Recent years have seen the flourishing of techniques devoted to best incorporate data in the models, either for the solution of inverse problems or for approximation purposes. This includes domain-aware Machine Learning techniques, dynamic mode decomposition or data driven model order reduction methods. This minisymposium aims to provide a venue for young researchers focusing on the theoretical analysis, the development and the application of these methodologies.
16:30
Data-model integration in cardiac electrophysiology
Stefano Pagani | Politecnico di Milano | Italy
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Authors:
Stefano Pagani | Politecnico di Milano | Italy
Andrea Manzoni | Politecnico di Milano | Italy
Alfio Quarteroni | Politecnico di Milano | Italy
We present a computationally efficient data-model integration in cardiac electrophysiology to better understand the mechanisms behind cardiac rhythm disorders.
The natural framework to address these problems is based on stochastic sampling techniques, such as (Markov chain) Monte Carlo simulations, thus implying overwhelming computational costs because of the huge amount of queries to the high-fidelity approximation of the coupled PDE-ODEs model.
Several methodologies have been developed to mitigate this computational burden, such as approximate sampling techniques in which the queries to the high-fidelity approximation are substituted with less expensive ones. This goal can be achieved by adopting model order reduction methods, physics-based Machine Learning techniques or black-box surrogate models, such as artificial neural network (ANN)-based models.
Numerical results show how the suitable combination of these physics-based techniques with data-driven methodologies leads to substantial advancements in terms of both sampling accuracy and overall computational efficiency.
This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement n. 740132).
17:00
Optimal Placement of Sensors to Assess Structural Damages
Caterina Bigoni | Ecole polytechnique fédérale de Lausanne (EPFL) | Switzerland
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Authors:
Caterina Bigoni | Ecole polytechnique fédérale de Lausanne (EPFL) | Switzerland
Zhenying Zhang | Ecole polytechnique fédérale de Lausanne (EPFL) | Switzerland
Jan Hesthaven | Ecole polytechnique fédérale de Lausanne (EPFL) | Switzerland
In Structural Health Monitoring (SHM), risk assessment and decision strategies rely primarily on sensor responses. Simulated data can be generated to emulate the monitoring phenomena under different natural operational and environmental conditions in order to discriminate relevant features and thus identify potential anomalies. Reduced order modelling techniques and one-class machine learning algorithms allow us to efficiently achieve this goal for a fixed number and location of sensors. However, since the number of sensors available on a structure is often a limitation to SHM, identifying the optimal locations that maximize the observability of the discriminant features becomes a fundamental task. In this work, variational inference of sparse Gaussian Processes (GP) allows us to identify sensor locations with inducing inputs. In this way, through few measurements, we recover the best estimate of the monitoring feature at all ``unsensed'' locations. This technique is tested on several numerical examples and demonstrates to be efficient in detecting damages. In particular, it allows us to consider the realistic case in which damage types and locations are a priori unknown, thus overcoming the main limitation of existing optimal sensor placement strategies for SHM.
17:30
Data-driven discovery of coordinates for parsimonious dynamical models
Kathleen Champion | University of Washington | United States
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Authors:
Kathleen Champion | University of Washington | United States
Bethany Lusch | Argonne National Laboratory | United States
J. Nathan Kutz | University of Washington | United States
Steven L Brunton | University of Washington | United States
A central challenge in using machine learning for dynamical systems is discovering models that are interpretable. While approaches like deep learning have demonstrated impressive performance at modeling and predictive tasks, the resulting models typically have many parameters, making them difficult to interpret as compared with parsimonious models containing only a few terms. A key step to finding parsimonious models is discovering coordinates in which the dynamics become simple. We present a method for the simultaneous discovery of coordinates and parsimonious dynamical models from high-dimensional data.
18:00
Controlling oscillations in spectral schemes using deep learning
Deep Ray | Rice University | United States
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Authors:
Lukas Schwander | Ecole polytechnique fédérale de Lausanne (EPFL) | Switzerland
Jan Hesthaven | Ecole polytechnique fédérale de Lausanne (EPFL) | Switzerland
Cecilia Pagliantini | Ecole polytechnique fédérale de Lausanne (EPFL) | Switzerland
Deep Ray | Rice University | United States
Fourier spectral methods are quite appealing for solving conservation laws, beating most traditional high-order methods in terms of accuracy and computational efficiency. However, they suffer from spurious Gibbs oscillations when used to approximate discontinuous solutions. While techniques like the use of exponential filters have been proposed to resolve this issue, they are usually unable to suppress the oscillations without being overly dissipative.
Recently, artificial neural networks have been successfully used to control Gibbs oscillations in methods with a local basis representation, such as discontinuous Galerkin schemes. In this talk, we propose a similar methodology for spectral methods. In particular, we train a network to predict a suitable amount of artificial viscosity based on the local regularity of the underlying solution. Several numerical results are presented to demonstrate the robustness of the network, on both uniform and non-uniform grids.