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We introduce the Differentiable Weightless Neural Network (DWN), a model based on interconnected lookup tables. Training of DWNs is enabled by a novel Extended Finite Difference technique for approximate differentiation of binary values. We…
Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a…
Solving high-dimensional partial differential equations (PDEs) efficiently requires handling multi-scale features across varying resolutions. To address this challenge, we present the Multiwavelet-based Multigrid Neural Operator (M2NO), a…
Modern microelectronic devices are composed of interfaces between a large number of materials, many of which are in amorphous or polycrystalline phases. Modeling such non-crystalline materials using first-principles methods such as density…
Classical density functional theory (cDFT) provides a systematic approach to predict the structure and thermodynamic properties of chemical systems through the single-molecule density profiles. Whereas the statistical-mechanical framework…
Density functional theory underlies the most successful and widely used numerical methods for electronic structure prediction of solids. However, it has the fundamental shortcoming that the universal density functional is unknown. In…
Density-potential functional theory (DPFT) is an alternative formulation of orbital-free density functional theory that may be suitable for modeling the electronic structure of large systems. To date, DPFT has been applied mainly to quantum…
In this paper, we develop a Neural Likelihood Estimator and apply it to analyse real gravitational-wave (GW) data for the first time. We assess the usability of neural likelihood for GW parameter estimation and report the parameter space…
Gravitational waves (GWs) from binary neutron stars (BNSs) offer valuable understanding of the nature of compact objects and hadronic matter, and the science potential will be greatly enhanced by the third-generation (3G) GW detectors,…
Faithful representations of atomic environments and general models for regression can be harnessed to learn electron densities that are close to the ground state. One of the applications of data-derived electron densities is to orbital-free…
During oscillations of cosmology inflation around the minimum of a cuspy potential after inflation, the existence of extra high frequency gravitational waves (HFGWs) (GHz) has been proven effectively recently. Based on the electromagnetic…
The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly non-uniformly distributed, it is challenging to use…
In this paper, we develop a physics-informed deep operator learning framework for solving multi-term time-fractional mixed diffusion-wave equations (TFMDWEs). We begin by deriving an $L_2$ approximation, which achieves first-order accuracy…
Fourier Neural Operators (FNOs) have demonstrated exceptional accuracy in mapping functional spaces by leveraging Fourier transforms to establish a connection with underlying physical principles. However, their opaque inner workings often…
The $GW$ approach of many-body perturbation theory (MBPT) has become a common tool for calculating the electronic structure of materials. However, with increasing number of published results, discrepancies between the values obtained by…
Hybrid-Vlasov simulations resolve ion-kinetic effects in the solar wind-magnetosphere interaction, but even 5D (2D + 3V) configurations are computationally expensive. We show that graph-based machine learning emulators can learn the…
This paper introduces an operator-based neural network, the mirror-padded Fourier neural operator (MFNO), designed to learn the dynamics of stochastic systems. MFNO extends the standard Fourier neural operator (FNO) by incorporating mirror…
In the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning enables solving partial differential equations, including wave equations, by applying…
We present a $GW$ space-time algorithm for periodic systems in a Gaussian basis including spin-orbit coupling. We employ lattice summation to compute the irreducible density response and the self-energy, while we employ $k$-point sampling…
Deep learning-based surrogate models have been widely applied in geological carbon storage (GCS) problems to accelerate the prediction of reservoir pressure and CO2 plume migration. Large amounts of data from physics-based numerical…