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PINNs for Electromagnetic Wave Propagation
Authors:
Nilufer K. Bulut
Abstract:
Physics-Informed Neural Networks (PINNs) solve physical systems by incorporating governing partial differential equations directly into neural network training. In electromagnetism, where well-established methodologies such as FDTD and FEM already exist, new methodologies are expected to provide clear advantages to be accepted. Despite their mesh-free nature and applicability to inverse problems,…
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Physics-Informed Neural Networks (PINNs) solve physical systems by incorporating governing partial differential equations directly into neural network training. In electromagnetism, where well-established methodologies such as FDTD and FEM already exist, new methodologies are expected to provide clear advantages to be accepted. Despite their mesh-free nature and applicability to inverse problems, PINNs can exhibit deficiencies in accuracy and energy metrics compared to FDTD. This study demonstrates that hybrid training strategies can bring PINNs closer to FDTD-level accuracy and energy consistency. A hybrid methodology addressing common challenges in wave propagation is presented. Causality collapse in time-dependent PINN training is addressed via time marching and causality-aware weighting. To mitigate discontinuities introduced by time marching, a two stage interface continuity loss is applied. To suppress cumulative energy drift in electromagnetic waves, a local Poynting-based regularizer is developed. In the developed PINN model, high field accuracy is achieved with an average 0.09% NRMSE and 1.01% $L^2$ error over time. Energy conservation is achieved with only a 0.02% relative energy mismatch in the 2D PEC cavity scenario. Training is performed without labeled field data, using only physics-based residual losses; FDTD is used solely for post-training evaluation. The results demonstrate that PINNs can achieve competitive results with FDTD in canonical electromagnetic examples and are a viable alternative.
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Submitted 12 February, 2026; v1 submitted 29 December, 2025;
originally announced December 2025.
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TF-GNN: Graph Neural Networks in TensorFlow
Authors:
Oleksandr Ferludin,
Arno Eigenwillig,
Martin Blais,
Dustin Zelle,
Jan Pfeifer,
Alvaro Sanchez-Gonzalez,
Wai Lok Sibon Li,
Sami Abu-El-Haija,
Peter Battaglia,
Neslihan Bulut,
Jonathan Halcrow,
Filipe Miguel Gonçalves de Almeida,
Pedro Gonnet,
Liangze Jiang,
Parth Kothari,
Silvio Lattanzi,
André Linhares,
Brandon Mayer,
Vahab Mirrokni,
John Palowitch,
Mihir Paradkar,
Jennifer She,
Anton Tsitsulin,
Kevin Villela,
Lisa Wang
, et al. (2 additional authors not shown)
Abstract:
TensorFlow-GNN (TF-GNN) is a scalable library for Graph Neural Networks in TensorFlow. It is designed from the bottom up to support the kinds of rich heterogeneous graph data that occurs in today's information ecosystems. In addition to enabling machine learning researchers and advanced developers, TF-GNN offers low-code solutions to empower the broader developer community in graph learning. Many…
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TensorFlow-GNN (TF-GNN) is a scalable library for Graph Neural Networks in TensorFlow. It is designed from the bottom up to support the kinds of rich heterogeneous graph data that occurs in today's information ecosystems. In addition to enabling machine learning researchers and advanced developers, TF-GNN offers low-code solutions to empower the broader developer community in graph learning. Many production models at Google use TF-GNN, and it has been recently released as an open source project. In this paper we describe the TF-GNN data model, its Keras message passing API, and relevant capabilities such as graph sampling and distributed training.
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Submitted 23 July, 2023; v1 submitted 7 July, 2022;
originally announced July 2022.
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Hyperfine excitation of SH$^+$ by H
Authors:
François Lique,
Alexandre Zanchet,
Niyazi Bulut,
Javier R. Goicoechea,
Octavio Roncero
Abstract:
SH$^+$ is a surprisingly widespread molecular ion in diffuse interstellar clouds. There, it plays an important role triggering the sulfur chemistry. In addition, SH$^+$ emission lines have been detected at the UV-illuminated edges of dense molecular clouds, \mbox{so-called} photo-dissociation regions (PDRs), and toward high-mass protostars. An accurate determination of the SH$^+$ abundance and of…
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SH$^+$ is a surprisingly widespread molecular ion in diffuse interstellar clouds. There, it plays an important role triggering the sulfur chemistry. In addition, SH$^+$ emission lines have been detected at the UV-illuminated edges of dense molecular clouds, \mbox{so-called} photo-dissociation regions (PDRs), and toward high-mass protostars. An accurate determination of the SH$^+$ abundance and of the physical conditions prevailing in these energetic environments relies on knowing the rate coefficients of inelastic collisions between SH$^+$ molecules and hydrogen atoms, hydrogen molecules, and electrons. In this paper, we derive SH$^+$--H fine and hyperfine-resolved rate coefficients from the recent quantum calculations for the SH$^+$--H collisions, including inelastic, exchange and reactive processes. The method used is based on the infinite order sudden approach. State-to-state rate coefficients between the first 31 fine levels and 61 hyperfine levels of SH$^+$ were obtained for temperatures ranging from 10 to 1000 K. Fine structure-resolved rate coefficients present a strong propensity rule in favour of $Δj = ΔN$ transitions. The $Δj = ΔF$ propensity rule is observed for the hyperfine transitions. {The new rate coefficients will help significantly in the interpretation of SH$^+$ spectra from PDRs and UV-irradiated shocks where the abundance of hydrogen atoms with respect to hydrogen molecules can be significant.
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Submitted 26 April, 2020;
originally announced April 2020.
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Magnetic mechanism for the biological functioning of hemoglobin
Authors:
Selma Mayda,
Zafer Kandemir,
Nejat Bulut,
Sadamichi Maekawa
Abstract:
The role of magnetism in the biological functioning of hemoglobin has been debated since its discovery by Pauling and Coryell in 1936. The hemoglobin molecule contains four heme groups each having a porphyrin layer with a Fe ion at the center. Here, we present combined density-functional theory and quantum Monte Carlo calculations for an effective model of Fe in a heme cluster. In comparison with…
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The role of magnetism in the biological functioning of hemoglobin has been debated since its discovery by Pauling and Coryell in 1936. The hemoglobin molecule contains four heme groups each having a porphyrin layer with a Fe ion at the center. Here, we present combined density-functional theory and quantum Monte Carlo calculations for an effective model of Fe in a heme cluster. In comparison with these calculations, we analyze the experimental data on human adult hemoglobin (HbA) from the magnetic susceptibility, Mossbauer and magnetic circular dichroism (MCD) measurements. In both the deoxygenated (deoxy) and the oxygenated (oxy) cases, we show that local magnetic moments develop in the porphyrin layer with antiferromagnetic coupling to the Fe moment. Our calculations reproduce the magnetic susceptibility measurements on deoxy and oxy-HbA. For deoxy-HbA, we show that the anomalous MCD signal in the UV region is an experimental evidence for the presence of antiferromagnetic Fe-porphyrin correlations. The various important properties of hemoglobin are explained based on the antiferromagnetic correlations including the Bohr effect and cooperativity. This analysis shows that magnetism is involved in a fundamental way in the functioning of hemoglobin.
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Submitted 13 November, 2019;
originally announced November 2019.
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Electronic structure and correlations of vitamin B12 studied within the Haldane-Anderson impurity model
Authors:
Zafer Kandemir,
Selma Mayda,
Nejat Bulut
Abstract:
We study the electronic structure and correlations of vitamin B12 (cyanocobalamine) by using the framework of the multi-orbital single-impurity Haldane-Anderson model of a transition-metal impurity in a semiconductor host. The parameters of the effective Haldane-Anderson model are obtained within the Hartree-Fock (HF) approximation. The quantum Monte Carlo (QMC) technique is then used to calculate…
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We study the electronic structure and correlations of vitamin B12 (cyanocobalamine) by using the framework of the multi-orbital single-impurity Haldane-Anderson model of a transition-metal impurity in a semiconductor host. The parameters of the effective Haldane-Anderson model are obtained within the Hartree-Fock (HF) approximation. The quantum Monte Carlo (QMC) technique is then used to calculate the one-electron and magnetic correlation functions of this effective model. We observe that new states form inside the semiconductor gap found by HF due to the intra-orbital Coulomb interaction at the impurity 3d orbitals. In particular, the lowest unoccupied states correspond to an impurity bound state, which consists of states from mainly the CN axial ligand and the corring ring as well as the Co e_g-like orbitals. We also observe that the Co(3d) orbitals can develop antiferromagnetic correlations with the surrounding atoms depending on the filling of the impurity bound states. In addition, we make comparisons of the HF+QMC data with the density functional theory calculations. We also discuss the photoabsorption spectrum of cyanocobalamine.
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Submitted 26 August, 2015; v1 submitted 12 August, 2015;
originally announced August 2015.
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OH+ in astrophysical media: state-to-state formation rates, Einstein coefficients and inelastic collision rates with He
Authors:
S. Gomez-Carrasco,
B. Godard,
F. Lique,
N. Bulut,
J. Klos,
O. Roncero,
A. Aguado,
F. J. Aoiz,
J. F. Castillo,
J. R. Goicoechea,
M. Etxaluze,
J. Cernicharo
Abstract:
The rate constants required to model the OH$^+$ observations in different regions of the interstellar medium have been determined using state of the art quantum methods.
First, state-to-state rate constants for the H$_2(v=0,J=0,1)$+ O$^+$($^4S$) $\rightarrow$ H + OH$^+(X ^3Σ^-, v', N)$ reaction have been obtained using a quantum wave packet method. The calculations have been compared with time-i…
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The rate constants required to model the OH$^+$ observations in different regions of the interstellar medium have been determined using state of the art quantum methods.
First, state-to-state rate constants for the H$_2(v=0,J=0,1)$+ O$^+$($^4S$) $\rightarrow$ H + OH$^+(X ^3Σ^-, v', N)$ reaction have been obtained using a quantum wave packet method. The calculations have been compared with time-independent results to asses the accuracy of reaction probabilities at collision energies of about 1 meV. The good agreement between the simulations and the existing experimental cross sections in the $0.01-$1 eV energy range shows the quality of the results.
The calculated state-to-state rate constants have been fitted to an analytical form. Second, the Einstein coefficients of OH$^+$ have been obtained for all astronomically significant ro-vibrational bands involving the $X^3Σ^-$ and/or $A^3Π$ electronic states.
For this purpose the potential energy curves and electric dipole transition moments for seven electronic states of OH$^+$ are calculated with {\it ab initio} methods at the highest level and including spin-orbit terms, and the rovibrational levels have been calculated including the empirical spin-rotation and spin-spin terms. Third, the state-to-state rate constants for inelastic collisions between He and OH$^+(X ^3Σ^-)$ have been calculated using a time-independent close coupling method on a new potential energy surface. All these rates have been implemented in detailed chemical and radiative transfer models. Applications of these models to various astronomical sources show that inelastic collisions dominate the excitation of the rotational levels of OH$^+$. In the models considered the excitation resulting from the chemical formation of OH$^+$ increases the line fluxes by about 10 % or less depending on the density of the gas.
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Submitted 16 May, 2014;
originally announced May 2014.