Related papers: Mapping Microstructure: Manifold Construction for …
We consider the relation for the stochastic equilibrium states between the reduced system on a random slow manifold and the original system. This provides a theoretical basis for the reduction about sophisti- cated detailed models by the…
The concept of concurrent material and structure optimization aims at alleviating the computational discovery of optimum microstructure configurations in multiphase hierarchical systems, whose macroscale behavior is governed by their…
Nature-inspired stochastic metamaterials with disordered and multiscale architectures have shown great promise towards extraordinary functionalities, including high mechanical resilience, stress modulation and biased stiffness…
For many materials, macroscopic mechanical behavior is determined by an intricate microstructure. Understanding the relation between these two scales helps scientists and engineers design better materials. The relation which maps…
The problem of generating microstructures of complex materials in silico has been approached from various directions including simulation, Markov, deep learning and descriptor-based approaches. This work presents a hybrid method that is…
Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image…
We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only…
Understanding structure-property relations is essential to optimally design materials for specific applications. Two-scale simulations are often employed to analyze the effect of the microstructure on a component's macroscopic properties.…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
Microstructure evolution, which plays a critical role in determining materials properties, is commonly simulated by the high-fidelity but computationally expensive phase-field method. To address this, we approximate microstructure evolution…
The research and development cycle of advanced manufacturing processes traditionally requires a large investment of time and resources. Experiments can be expensive and are hence conducted on relatively small scales. This poses problems for…
In order to optimally design materials, it is crucial to understand the structure-property relations in the material by analyzing the effect of microstructure parameters on the macroscopic properties. In computational homogenization, the…
We consider problems of dimensionality reduction and learning data representations for continuous spaces with two or more independent degrees of freedom. Such problems occur, for example, when observing shapes with several components that…
We focus on the problem of manifold estimation: given a set of observations sampled close to some unknown submanifold $M$, one wants to recover information about the geometry of $M$. Minimax estimators which have been proposed so far all…
Materials performance is deeply linked to their microstructures, which govern key properties such as strength, durability, and fatigue resistance. EBSD is a major technique for characterizing these microstructures, but acquiring large and…
Microgrids are recognized as a relevant tool to absorb decentralized renewable energies in the energy mix. However, the sequential handling of multiple stochastic productions and demands, and of storage, make their management a delicate…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
We study nonparametric regression under covariate shift with structured data, where a small amount of labeled target data is supplemented by a large labeled source dataset. In many real-world settings, the covariates in the target domain…
Understanding the microstructural influence on the failure mechanisms in multi-phase materials calls for the identification of the worst-case scenario. This necessitates a statistical approach. By performing simulations directly based on…
Atomic simulations of material microstructure require significant resources to generate, store and analyze. Here, atomic descriptor functions are proposed as a general latent space to compress atomic microstructure, ideal for use in…