Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on constrained Gaussian processes and leverage it to build a computationally and data efficient algorithm for state and parameter inference. In an extensive set of experiments, our approach outperforms the current state of the art for parameter inference both in terms of accuracy and computational cost. It also shows promising results for the much more challenging problem of model selection.

Recently there has been a significant interest in learning disentangled representations, as they promise increased interpretability, generalization to unseen scenarios and faster learning on downstream tasks. In this paper, we investigate the usefulness of different notions of disentanglement for improving the fairness of downstream prediction tasks based on representations. We consider the setting where the goal is to predict a target variable based on the learned representation of high-dimensional observations (such as images) that depend on both the target variable and an unobserved sensitive variable. We show that in this setting both the optimal and empirical predictions can be unfair, even if the target variable and the sensitive variable are independent. Analyzing more than 12 600 trained representations of state-of-the-art disentangled models, we observe that various disentanglement scores are consistently correlated with increased fairness, suggesting that disentanglement may be a useful property to encourage fairness when sensitive variables are not observed.Preprint. Under review.

Summary The distribution of forces on the surface of complex, deforming geometries is an invaluable output of flow simulations. One particular example of such geometries involves self‐propelled swimmers. Surface forces can provide significant information about the flow field sensed by the swimmers and are difficult to obtain experimentally. At the same time, simulations of flow around complex, deforming shapes can be computationally prohibitive when body‐fitted grids are used. Alternatively, such simulations may use penalization techniques. Penalization methods rely on simple Cartesian grids to discretize the governing equations, which are enhanced by a penalty term to account for the boundary conditions. They have been shown to provide a robust estimation of mean quantities, such as drag and propulsion velocity, but the computation of surface force distribution remains a challenge. We present a method for determining flow‐induced forces on the surface of both rigid and deforming bodies, in simulations using remeshed vortex methods and Brinkman penalization. The pressure field is recovered from the velocity by solving a Poisson's equation using the Green's function approach, augmented with a fast multipole expansion and a tree‐code algorithm. The viscous forces are determined by evaluating the strain‐rate tensor on the surface of deforming bodies, and on a “lifted” surface in simulations involving rigid objects. We present results for benchmark flows demonstrating that we can obtain an accurate distribution of flow‐induced surface forces. The capabilities of our method are demonstrated using simulations of self‐propelled swimmers, where we obtain the pressure and shear distribution on their deforming surfaces.

The most common reason for spinal surgery in elderly patients is lumbar spinal stenosis (LSS). For LSS, treatment decisions based on clinical and radiological information as well as personal experience of the surgeon shows large variance. Thus a standardized support system is of high value for a more objective and reproducible decision. In this work, we develop an automated algorithm to localize the stenosis causing the symptoms of the patient in magnetic resonance imaging (MRI). With 22 MRI features of each of five spinal levels of 321 patients, we show it is possible to predict the location of lesion triggering the symptoms. To support this hypothesis, we conduct an automated analysis of labeled and unlabeled MRI scans extracted from 788 patients. We confirm quantitatively the importance of radiological information and provide an algorithmic pipeline for working with raw MRI scans.

Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on constrained Gaussian processes and leverage it to build a computationally and data efficient algorithm for state and parameter inference. In an extensive set of experiments, our approach outperforms the current state of the art for parameter inference both in terms of accuracy and computational cost. It also shows promising results for the much more challenging problem of model selection.