We resort to game theory in order to formulate Data-Driven methods for solid mechanics in which stress and strain players pursue different objectives. The objective of the stress player is to minimize the discrepancy to a material data set, whereas the objective of the strain player is to ensure the admissibility of the mechanical state, in the sense of compatibility and equilibrium. We show that, unlike the cooperative Data-Driven games proposed in the past, the new non-cooperative Data-Driven games identify an effective material law from the data and reduce to conventional displacement boundary-value problems, which facilitates their practical implementation. However, unlike supervised machine learning methods, the proposed non-cooperative Data-Driven games are unsupervised, ansatz-free and parameter-free. In particular, the effective material law is learned from the data directly, without recourse to regression to a parameterized class of functions such as neural networks. We present analysis that elucidates sufficient conditions for convergence of the Data-Driven solutions with respect to the data. We also present selected examples of implementation and application that demonstrate the range and versatility of the approach.

Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains difficult to deal with high-dimensional applications and extrapolative generalization. This paper introduces deep learning techniques under the data-driven framework to address these fundamental issues in nonlinear materials modeling. To this end, an autoencoder neural network architecture is introduced to learn the underlying low-dimensional representation (embedding) of the given material database. The offline trained autoencoder and the discovered embedding space are then incorporated in the online data-driven computation such that the search of optimal material state from database can be performed on a low-dimensional space, aiming to enhance the robustness and predictability with projected material data. To ensure numerical stability and representative constitutive manifold, a convexity-preserving interpolation scheme tailored to the proposed autoencoder-based data-driven solver is proposed for constructing the material state. In this study, the applicability of the proposed approach is demonstrated by modeling nonlinear biological tissues. A parametric study on data noise, data size and sparsity, training initialization, and model architectures, is also conducted to examine the robustness and convergence property of the proposed approach.

Verusen is a leading technology company that uses artificial intelligence to provide visibility, digitization and prediction of materials data and inventory for complex supply chains. Intelligent controls enforce inventory procedures to help prevent future inventory spikes, while predictive capabilities optimize allocation and procurement needs. The result is a data foundation you can trust to move quickly to innovate and support related Industry 4.0 initiatives. Verusen is venture-backed by leading investors from San Francisco to Boston, and is a Signature Company at Georgia Tech's Advanced Technology Development Center (ATDC). Verusen is a portfolio company of SAP.iO.

Verusen is a leading technology company that uses artificial intelligence to provide visibility, digitization and prediction of materials data and inventory for complex supply chains. Intelligent controls enforce inventory procedures to help prevent future inventory spikes, while predictive capabilities optimize allocation and procurement needs. The result is a data foundation you can trust to move quickly to innovate and support related Industry 4.0 initiatives. Verusen is venture-backed by leading investors from San Francisco to Boston, and is a Signature Company at Georgia Tech's Advanced Technology Development Center (ATDC). Verusen is a portfolio company of SAP.iO.

What is Ai? Shake the material data in a grid (forward propagation) Compare the remaining material data with the standard (teacher data) Adjust the fineness of the grid (backpropagation) Repeat until the teacher data is satisfied Finally statistical processing do.

Recent reports, reviews, symposia, and workshops have heralded machine learning (ML) and artificial intelligence (AI) methods as the next scientific paradigm in materials discovery and optimization [1–5]. Applications to materials science have exploded, spanning data analysis, knowledge extraction, and experiment selection [1, 6–9]. The numerous reasons for this trend are related to the omnipresence of ML systems in our everyday lives, the free availability software, and the demonstrated successes in materials discovery and on-the-fly data acquisition inspired by the Materials Genome Initiative (MGI) [1, 10–12]. However, despite their recent prominence, these techniques have been applied in a variety of materials science fields since the early 1960's [13–17]. Some recent examples of the successful implementation of ML to materials science were demonstrated by the high-throughput experimental (HTE, also known as'combinatorial') community. Parallel material synthesis and rapid characterization introduces a critical bottleneck in the analysis of hundreds to thousands of high-quality measurements correlated in composition, processing and microstructure [18–21]. There have been several international efforts to standardize data formats and create data analysis and interpretation tools for large scale data sets [22–24].

Citrine is a company that builds data infrastructure and predictive data analysis software for the materials industry. Machine learning is a key tool in our toolbox. I have had a few professors and students in materials departments ask me (1) how machine learning could help in their research; and (2) how to quickly come up to speed in machine learning without going back to school for a degree in computer science. While a variety of machine learning courses and how-tos exist on the web already (see here, here, or here), none are specific to the field of materials science. I think the best way to master a new concept is by directly applying it, so this tutorial will show you how to build a machine learning-based model of a canonical solid-state materials property: band gap.