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Fluid thermodynamics underpins atmospheric dynamics, climate science, industrial applications, and energy systems. However, direct numerical simulations (DNS) of such systems can be computationally prohibitive. To address this, we present a…
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Based on deep neural networks (DNNs), deep learning has been successfully applied to many problems, but its mechanism is still not well understood -- especially the reason why over-parametrized DNNs can generalize. A recent statistical…
Nuclear power plant operators face significant challenges due to unpredictable deviations between offline and online thermal limits, a phenomenon known as thermal limit bias, which leads to conservative design margins, increased fuel costs,…
Advances in machine learning have led to the development of foundation models for atomistic materials chemistry, enabling quantum-accurate descriptions of interatomic forces across chemically diverse compounds at reduced computational cost.…
Theoretical understanding of how deep neural network (DNN) extracts features from input images is still unclear, but it is widely believed that the extraction is performed hierarchically through a process of coarse-graining. It reminds us…
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A goal of supernova remnant (SNR) evolution models is to relate fundamental parameters of a supernova (SN) explosion and progenitor star to the current state of its SNR. The SNR hot plasma is characterized by its observed X-ray spectrum,…
We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression…