214 research outputs found
Deep Convolutional Architectures for Extrapolative Forecast in Time-dependent Flow Problems
Physical systems whose dynamics are governed by partial differential
equations (PDEs) find applications in numerous fields, from engineering design
to weather forecasting. The process of obtaining the solution from such PDEs
may be computationally expensive for large-scale and parameterized problems. In
this work, deep learning techniques developed especially for time-series
forecasts, such as LSTM and TCN, or for spatial-feature extraction such as CNN,
are employed to model the system dynamics for advection dominated problems.
These models take as input a sequence of high-fidelity vector solutions for
consecutive time-steps obtained from the PDEs and forecast the solutions for
the subsequent time-steps using auto-regression; thereby reducing the
computation time and power needed to obtain such high-fidelity solutions. The
models are tested on numerical benchmarks (1D Burgers' equation and Stoker's
dam break problem) to assess the long-term prediction accuracy, even outside
the training domain (extrapolation). Non-intrusive reduced-order modelling
techniques such as deep auto-encoder networks are utilized to compress the
high-fidelity snapshots before feeding them as input to the forecasting models
in order to reduce the complexity and the required computations in the online
and offline stages. Deep ensembles are employed to perform uncertainty
quantification of the forecasting models, which provides information about the
variance of the predictions as a result of the epistemic uncertainties
Embedding Physics to Learn Spatiotemporal Dynamics from Sparse Data
Modeling nonlinear spatiotemporal dynamical systems has primarily relied on
partial differential equations (PDEs) that are typically derived from first
principles. However, the explicit formulation of PDEs for many underexplored
processes, such as climate systems, biochemical reaction and epidemiology,
remains uncertain or partially unknown, where very sparse measurement data is
yet available. To tackle this challenge, we propose a novel deep learning
architecture that forcibly embedded known physics knowledge in a
residual-recurrent -block network, to facilitate the learning of the
spatiotemporal dynamics in a data-driven manner. The coercive embedding
mechanism of physics, fundamentally different from physics-informed neural
networks based on loss penalty, ensures the network to rigorously obey given
physics. Numerical experiments demonstrate that the resulting learning paradigm
that embeds physics possesses remarkable accuracy, robustness, interpretability
and generalizability for learning spatiotemporal dynamics.Comment: 18 pages. arXiv admin note: substantial text overlap with
arXiv:2105.0055
NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decomposition
Neural networks have shown great potential in accelerating the solution of
partial differential equations (PDEs). Recently, there has been a growing
interest in introducing physics constraints into training neural PDE solvers to
reduce the use of costly data and improve the generalization ability. However,
these physics constraints, based on certain finite dimensional approximations
over the function space, must resolve the smallest scaled physics to ensure the
accuracy and stability of the simulation, resulting in high computational costs
from large input, output, and neural networks. This paper proposes a general
acceleration methodology called NeuralStagger by spatially and temporally
decomposing the original learning tasks into several coarser-resolution
subtasks. We define a coarse-resolution neural solver for each subtask, which
requires fewer computational resources, and jointly train them with the vanilla
physics-constrained loss by simply arranging their outputs to reconstruct the
original solution. Due to the perfect parallelism between them, the solution is
achieved as fast as a coarse-resolution neural solver. In addition, the trained
solvers bring the flexibility of simulating with multiple levels of resolution.
We demonstrate the successful application of NeuralStagger on 2D and 3D fluid
dynamics simulations, which leads to an additional speed-up.
Moreover, the experiment also shows that the learned model could be well used
for optimal control.Comment: ICML 2023 accepte
Étude de la propagation acoustique en milieu complexe par des réseaux de neurones profonds
Abstract : Predicting the propagation of aerocoustic noise is a challenging task in the presence of complex mean flows and geometry installation effects. The design of future quiet propul- sion systems requires tools that are able to perform many accurate evaluations with a low computational cost. Analytical models or hybrid numerical approaches have tradition- ally been employed for that purpose. However, such methods are typically constrained by simplifying hypotheses that are not easily relaxed. Thus, the main objective of this thesis is to develop and validate novel methods for the fast and accurate prediction of aeroacoustic propagation in complex mean flows and geometries. For that, data-driven deep convolutional neural networks acting as auto-regressive spatio-temporal predictors are considered. These surrogates are trained on high-fidelity data, generated by direct aeroacoustic numerical solvers. Such datasets are able to model complex flow phenomena, along with complex geometrical parameters. The neural network is designed to substitute the high-fidelity solver at a much lower computational cost once the training is finished, while predicting the time-domain acoustic propagation with sufficient accuracy. Three test cases of growing complexity are employed to test the approach, where the learned surrogate is compared to analytical and numerical solutions. The first one corresponds to the two-dimensional propagation of Gaussian pulses in closed domains, which allows understanding the fundamental behavior of the employed convolution neural networks. Second, the approach is extended in order to consider a variety of boundary conditions, from non-reflecting to curved reflecting obstacles, including the reflection and scattering of waves at obstacles. This allows the prediction of acoustic propagation in configurations closer to industrial problems. Finally, the effects of complex mean flows is investigated through a dataset of acoustic waves propagating inside sheared flows. These applications highlight the flexibility of the employed data-driven methods using convolutional neural networks. They allow a significant acceleration of the acoustic predictions, while keeping an adequate accuracy and being also able to correctly predict the acoustic propagation outside the range of the training data. For that, prior knowledge about the wave propa- gation physics is included during and after the neural network training phase, allowing an increased control over the error performed by the surrogate. Among this prior knowledge, the conservation of physics quantities and the correct treatment of boundary conditions are identified as key parameters that improve the surrogate predictions.Prédire la propagation du bruit aéroacoustique est une tâche difficile en présence d’écoulements
moyens complexes et d’effets géométriques d’installation. La conception des futurs
systèmes de propulsion silencieux appelle au développement d’outils capables d’effectuer
de nombreuses évaluations avec une faible erreur et un faible coût de calcul. Traditionnellement,
des modèles analytiques ou des approches numériques hybrides ont été utilisés
à cette fin. Cependant, ces méthodes sont généralement contraintes par des hypothèses
simplificatrices qui ne sont pas facilement assouplies. Ainsi, l’objectif principal de cette
thèse est de développer et de valider de nouvelles méthodes pour la prédiction rapide et
précise de la propagation aéroacoustique dans des écoulements moyens et des géométries
complexes. Pour cela, des réseaux de neurones profonds à convolution, entraînés sur des
données, et agissant comme prédicteurs spatio-temporels sont considérés. Ces modèles par
substitution sont entraînés sur des données de haute fidélité, générées par des solveurs
numériques aérocoustiques directs. De telles bases de données sont capables de modéliser
des phénomènes d’écoulement, ainsi que des paramètres géométriques complexes. Le réseau
de neurones est conçu pour remplacer le solveur haute fidélité à un coût de calcul
beaucoup plus faible une fois la phase d’entraînement terminée, tout en prédisant la propagation
acoustique dans le domaine temporel avec une précision suffisante. Trois cas de
test, de complexité croissante, sont utilisés pour tester l’approche, où le substitut appris
est comparé à des solutions analytiques et numériques. Le premier cas correspond à la
propagation acoustique bidimensionnelle dans des domaines fermés, où des sources impulsionnelles
Gaussiennes sont considérées. Ceci permet de comprendre le comportement
fondamental des réseaux de neurones à convolution étudiés. Deuxièmement, l’approche
est étendue afin de prendre en compte une variété de conditions aux limites, notamment
des conditions aux limites non réfléchissantes et des obstacles réfléchissants de géométrie
arbitraire, modélisant la réflexion et la diffusion des ondes acoustiques sur ces obstacles.
Cela permet de prédire la propagation acoustique dans des configurations plus proches
des problématiques industrielles. Enfin, les effets des écoulements moyens complexes sont
étudiés à travers une base de données d’ondes acoustiques qui se propagent à l’intérieur
d’écoulements cisaillés. Ces applications mettent en évidence la flexibilité des méthodes basées sur les données, utilisant des réseaux de neurones à convolution. Ils permettent
une accélération significative des prédictions acoustiques, tout en gardant une précision
adéquate et en étant également capables de prédire correctement la propagation acoustique
en dehors de la gamme de paramètres des données d’apprentissage. Pour cela, des
connaissances préalables sur la physique de propagation des ondes sont incluses pendant
et après la phase d’apprentissage du réseau de neurones, permettant un contrôle accru
sur l’erreur effectuée par le substitut. Parmi ces connaissances préalables, la conservation
des grandeurs physiques et le traitement correct des conditions aux limites sont identifiés
comme des paramètres clés qui améliorent les prédictions du modèle proposé
Probabilistic Physics-integrated Neural Differentiable Modeling for Isothermal Chemical Vapor Infiltration Process
Chemical vapor infiltration (CVI) is a widely adopted manufacturing technique
used in producing carbon-carbon and carbon-silicon carbide composites. These
materials are especially valued in the aerospace and automotive industries for
their robust strength and lightweight characteristics. The densification
process during CVI critically influences the final performance, quality, and
consistency of these composite materials. Experimentally optimizing the CVI
processes is challenging due to long experimental time and large optimization
space. To address these challenges, this work takes a modeling-centric
approach. Due to the complexities and limited experimental data of the
isothermal CVI densification process, we have developed a data-driven
predictive model using the physics-integrated neural differentiable (PiNDiff)
modeling framework. An uncertainty quantification feature has been embedded
within the PiNDiff method, bolstering the model's reliability and robustness.
Through comprehensive numerical experiments involving both synthetic and
real-world manufacturing data, the proposed method showcases its capability in
modeling densification during the CVI process. This research highlights the
potential of the PiNDiff framework as an instrumental tool for advancing our
understanding, simulation, and optimization of the CVI manufacturing process,
particularly when faced with sparse data and an incomplete description of the
underlying physics
Bi-fidelity Variational Auto-encoder for Uncertainty Quantification
Quantifying the uncertainty of quantities of interest (QoIs) from physical
systems is a primary objective in model validation. However, achieving this
goal entails balancing the need for computational efficiency with the
requirement for numerical accuracy. To address this trade-off, we propose a
novel bi-fidelity formulation of variational auto-encoders (BF-VAE) designed to
estimate the uncertainty associated with a QoI from low-fidelity (LF) and
high-fidelity (HF) samples of the QoI. This model allows for the approximation
of the statistics of the HF QoI by leveraging information derived from its LF
counterpart. Specifically, we design a bi-fidelity auto-regressive model in the
latent space that is integrated within the VAE's probabilistic encoder-decoder
structure. An effective algorithm is proposed to maximize the variational lower
bound of the HF log-likelihood in the presence of limited HF data, resulting in
the synthesis of HF realizations with a reduced computational cost.
Additionally, we introduce the concept of the bi-fidelity information
bottleneck (BF-IB) to provide an information-theoretic interpretation of the
proposed BF-VAE model. Our numerical results demonstrate that BF-VAE leads to
considerably improved accuracy, as compared to a VAE trained using only HF
data, when limited HF data is available
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