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Property prediction accuracy has long been a key parameter of machine learning in materials informatics. Accordingly, advanced models showing state-of-the-art performance turn into highly parameterized black boxes missing interpretability.…

Rule-based models, e.g., decision trees, are widely used in scenarios demanding high model interpretability for their transparent inner structures and good model expressivity. However, rule-based models are hard to optimize, especially on…

The formulation of rheological constitutive equations -- models that relate internal stresses and deformations in complex fluids -- is a critical step in the engineering of systems involving soft materials. While data-driven models provide…

This paper describes methods for comparative evaluation of the interpretability of models of high dimensional time series data inferred by unsupervised machine learning algorithms. The time series data used in this investigation were logs…

Society's capacity for algorithmic problem-solving has never been greater. Artificial Intelligence is now applied across more domains than ever, a consequence of powerful abstractions, abundant data, and accessible software. As capabilities…

This chapter provides an introduction to data-driven techniques for the development and calibration of closure models for the Reynolds-Averaged Navier--Stokes (RANS) equations. RANS models are the workhorse for engineering applications of…

The ability to interpret Machine Learning (ML) models is becoming increasingly essential. However, despite significant progress in the field, there remains a lack of rigorous characterization regarding the innate interpretability of…

Inspired by the complexity of certain real-world datasets, this article introduces a novel flexible linear spline index regression model. The model posits piecewise linear effects of an index on the response, with continuous changes…

Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…

Scientific measurements are often bottlenecked by suboptimal conditions, whether that be noise, incomplete spatial coverage, or limited resolution, rendering accurate field reconstruction a difficult task. We introduce LatentPDE, a latent…

Due to the increasing availability of large-scale observation and simulation datasets, data-driven representations arise as efficient and relevant computation representations of dynamical systems for a wide range of applications, where…

In many scientific problems such as video surveillance, modern genomics, and finance, data are often collected from diverse measurements across time that exhibit time-dependent heterogeneous properties. Thus, it is important to not only…

The use of machine learning to predict wave dynamics is a topic of growing interest, but commonly-used deep learning approaches suffer from a lack of interpretability of the trained models. Here we present an interpretable machine learning…

The evaluation of the long term stability of a material requires the estimation of its long-time dynamics. For amorphous materials such as structural glasses, it has proven difficult to predict the long-time dynamics starting from static…

The use of kernels for nonlinear prediction is widespread in machine learning. They have been popularized in support vector machines and used in kernel ridge regression, amongst others. Kernel methods share three aspects. First, instead of…

We present a robust framework to perform linear regression with missing entries in the features. By considering an elliptical data distribution, and specifically a multivariate normal model, we are able to conditionally formulate a…

We provide a theoretical perspective on the glass transition in molecular liquids at thermal equilibrium, on the spatially heterogeneous and aging dynamics of disordered materials, and on the rheology of soft glassy materials. We start with…

High-dimensional categorical data arise in diverse scientific domains and are often accompanied by covariates. Latent class regression models are routinely used in such settings, reducing dimensionality by assuming conditional independence…

Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…

When multiple models are considered in regression problems, the model averaging method can be used to weigh and integrate the models. In the present study, we examined how the goodness-of-prediction of the estimator depends on the…