Nathanael Perraudin

Denoising diffusion probabilistic models and score-matching models have proven to be very powerful for generative tasks. While these approaches have also been applied to the generation of discrete graphs, they have, so far, relied on continuous Gaussian perturbations. Instead, in this work, we suggest using discrete noise for the forward Markov process. This ensures that in every intermediate step the graph remains discrete. Compared to the previous approach, our experimental results on four datasets and multiple architectures show that using a discrete noising process results in higher quality generated samples indicated with an average MMDs reduced by a factor of 1.5. Furthermore, the number of denoising steps is reduced from 1000 to 32 steps, leading to a 30 times faster sampling procedure.

We propose a probabilistic deep learning approach for the prediction of maximum water depth hazard maps at high spatial resolutions, which assigns well-calibrated uncertainty estimates to every predicted water depth. Efficient, accurate, and trustworthy methods for urban flood management have become increasingly important due to higher rainfall intensity caused by climate change, the expansion of cities, and changes in land use. While physically based flood models can provide reliable forecasts for water depth at every location of a catchment, their high computational burden is hindering their application to large urban areas at high spatial resolution. While deep learning models have been used to address this issue, a disadvantage is that they are often perceived as “black-box” models and are overconfident about their predictions, therefore decreasing their reliability. Our deep learning model learns the underlying phenomena a priori from simulated hydrodynamic data, obviating the need for manual parameter setting for every new rainfall event at test time. The only inputs needed at the test time are a rainfall forecast and parameters of the terrain such as a digital elevation model to predict the maximum water depth with uncertainty estimates for complete rainfall events. We validate the accuracy and generalisation capabilities of our approach through experiments on a dataset consisting of catchments within Switzerland and Portugal and 18 rainfall patterns. Our method produces flood hazard maps at 1 m resolution and achieves mean absolute errors as low as 21 cm for extreme flood cases with water above 1 m. Most importantly, we demonstrate that our approach is able to provide an uncertainty estimate for every water depth within the predicted hazard map, thus increasing the model’s trustworthiness during flooding events.

We studied the ability of deep neural networks (DNNs) to restore missing audio content based on its context, a process usually referred to as audio inpainting. We focused on gaps in the range of tens of milliseconds. The proposed DNN structure was trained on audio signals containing music and musical instruments, separately, with 64-ms long gaps. The input to the DNN was the context, i.e., the signal surrounding the gap, transformed into time-frequency (TF) coefficients. Our results were compared to those obtained from a reference method based on linear predictive coding (LPC). For music, our DNN significantly outperformed the reference method, demonstrating a generally good usability of the proposed DNN structure for inpainting complex audio signals like music.

Learning system dynamics directly from observations is a promising direction in machine learning due to its potential to significantly enhance our ability to understand physical systems. However, the dynamics of many real-world systems are challenging to learn due to the presence of nonlinear potentials and a number of interactions that scales quadratically with the number of particles N, as in the case of the N-body problem. In this work we introduce an approach that transforms a fully-connected interaction graph into a hierarchical one which reduces the number of edges to O(N). This results in a linear time and space complexity while the pre-computation of the hierarchical graph requires O(N log (N)) time and O(N) space. Using our approach, we are able to train models on much larger particle counts, even on a single GPU. We evaluate how the phase space position accuracy and energy conservation depend on the number of simulated particles. Our approach retains high accuracy and efficiency even on large-scale gravitational N-body simulations which are impossible to run on a single machine if a fully-connected graph is used. Similar results are also observed when simulating Coulomb interactions. Furthermore, we make several important observations regarding the performance of this new hierarchical model, including: i) its accuracy tends to improve with the number of particles in the simulation and ii) its generalisation to unseen particle counts is also much better than for models that use all O(N^2) interactions.