A thermodynamics-constrained ML framework learns robust, consistent constitutive models for inelastic materials from macroscopic stress-strain data and generalizes to unseen paths.
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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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Learning inelastic constitutive models from stress-strain data under hard thermodynamic constraints
A thermodynamics-constrained ML framework learns robust, consistent constitutive models for inelastic materials from macroscopic stress-strain data and generalizes to unseen paths.
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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.