Probabilistic Deep Learning on Spheres for Weather/Climate Applications

Wentao Feng
2020
Projet étudiant

Résumé

The climate and weather are modeled by running computer simulations. In a data-driven approach, scientists tailor the simulation to resemble reality (partly through an understanding of the physical processes, partly through their parameterization). With the availability of large data and compute, we can hope for machines to help in the automatic discovery of principles from data. The integration of machine learning (deep learning) within simulations opens up the exploration of new tradeoffs between accuracy and computational cost.

Source officielle

https://infoscience.epfl.ch/record/282285?ln=fr

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Mechanical intelligence for learning embodied sensor-object relationships

Ahalya Prabhakar

Intelligence involves processing sensory experiences into representations useful for prediction. Understanding sensory experiences and building these contextual representations without prior knowledge of sensor models and environment is a challenging unsupervised learning problem. Current machine learning methods process new sensory data using prior knowledge defined by either domain knowledge or datasets. When datasets are not available, data acquisition is needed, though automating exploration in support of learning is still an unsolved problem. Here we develop a method that enables agents to efficiently collect data for learning a predictive sensor model-without requiring domain knowledge, human input, or previously existing data-using ergodicity to specify the data acquisition process. This approach is based entirely on data-driven sensor characteristics rather than predefined knowledge of the sensor model and its physical characteristics. We learn higher quality models with lower energy expenditure during exploration for data acquisition compared to competing approaches, including both random sampling and information maximization. In addition to applications in autonomy, our approach provides a potential model of how animals use their motor control to develop high quality models of their sensors (sight, sound, touch) before having knowledge of their sensor capabilities or their surrounding environment. Information-based search strategies are relevant for the learning of interacting agents dynamics and usually need predefined data. The authors propose a method to collect data for learning a predictive sensor model, without requiring domain knowledge, human input, or previously existing data.

NATURE PORTFOLIO2022

Data-driven and model-driven methodologies can be regarded as competitive fields since they tackle similar problems such as prediction. However, these two fields can learn from each other to improve themselves. Indeed, data-driven methodologies have been developed to use advanced methodologies based on Big Data technologies. On the other hand, model-driven methodologies concentrate on developing mathematical models based on theory and expert knowledge to allow for interpretability and control. Through three main contributions, this thesis aims to bridge the gap between these two fields by using their strengths and applying them to its counterpart.Discrete Choice Models (DCMs) have shown tremendous success in many fields, such as transportation. However, they have not evolved to tackle the growing amount of available data. On the other hand, Machine Learning (ML) researchers have developed optimization algorithms to efficiently estimate complex models on large datasets. Similarly, faster estimation of DCMs on larger datasets would improve the efficiency of modelers as well as enable new research axes. Thus, we take inspiration from the large body of existing research in efficient parameter estimation with extensive data and large numbers of parameters in deep learning and apply it to DCMs. The first chapter of this thesis introduces the HAMABS algorithm, which combines three fundamental principles to enable faster parameter estimation of DCMs (20x speedup compared to standard estimation) without compromising the precision of the parameter estimates.Collecting large amounts of data can be cumbersome and costly, even in the era of Big Data. For example, ML researchers in Computer Vision have been developing generative deep learning models to augment datasets. DCM researchers face similar issues with tabular data, e.g. travel surveys. In addition, if the collection process is not performed correctly, these datasets can contain bias, lack consistency, or be unrepresentative of the actual population. The second chapter of this thesis introduces the DATGAN, a Generative Adversarial Network (GAN) integrating expert knowledge to control the generation process. This new architecture allows modelers to generate controlled and representative synthetic data, outperforming similar state-of-the-art generative models. Finally, researchers are increasingly developing fully disaggregate agent-based simulation models, which use detailed synthetic populations to generate aggregate passenger flows. However, detailed disaggregate socioeconomic data is usually expensive to collect and heavily restricted in terms of access and usage. As such, synthetic populations are typically either drawn randomly from aggregate level control totals, limiting their quality, or tightly controlled, limiting their application and usefulness. To combat this, the third chapter extends the DATGAN methodology to generate highly detailed and consistent synthetic populations from small sample data. First, ciDATGAN learns to generate the variables in a low-sample highly detailed dataset, e.g. household travel survey. It then completes a high-sample dataset with few variables, e.g. microdata census, by generating the previously learned variables. The results show that this methodology can correct for bias and may enable the transfer of synthetic populations to new areas/contexts.

EPFL2022

Inverse Modelling and Predictive Inference in Continuum Mechanics: a Data-Driven Approach

Claire Marianne Charlotte Capelo

The explosive growth of machine learning in the age of data has led to a new probabilistic and data-driven approach to solving very different types of problems. In this paper we study the feasibility of using such data-driven algorithms to solve classic physical and mathematical problems. In particular, we try to model the solution of an inverse continuum mechanics problem in the context of linear elasticity using deep neural networks. To better address the inverse function, we start first by studying the simplest related task,consisting of a building block of the actual composite problem. By empirically proving the learnability of simpler functions, we aim to draw conclusions with respect to the initial problem.The basic inverse problem that motivates this paper is that of a 2D plate with inclusion under specific loading and boundary conditions. From measurements at static equilibrium,we wish to recover the position of the hole. Although some analytical solutions have been formulated for 3D-infinite solids - most notably Eshelby’s inclusion problems - finite problems with particular geometries, material inhomogeneities, loading and boundary conditions require the use of numerical methods which are most often efficient solutions to the forward problem, the mapping from the parameter space to the measurement/signal space, i.e. in our case computing displacements and stresses knowing the size and position of the inclusion. Using numerical data generated from the well-defined forward problem,we train a neural network to approximate the inverse function relating displacements and stresses to the position of the inclusion. The preliminary results on the 2D-finite problem are promising, but the black-box nature of neural networks is a huge issue when it comes to understanding the solution.For this reason, we study a 3D-infinite continuous isotropic medium with unique concentrated load, for which the Green’s function gives an analytical mathematical expression relating relative position of the point force and the displacements in the solid. After de-riving the expression of the inverse, namely recovering the relative position of the force from the Green’s matrix computed at a given point in the medium, we are able to study the sensitivity of the inverse function. From both the expression of the Green’s function and its inverse, we highlight what issues might arise when training neural networks to solve the inverse problem. As the Green’s function is not bijective, bijection must been forced when training for regression. Moreover, due to displacements growing to infinity as we approach the singularity at zero, the training domain must be constrained to be some distance away from the singularity. As we train a neural network to fit the inverse of the Green’s function, we show that the input parameters should include the least possible redundant information to ensure the most efficient training.We then extend our analysis to two point forces. As more loads are added, bijection is harder to enforce as permutations of forces must be taken into account and more collisions may arise, i.e. multiple specific combinations of forces might yield the same measurements.One obvious solution is to increase the number of nodes where displacements are measured to limit the possibility of collision. Through new experiments, we show again that the best training is achieved for the least possible amount of nodes, as long as the training data generated is indeed bijective. As the medium is elastic, we propose a neural network architecture that matches the composite nature of the inverse problem. We also present another formulation of the problem which is invariant to permutations of the forces,namely multilabel classification, and yields good performance in the two-load case.Finally, we study the composite inverse function for 2, 3, 4 and 5 forces. By comparing training and accuracy for different neural network architectures, we expose the model easiest to train. Moreover, the evolution of the final accuracy as more loads are added indicates that deep-neural networks (DNNs) are not well suited to fit a non-linear mapping from and to a high-dimensional space. The results are more convincing for multilabel classification.

2020

Inverse Modelling and Predictive Inference in Continuum Mechanics: a Data-Driven Approach

Claire Marianne Charlotte Capelo

2020

EPFL2022