Machine learning for the identification of phase transitions in interacting agent-based systems: A Desai-Zwanzig example.

Deriving closed-form analytical expressions for reduced-order models, and judiciously choosing the closures leading to them, has long been the strategy of choice for studying phase- and noise-induced transitions for agent-based models (ABMs). In this paper, we propose a data-driven framework that pinpoints phase transitions for an ABM-the Desai-Zwanzig model-in its mean-field limit, using a smaller number of variables than traditional closed-form models. To this end, we use the manifold learning algorithm Diffusion Maps to identify a parsimonious set of data-driven latent variables, and we show that they are in one-to-one correspondence with the expected theoretical order parameter of the ABM.

Revealing the hidden structure of disordered materials by parameterizing their local structural manifold.

Durable interest in developing a framework for the detailed structure of glassy materials has produced numerous structural descriptors that trade off between general applicability and interpretability. However, none approach the combination of simplicity and wide-ranging predictive power of the lattice-grain-defect framework for crystalline materials. Working from the hypothesis that the local atomic environments of a glassy material are constrained by enthalpy minimization to a low-dimensional manifold in atomic coordinate space, we develop a generalized distance function, the Gaussian Integral Inner Product (GIIP) distance, in connection with agglomerative clustering and diffusion maps, to parameterize that manifold.

Effect of Human Head Shape on the Risk of Traumatic Brain Injury: A Gaussian Process Regression-Based Machine Learning Approach.

Introduction: Computational head injury models are promising tools for understanding and predicting traumatic brain injuries. However, most available head injury models are "average" models that employ a single set of head geometry (e.g.

Data-driven Uncertainty Quantification in Computational Human Head Models.

Computational models of the human head are promising tools for estimating the impact-induced response of the brain, and thus play an important role in the prediction of traumatic brain injury. The basic constituents of these models (i.e.