Related papers: Learning Markovian Homogenized Models in Viscoelas…

In this work we employ data-driven homogenization approaches to predict the particular mechanical evolution of polycrystalline aggregates with tens of individual crystals. In these oligocrystals the differences in stress response due to…

Heterogeneous porous materials play a crucial role in various engineering systems. Microstructure characterization and reconstruction provide effective means for modeling these materials, which are critical for conducting physical property…

We propose a computational framework, Hetero-EUCLID, for segmentation and parameter identification to characterize the full hyperelastic behavior of all constituents of a heterogeneous material. In this work, we leverage the Bayesian-EUCLID…

Computational imaging has been revolutionized by compressed sensing algorithms, which offer guaranteed uniqueness, convergence, and stability properties. Model-based deep learning methods that combine imaging physics with learned…

Deep learning algorithms, especially Transformer-based models, have achieved significant performance by capturing long-range dependencies and historical information. However, the power of convolution has not been fully investigated.…

In this paper we present a fully-coupled, two-scale homogenization method for dynamic loading in the spirit of FE$^2$ methods. The framework considers the balance of linear momentum including inertia at the microscale to capture possible…

We introduce a generalized machine learning framework to probabilistically parameterize upper-scale models in the form of nonlinear PDEs consistent with a continuum theory, based on coarse-grained atomistic simulation data of mechanical…

Homogenization is a fundamental tool for studying multiscale physical phenomena. Traditional numerical homogenization methods, heavily reliant on finite element analysis, demand significant computational resources, especially for complex…

Direct prediction of material properties from microstructures through statistical models has shown to be a potential approach to accelerating computational material design with large design spaces. However, statistical modeling of highly…

Micromorphic theories became an established tool to model size effects in materials like dispersion, localization phenomena or (apparently) size dependent properties. However, the formulation of adequate constitutive relations with its…

We present stochastic homogenization results for viscous Hamilton-Jacobi equations using a new argument which is based only on the subadditive structure of maximal subsolutions (solutions of the "metric problem"). This permits us to give…

Real-world datasets are inherently heterogeneous, yet how per-class structural differences and sampling imbalance shape the training dynamics of diffusion models-and potentially exacerbate disparities-remains poorly understood. While models…

Many material response functions depend strongly on microstructure, such as inhomogeneities in phase or orientation. Homogenization presents the task of predicting the mean response of a sample of the microstructure to external loading for…

Model merging has attracted significant attention as a powerful paradigm for model reuse, facilitating the integration of task-specific models into a singular, versatile framework endowed with multifarious capabilities. Previous studies,…

Mesoscale behavior of polymers is frequently described by universal laws. This physical property motivates us to propose a new modeling concept, grouping polymers into classes with a common long-wavelength representation. In the same class…

The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at…

A homogeneous mass-fragmentation, as it has been defined in \cite{RFC}, describes the evolution of the collection of masses of fragments of an object which breaks down into pieces as time passes. Here, we show that this model can be…

We propose a neural network-based approach to the homogenization of multiscale problems. The proposed method uses a derivative-free formulation of a training loss, which incorporates Brownian walkers to find the macroscopic description of a…

Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian…

The homogenization of one-dimensional acoustic or elastic structures of finite extent is considered. A new homogenization method based on transfer matrices is derived. The new homogenization method may account for variable cross sectional…