相关论文: Stochastic Modelling of Symmetric Positive Definit…

We present a novel framework for the probabilistic modelling of random fourth order material tensor fields, with a focus on tensors that are physically symmetric and positive definite (SPD), of which the elasticity tensor is a prime…

Machine learning models can be used to predict physical quantities like homogenized elasticity stiffness tensors, which must always be symmetric positive definite (SPD) based on conservation arguments. Two datasets of homogenized elasticity…

Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and…

In this paper, we consider higher order paired symmetric tensors and strongly paired symmetric tensors. Elasticity tensors and higher order elasticity tensors in solid mechanics are strongly paired symmetric tensors. A (strongly) paired…

Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…

For most materials, the symmetry group is known a priori and deduced from the realization process. This allows many simplifications for the measurements of the stiffness tensor. We deal here with the case where the symmetry is a priori…

Anisotropic material properties, such as the thermal conductivities of engineering composites, exhibit variability due to inherent material heterogeneity and manufacturing-related uncertainties. Mathematically, these properties are modeled…

The representation theory of tensor functions is essential to constitutive modeling of materials including both mechanical and physical behaviors. Generally, material symmetry is incorporated in the tensor functions through a structural or…

The canonical tensor model (CTM) is a tensor model proposing a classically and quantum mechanically consistent model of gravity, formulated as a first-class constraint system with structural similarities to the ADM formalism of general…

Using electromagnetism to study analogue space-times is tantamount to considering consistency conditions for when a given (meta-)material would provide an analogue space-time model or --- vice versa --- characterizing which given metric…

Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models…

We investigate the implications of a given symmetry of a random microstructure on the obtained effective tensor and its fluctuation in the context of thermal conductivity, and study strategies for enforcing these symmetries in…

Physical symmetries provide a strong inductive bias for constructing functions to analyze data. In particular, this bias may improve robustness, data efficiency, and interpretability of machine learning models. However, building machine…

Recent advances in physics-augmented neural networks have enabled thermodynamically consistent data-driven constitutive modeling of complex inelastic materials. Most existing approaches, however, implicitly adopt a specific thermodynamic…

Third-order tensors are widely used as a mathematical tool for modeling physical properties of media in solid state physics. In most cases, they arise as constitutive tensors of proportionality between basic physics quantities. The…

Heterogeneity of many building materials complicates numerical modelling of structural behaviour. The material randomicity can be manifested by different values of material parameters of each material specimen. To capture inherent…

Symmetric second-order tensors are fundamental in various scientific and engineering domains, as they can represent properties such as material stresses or diffusion processes in brain tissue. In recent years, several approaches have been…

Humans perceive and interact with hundreds of objects every day. In doing so, they need to employ mental models of these objects and often exploit symmetries in the object's shape and appearance in order to learn generalizable and…

The class of Divergence-free symmetric tensors is ubiquitous in Continuum Mechanics. We show its invariance under projective transformations of the independent variables. This action, which preserves the positiveness, extends Sophus Lie's…

When discretizing symmetric stress tensors in variational problems arising in continuum mechanics, one has to choose how to enforce the symmetry of the stress tensor: (i) strongly by requiring the discrete tensors to be pointwise symmetric…