell pattern and radius, but not the absolute energy, to a previously unseen $A=140$ system.

physics.comp-ph↗

arXiv2026

Analytic structure and asymptotic analysis of screened second-order exchange in the uniform electron gas

The uniform electron gas underlies the local-density approximation of density-functional theory, yet correlation contributions beyond the random-phase approximation (RPA) are known mainly through high-dimensional numerical evaluation, not in closed form. We study the screened second-order exchange (``kite'') diagram, in which one interaction line carries a frequency-dependent screened interaction. For a single-pole reference model with a momentum-independent screening scale, we perform the frequency and loop integrals analytically and reduce the diagram to a one-dimensional integral, whose static limit reproduces in closed form the exact Onsager-Mittag-Stephen second-order exchange, fixing the absolute energy scale with no free parameter. A Mellin-Barnes analysis with rigorous remainder estimates gives the behaviour in both screening limits. Using the linearity of the reduced functional in the screened line, we replace the bare interaction by the physical static RPA (Lindhard) screening, so that the density enters only through the Thomas-Fermi scale rather than an assumed map, and its dependence is set by the endpoints of a single geometric kernel with exponents fixed by the diagram. We prove that this kernel is even and that its quadratic coefficient vanishes identically, so the high-density expansion contains no half-integer power; this justifies the integer-power-times-logarithm form used in recent numerical work and identifies a half-integer term there as an interpolation artifact. The construction extends to arbitrary spin polarization, the bare diagram being polarization-independent, and a dynamical adiabatic-connection evaluation normalized only to that limit reproduces the numerically evaluated kite for both the unpolarized and fully polarized gas, including the low-density sign change. The result is a controllable analytic reference for screened exchange beyond the RPA.

physics.comp-ph↗

arXiv2026

Semilocal exchange functionals from the exact-exchange condition for the hydrogen atom: Hydrogenic exactness and recovery of Rydberg-like bound states

In semilocal density functionals the exchange potential decays too rapidly outside atoms and molecules and lacks the correct $-1/r$ tail; as a consequence, functionals from PBE to modern meta-GGAs such as SCAN support no bound Rydberg-like state of an atom. We revisit the gradient-corrected exchange functional that Gill and Pople (GP93) constructed to reproduce the exact exchange potential of the hydrogen atom, solve their equation as an inverse problem, and use the resulting enhancement factor -- the GP93 factor -- as a tail-generating ingredient of a switched semilocal functional. The GP93 factor is exact on the hydrogen $1s$ density and, by uniform coordinate scaling, on hydrogenic $1s$ ions, where it yields the eigenvalue $-Z^2/2$ exactly (hydrogenic exactness). Its large-gradient growth has the hydrogen-exact form $O[s(\ln s)^{2/3}]$, distinct from the $s\ln s$ form of Armiento and Kümmel. The factor is combined with a kinetic-energy-density indicator so that its divergent branch acts only in one-electron-like regions; the GP93 ingredient is nonempirical, while a few switching parameters are calibrated to balance tail recovery against self-consistent-field stability. The resulting functional produces Rydberg-like series of bound virtual Kohn--Sham states in systems whose outermost shell is a one-electron-like $s$ shell -- all-electron H and He, and Li, Na, and K with large-core pseudopotentials -- and moves the highest-occupied eigenvalue toward the experimental ionization energy. For $p$-shell atoms (Ne, Ar) the switch closes, so the domain of applicability is fixed by design. Fixed-density tests indicate that a reduced-Laplacian switch distinguishes atomic tails from covalent bond centers, and that a density-only kinetic-energy functional renders the entire switch orbital-independent, so that no generalized Kohn--Sham solver is required.

physics.comp-ph↗

arXiv2026

Unified description of cuprate superconductors by fractionalized electrons emerging from integrated analyses of photoemission spectra and quasiparticle interference

Electronic structure of high-temperature superconducting cuprates is studied by analyzing experimental data independently obtained from two complementary spectroscopies, one, quasiparticle interference (QPI) measured by scanning-tunneling microscopy and the other, angle-resolved photoemission spectroscopy (ARPES) and by combining these two sets of data in a unified theoretical analysis. Through explicit calculations of experimentally measurable quantities, we show that a simple two-component fermion model (TCFM) representing electron fractionalization succeeds in reproducing various detailed features of these experimental data: ARPES and QPI data are concomitantly reproduced by the TCFM in full energy and momentum spaces. The measured QPI pattern reveals a signature characteristic of the TCFM, distinct from the conventional single-component prediction, supporting the validity of the electron fractionalization in the cuprate. The integrated analysis also solves the puzzles of ARPES and QPI data that are seemingly inconsistent with each other. The overall success of the TCFM offers a comprehensive understanding of the electronic structure of the cuprates. We further predict that a characteristic QPI pattern should appear in the unoccupied high-energy part if the fractionalization is at work. We propose that integrated-spectroscopy analyses offer a promising way to explore challenging issues of strongly correlated electron systems.

cond-mat.str-el↗

arXiv2021

Order-$N$ orbital-free density-functional calculations with machine learning of functional derivatives for semiconductors and metals

Orbital-free density functional theory (OFDFT) offers a challenging way of electronic-structure calculations scaled as $\mathcal{O}(N)$ computation for system size $N$. We here develop a scheme of the OFDFT calculations based on the accurate and transferrable kinetic-energy density functional (KEDF) which is created in an unprecedented way using appropriately constructed neural network (NN). We show that our OFDFT scheme reproduces the electron density obtained in the state-of-the-art DFT calculations and then provides accurate structural properties of 24 different systems, ranging from atoms, molecules, metals, semiconductors and an ionic material. The accuracy and the transferability of our KEDF is achieved by our NN training system in which the kinetic-energy functional derivative (KEFD) at each real-space grid point is used. The choice of the KEFD as a set of training data is essentially important, because first it appears directly in the Euler equation which one should solve and second, its learning assists in reproducing the physical quantity expressed as the first derivative of the total energy. More generally, the present development of KEDF $T[ρ]$ is in the line of systematic expansion in terms of the functional derivatives $δ^{\ell_1} T/δρ^{\ell_1}$ through progressive increase of $\ell_1$. The present numerical success demonstrates the validity of this approach. The computational cost of the present OFDFT scheme indeed shows the $\mathcal{O}(N)$ scaling, as is evidenced by the computations of the semiconductor SiC used in power electronics.

physics.comp-ph↗

arXiv2016

Microscopic mechanisms of initial formation process of graphene on SiC(0001) surfaces

We report total-energy calculations based on the density-functional theory that clarify microscopic mechanisms of initial stage of graphene formation on the SiC(0001) surface. We explore favorable reactions for desorption of either Si or C atoms from the stepped surface by determining the desorption and the subsequent migration pathways and calculating the corresponding energy barriers for the first time. We find that the energy barrier for the desorption of an Si atom at the step edge and the subsequent migration toward stable terrace sites are lower than that of a C atom by 0.75 eV, indicative of the selective desorption of Si from the SiC surface. We also find that the subsequent Si desorption is an exothermic reaction. This exothermicity comes from the energy gain due to the bond formation of C atoms being left near the step edges. This is certainly a seed of graphene flakes.

cond-mat.mtrl-sci↗