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It is important to develop sustainable processes in materials science and manufacturing that are environmentally friendly. AI can play a significant role in decision support here as evident from our earlier research leading to tools…
In homogenization theory, mathematical models at the macro level are constructed based on the solution of auxiliary cell problems at the micro level within a single periodicity cell. These problems are formulated using asymptotic expansions…
Modeling the dynamics of non-stationary stochastic systems requires balancing the representational power of deep learning with the mathematical transparency of classical models. While classical Markov transition operators provide explicit,…
Continual learning is inherently a constrained learning problem. The goal is to learn a predictor under a no-forgetting requirement. Although several prior studies formulate it as such, they do not solve the constrained problem explicitly.…
Advanced microscopy and/or spectroscopy tools play indispensable role in nanoscience and nanotechnology research, as it provides rich information about the growth mechanism, chemical compositions, crystallography, and other important…
The use of machine learning techniques to homogenize the effective behavior of arbitrary microstructures has been shown to be not only efficient but also accurate. In a recent work, we demonstrated how to combine state-of-the-art…
We study the problem of learning feature representations from a pair of random variables, where we focus on the representations that are induced by their dependence. We provide sufficient and necessary conditions for such dependence induced…
The problem of high-dimensional and large-scale representation of visual data is addressed from an unsupervised learning perspective. The emphasis is put on discrete representations, where the description length can be measured in bits and…
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…
The influence of the microstructure of a polycrystalline material on its macroscopic deformation response is still one of the major problems in materials engineering. For materials characterized by elastic-plastic deformation responses,…
We use machine learning (ML) to infer stress and plastic flow rules using data from repre- sentative polycrystalline simulations. In particular, we use so-called deep (multilayer) neural networks (NN) to represent the two response…
Tissue engineering aims to grow artificial tissues \emph{in vitro} to replace those in the body that have been damaged through age, trauma or disease. A recent approach to engineer artificial cartilage involves seeding cells within a…
The morphology of nanostructured materials exhibiting a polydisperse porous space, such as aerogels, is very open porous and fine grained. Therefore, a simulation of the deformation of a large aerogel structure resolving the nanostructure…
The optimization along the chain processing-structure-properties-performance is one of the core objectives in data-driven materials science. In this sense, processes are supposed to manufacture workpieces with targeted material…
Partially observed control problems are a challenging aspect of reinforcement learning. We extend two related, model-free algorithms for continuous control -- deterministic policy gradient and stochastic value gradient -- to solve partially…
In recent years, there has been a growing interest in accelerated materials innovation in the context of the process-structure-property chain. In this regard, it is essential to take into account manufacturing processes and tailor materials…
We introduce a novel computational framework for the multiscale simulation of higher-order continua that allows for the consideration of first-, second- and third- order effects at both micro- and macro-level. In line with classical…
The automated construction of coarse-grained models represents a pivotal component in computer simulation of physical systems and is a key enabler in various analysis and design tasks related to uncertainty quantification. Pertinent methods…
In this work, a two-dimensional time-fractional subdiffusion model is developed to investigate the underlying transport phenomena evolving in a binary medium comprised of two sub-domains occupied by homogeneous material. We utilise an…
Neural network based models have emerged as a powerful tool in multiscale modeling of materials. One promising approach is to use a neural network based model, trained using data generated from repeated solution of an expensive small scale…