Georges Tod

Georges Tod, Jean Bruggeman, Evert Bevernage et al.

Train operational incidents are so far diagnosed individually and manually by train maintenance technicians. In order to assist maintenance crews in their responsiveness and task prioritization, a learning machine is developed and deployed in production to suggest diagnostics to train technicians on their phones, tablets or laptops as soon as a train incident is declared. A feedback loop allows to take into account the actual diagnose by designated train maintenance experts to refine the learning machine. By formulating the problem as a discrete set classification task, feature engineering methods are proposed to extract physically plausible sets of events from traces generated on-board railway vehicles. The latter feed an original ensemble classifier to class incidents by their potential technical cause. Finally, the resulting model is trained and validated using real operational data and deployed on a cloud platform. Future work will explore how the extracted sets of events can be used to avoid incidents by assisting human experts in the creation predictive maintenance alerts.

Georges Tod, Gert-Jan Both, Remy Kusters

Automated model discovery of partial differential equations (PDEs) usually considers a single experiment or dataset to infer the underlying governing equations. In practice, experiments have inherent natural variability in parameters, initial and boundary conditions that cannot be simply averaged out. We introduce a randomised adaptive group Lasso sparsity estimator to promote grouped sparsity and implement it in a deep learning based PDE discovery framework. It allows to create a learning bias that implies the a priori assumption that all experiments can be explained by the same underlying PDE terms with potentially different coefficients. Our experimental results show more generalizable PDEs can be found from multiple highly noisy datasets, by this grouped sparsity promotion rather than simply performing independent model discoveries.

Georges Tod, Gert-Jan Both, Remy Kusters

Discovering the partial differential equations underlying spatio-temporal datasets from very limited and highly noisy observations is of paramount interest in many scientific fields. However, it remains an open question to know when model discovery algorithms based on sparse regression can actually recover the underlying physical processes. In this work, we show the design matrices used to infer the equations by sparse regression can violate the irrepresentability condition (IRC) of the Lasso, even when derived from analytical PDE solutions (i.e. without additional noise). Sparse regression techniques which can recover the true underlying model under violated IRC conditions are therefore required, leading to the introduction of the randomised adaptive Lasso. We show once the latter is integrated within the deep learning model discovery framework DeepMod, a wide variety of nonlinear and chaotic canonical PDEs can be recovered: (1) up to $\mathcal{O}(2)$ higher noise-to-sample ratios than state-of-the-art algorithms, (2) with a single set of hyperparameters, which paves the road towards truly automated model discovery.

Gert-Jan Both, Georges Tod, Remy Kusters

To improve the physical understanding and the predictions of complex dynamic systems, such as ocean dynamics and weather predictions, it is of paramount interest to identify interpretable models from coarsely and off-grid sampled observations. In this work, we investigate how deep learning can improve model discovery of partial differential equations when the spacing between sensors is large and the samples are not placed on a grid. We show how leveraging physics informed neural network interpolation and automatic differentiation, allow to better fit the data and its spatiotemporal derivatives, compared to more classic spline interpolation and numerical differentiation techniques. As a result, deep learning-based model discovery allows to recover the underlying equations, even when sensors are placed further apart than the data's characteristic length scale and in the presence of high noise levels. We illustrate our claims on both synthetic and experimental data sets where combinations of physical processes such as (non)-linear advection, reaction, and diffusion are correctly identified.