Wednesday, December 6, 2023

UQSay #67

The sixty-seventh UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, December 14, 2023.

2–3 PM — Pierre Humbert (LMO - INRIA)


One-Shot Federated Conformal Prediction

In this presentation, we will focus on a method for constructing prediction sets in a federated learning setting where only one round of communication between the agents and the server is allowed (one-shot). More precisely, by defining a particular estimator called the quantile-of-quantiles, we will prove that for any distribution, it is possible to produce marginally (and training-conditionally) valid prediction sets. Over a wide range of experiments, we will show that we are able to obtain prediction sets whose coverage and length are very similar to those obtained in a centralized setting, making our method particularly well-suited to perform conformal predictions in a one-shot federated learning setting.

Reference: P. Humbert, B. Le Bars, A. Bellet, S. Arlot, “One-Shot Federated Conformal Prediction”, 2023.

Joint work with Batiste Le Bars ( INRIA ) and Aurélien Bellet ( INRIA ) and Sylvain Arlot ( LMO-INRIA )

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S).

Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

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Friday, November 24, 2023

UQSay #66

The sixty-sixth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, November 30, 2023.

2–3 PM — Elaine Spiller (Marquette University)


Two recent advances in UQ with Gaussian process models:
the zGP and the PPLE

Gaussian processes (GPs) are an effective and widely used tools to emulate computer simulations of physical process models for uncertainty quantification (UQ). Over the last 10-15 years, GP modeling of computer simulations has advanced tremendously to handle challenges posed by complex and realistic simulators. We will discuss two recent challenges. The first challenge is the "zero-problem” — simulations that result in positive, real-valued output or zero. Such zero-censored data pose a significant obstacle to GP emulators because of both the inherent non-stationary and because GPs have full support. The second challenge we will explore is emulating high-dimensional multi-physics simulations. Here we will combine two recent GP approaches: linked GP emulation (for coupled physical simulations) and parallel partial emulators (PPEs) for emulating simulators with high-dimensional output. The resulting parallel partial linked GP emulator (PPLE) proves an efficient approach to emulate high-dimensional multi-physics simulators.

Reference: E.T. Spiller, R.W. Wolpert, P. Tierz & T.G. Asher, “The zero problem: Gaussian process emulators for range constrained computer models”, 2023. [github]

Joint work with Robert Wolpert (Duke Univ.) and Sue Minkoff (Univ. of Texas)

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S).

Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

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Sunday, November 5, 2023

UQSay #65

The sixty-fifth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, November 16, 2023.

2–3 PM — Michael I. Jordan (Berkeley, University of California.)


Prediction-Powered Inference

I introduce prediction-powered inference – a framework for performing valid statistical inference when an experimental data set is supplemented with predictions from a machine-learning system. Our framework yields provably valid conclusions without making any assumptions on the machine-learning algorithm that supplies the predictions. Higher accuracy of the predictions translates to smaller confidence intervals, permitting more powerful inference. Prediction-powered inference yields simple algorithms for computing valid confidence intervals for statistical objects such as means, quantiles, and linear and logistic regression coefficients. I demonstrate the benefits of prediction-powered inference with data sets from proteomics, genomics, electronic voting, remote sensing, census analysis, and ecology.

Reference: A. Angelopoulos, S. Bates, C. Fannjiang, M. I. Jordan, T. Zrnic, “Prediction-Powered Inference”, 2023.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S).

Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

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Monday, October 30, 2023

UQSay #64

The sixty-fourth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, November 2, 2023.

2–3 PM — Christoph Molnar & Timo Freiesleben (Machine Learning in Science Cluster, University of Tübingen.) — [slides]


Supervised Machine Learning in Science

From folding proteins and predicting tornadoes to studying human nature — machine learning has changed science. Science always had an intimate relationship with prediction, but machine learning intensifies this focus. Can this hyper-focus on prediction models be justified? Can a machine learning model be part of a scientific model? Or are we on the wrong track? We explore and justify the use of supervised machine learning in science. However, a pure and naive application of supervised learning won't get you far, because raw machine learning has so many insufficiencies that make it unusable in this form for science. Unintelligible models, lack of uncertainty quantification, lack of causality. But we already have all the puzzle pieces to fix machine learning, from incorporating domain knowledge and assuring the representativeness of the training data to robust, interpretable, and causal models. We bring together the philosophical justification and the solutions that make supervised machine learning a powerful tool for science.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S).

Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

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Saturday, October 14, 2023

UQSay #63

The sixty-third UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, October 19, 2023.

2–3 PM — Stefania Fresca (MOX, Dept. of Mathematics, Politecnico di Milano)


Deep learning-based reduced order models for the real-time approximation of parametrized PDEs

Conventional reduced order models (ROMs) anchored to the assumption of modal linear superimposition, such as proper orthogonal decomposition (POD), may reveal inefficient when dealing with nonlinear time-dependent parametrized PDEs, especially for problems featuring coherent structures propagating over time. To enhance ROM efficiency, we propose a nonlinear approach to set ROMs by exploiting deep learning (DL) algorithms, such as convolutional neural networks. In the resulting DL-ROM, both the nonlinear trial manifold and the nonlinear reduced dynamics are learned in a non-intrusive way by relying on DL algorithms trained on a set of full order model (FOM) snapshots, obtained for different parameter values. Performing then a former dimensionality reduction on FOM snapshots through POD enables, when dealing with large-scale FOMs, to speedup training times, and decrease the network complexity, substantially. Accuracy and efficiency of the DL-ROM technique are assessed on different parametrized PDE problems in cardiac electrophysiology, computational mechanics and fluid dynamics, possibly accounting for fluid-structure interaction (FSI) effects, where new queries to the DL-ROM can be computed in real-time. Moreover, numerical results obtained by the application of DL-ROMs to the solution of an industrial application, i.e. the approximation of the structural or the electromechanical behaviour of Micro-Electro-Mechanical Systems (MEMS), will be shown.

References:

  1. G. Gobat, S. Fresca, A. Manzoni, A. Frangi, “Reduced order modelling of nonlinear vibrating multiphysics microstructures with deep learning-based approaches”, Sensors, vol. 23, no. 6, pp. 3001, 2023 .
  2. S. Fresca, G. Gobat, P. Fedeli, A. Frangi, A. Manzoni, “Deep learning-based reduced order models for the real-time simulation of the nonlinear dynamics of microstructures”, International Journal for Numerical Methods in Engineering, vol. 123, no. 20, pp. 4749-4777, 2022 .
  3. S. Fresca, A. Manzoni, “POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition”, Computer Methods in Applied Mechanics and Engineering, vol. 388, pp. 114181, 2022 .
  4. S. Fresca, A. Manzoni, L. Dede’, A. Quarteroni, “POD-enhanced deep learning-based reduced order models for the real-time simulation of cardiac electrophysiology in the left atrium”, Frontiers in Physiology, vol. 12, pp. 1431, 2021 .
  5. S. Fresca, A. Manzoni, “Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models”, Fluids, vol. 6, no. 7, pp. 259, 2021 .
  6. S. Fresca, A. Manzoni, L. Dede’, “A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs”, Journal of Scientific Computing, vol. 87, no. 2, pp. 1-36, 2021 .

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S).

Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

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Friday, September 29, 2023

UQSay #62

The sixty-second UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, October 5, 2023.

2–3 PM — Sibo Cheng (Data Science Inst., Imperial College London) — [slides]


Machine learning and data assimilation for high dimensional dynamical systems

Data Assimilation (DA) and Machine Learning (ML) methods are extensively used in predicting and updating high-dimensional spatial-temporal dynamics. Typical applications span from computational fluid dynamics to geoscience and climate systems. In recent years, much effort has been given in combining DA and ML techniques with objectives including but not limited to dynamical system identification, reduced order surrogate modelling, error covariance specification and model error correction. This talk will provide an overview of state-of-the-art research in this interdisciplinary field, covering a wide range of applications. I will also present my unpublished work regarding efficient deep data assimilation with sparse observations and time-varying sensors. The proposed method, incorporating a deep learning inverse operator based on Voronoi tessellation into the assimilation objective function, is adept at handling sparse, unstructured, and time-varying sensor data.

Reference: S. Cheng, C. Quilodran-Casas, S. Ouala, A. Farchi, C. Liu, P. Tandeo, R. Fablet, D. Lucor, B. Iooss, J. Brajard, D. Xiao, T. Janjic, W. Ding, Y. Guo, A. Carrassi, M. Bocquet and R. Arcucci, “Machine Learning With Data Assimilation and Uncertainty Quantification for Dynamical Systems: A Review”, IEEE/CAA Journal of Automatica Sinica, vol. 10, no. 6, pp. 1361–1387, June 2023.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S).

Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

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Saturday, June 3, 2023

UQSay #61

The sixty-first UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, June 8, 2023.

2–3 PM — Sophie Ricci (CECI, CERFACS & UMR 5318) — [slides]


On the merits of using remote sensing Earth Observation data to reduce uncertainties in flood forecasting with ensemble-based data assimilation

Flood simulation and forecast capability have been greatly improved thanks to advances in data assimilation (DA) strategies incorporating various types of observations; many are derived from spatial Earth Observation. This paper focuses on the assimilation of 2D flood observations derived from Synthetic Aperture Radar (SAR) images acquired during a flood event with a dual state-parameter Ensemble Kalman Filter (EnKF). Binary wet/dry maps are here expressed in terms of wet surface ratios (WSR) over a number of subdomains of the floodplain. This ratio is further assimilated jointly with in-situ water-level observations to improve the flow dynamics within the floodplain. However, the non-Gaussianity of the observation errors associated with SAR-derived measurements break a major hypothesis for the application of the EnKF, thus jeopardizing the optimality of the filter analysis. The novelty of this paper lies in the treatment of the non-Gaussianity of the SAR-derived WSR observations with a Gaussian anamorphosis process (GA). This DA strategy was validated and applied over the Garonne Marmandaise catchment (South-west of France) represented with the TELEMAC-2D hydrodynamic model, first in a twin experiment and then for a major flood event that occurred in January-February 2021. It was shown that assimilating SAR-derived WSR observations, in complement to the in-situ water-level observations significantly improves the representation of the flood dynamics. Also, the GA transformation brings further improvement to the DA analysis, while not being a critical component in the DA strategy. This study heralds a reliable solution for flood forecasting over poorly gauged catchments thanks to available remote-sensing datasets.

Joint work with T. H. Nguyen & A. Piacentini (CECI, CERFACS), E. Simon (INP, IRIT), R. Rodriguez-Suquet & S. Peña-Luque (CNES).

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S).

Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

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