Symmetric convolutional autoencoders preserve manifold parametrization properties, yielding more accurate latent trajectories, lower reconstruction errors, and greater robustness than standard CAEs on 1D advection, Burgers, and Kuramoto-Sivashinsky test cases.
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A neural constitutive model with hard thermodynamic constraints learns inelastic stress-strain behavior from data and predicts unseen cyclic paths, including granular-media hysteresis.
The Transformer is interpreted as discretization of a structured integro-differential equation in continuous domains for tokens and features, unifying attention, feedforward, and normalization via operator and variational views.
A roadmap is outlined for digital twins in coronary artery disease that combine mathematical models with patient data through assimilation and probabilistic models to estimate wall shear stress and support clinical decisions for preventing infarcts.
citing papers explorer
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Convolutional Symmetric AutoEncoders: enhancing latent stability via differential geometry
Symmetric convolutional autoencoders preserve manifold parametrization properties, yielding more accurate latent trajectories, lower reconstruction errors, and greater robustness than standard CAEs on 1D advection, Burgers, and Kuramoto-Sivashinsky test cases.
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Learning inelastic constitutive models from stress-strain data under hard thermodynamic constraints
A neural constitutive model with hard thermodynamic constraints learns inelastic stress-strain behavior from data and predicts unseen cyclic paths, including granular-media hysteresis.
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A Mathematical Explanation of Transformers
The Transformer is interpreted as discretization of a structured integro-differential equation in continuous domains for tokens and features, unifying attention, feedforward, and normalization via operator and variational views.
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Digital Twins in Coronary Artery Disease: A Mathematical Roadmap
A roadmap is outlined for digital twins in coronary artery disease that combine mathematical models with patient data through assimilation and probabilistic models to estimate wall shear stress and support clinical decisions for preventing infarcts.