1,647 research outputs found
Machine Learning and Its Application to Reacting Flows
This open access book introduces and explains machine learning (ML) algorithms and techniques developed for statistical inferences on a complex process or system and their applications to simulations of chemically reacting turbulent flows. These two fields, ML and turbulent combustion, have large body of work and knowledge on their own, and this book brings them together and explain the complexities and challenges involved in applying ML techniques to simulate and study reacting flows. This is important as to the world’s total primary energy supply (TPES), since more than 90% of this supply is through combustion technologies and the non-negligible effects of combustion on environment. Although alternative technologies based on renewable energies are coming up, their shares for the TPES is are less than 5% currently and one needs a complete paradigm shift to replace combustion sources. Whether this is practical or not is entirely a different question, and an answer to this question depends on the respondent. However, a pragmatic analysis suggests that the combustion share to TPES is likely to be more than 70% even by 2070. Hence, it will be prudent to take advantage of ML techniques to improve combustion sciences and technologies so that efficient and “greener” combustion systems that are friendlier to the environment can be designed. The book covers the current state of the art in these two topics and outlines the challenges involved, merits and drawbacks of using ML for turbulent combustion simulations including avenues which can be explored to overcome the challenges. The required mathematical equations and backgrounds are discussed with ample references for readers to find further detail if they wish. This book is unique since there is not any book with similar coverage of topics, ranging from big data analysis and machine learning algorithm to their applications for combustion science and system design for energy generation
Discovering Causal Relations and Equations from Data
Physics is a field of science that has traditionally used the scientific
method to answer questions about why natural phenomena occur and to make
testable models that explain the phenomena. Discovering equations, laws and
principles that are invariant, robust and causal explanations of the world has
been fundamental in physical sciences throughout the centuries. Discoveries
emerge from observing the world and, when possible, performing interventional
studies in the system under study. With the advent of big data and the use of
data-driven methods, causal and equation discovery fields have grown and made
progress in computer science, physics, statistics, philosophy, and many applied
fields. All these domains are intertwined and can be used to discover causal
relations, physical laws, and equations from observational data. This paper
reviews the concepts, methods, and relevant works on causal and equation
discovery in the broad field of Physics and outlines the most important
challenges and promising future lines of research. We also provide a taxonomy
for observational causal and equation discovery, point out connections, and
showcase a complete set of case studies in Earth and climate sciences, fluid
dynamics and mechanics, and the neurosciences. This review demonstrates that
discovering fundamental laws and causal relations by observing natural
phenomena is being revolutionised with the efficient exploitation of
observational data, modern machine learning algorithms and the interaction with
domain knowledge. Exciting times are ahead with many challenges and
opportunities to improve our understanding of complex systems.Comment: 137 page
The ROMES method for statistical modeling of reduced-order-model error
This work presents a technique for statistically modeling errors introduced
by reduced-order models. The method employs Gaussian-process regression to
construct a mapping from a small number of computationally inexpensive `error
indicators' to a distribution over the true error. The variance of this
distribution can be interpreted as the (epistemic) uncertainty introduced by
the reduced-order model. To model normed errors, the method employs existing
rigorous error bounds and residual norms as indicators; numerical experiments
show that the method leads to a near-optimal expected effectivity in contrast
to typical error bounds. To model errors in general outputs, the method uses
dual-weighted residuals---which are amenable to uncertainty control---as
indicators. Experiments illustrate that correcting the reduced-order-model
output with this surrogate can improve prediction accuracy by an order of
magnitude; this contrasts with existing `multifidelity correction' approaches,
which often fail for reduced-order models and suffer from the curse of
dimensionality. The proposed error surrogates also lead to a notion of
`probabilistic rigor', i.e., the surrogate bounds the error with specified
probability
Machine Learning and Its Application to Reacting Flows
This open access book introduces and explains machine learning (ML) algorithms and techniques developed for statistical inferences on a complex process or system and their applications to simulations of chemically reacting turbulent flows. These two fields, ML and turbulent combustion, have large body of work and knowledge on their own, and this book brings them together and explain the complexities and challenges involved in applying ML techniques to simulate and study reacting flows. This is important as to the world’s total primary energy supply (TPES), since more than 90% of this supply is through combustion technologies and the non-negligible effects of combustion on environment. Although alternative technologies based on renewable energies are coming up, their shares for the TPES is are less than 5% currently and one needs a complete paradigm shift to replace combustion sources. Whether this is practical or not is entirely a different question, and an answer to this question depends on the respondent. However, a pragmatic analysis suggests that the combustion share to TPES is likely to be more than 70% even by 2070. Hence, it will be prudent to take advantage of ML techniques to improve combustion sciences and technologies so that efficient and “greener” combustion systems that are friendlier to the environment can be designed. The book covers the current state of the art in these two topics and outlines the challenges involved, merits and drawbacks of using ML for turbulent combustion simulations including avenues which can be explored to overcome the challenges. The required mathematical equations and backgrounds are discussed with ample references for readers to find further detail if they wish. This book is unique since there is not any book with similar coverage of topics, ranging from big data analysis and machine learning algorithm to their applications for combustion science and system design for energy generation
Fourier neural operator for real-time simulation of 3D dynamic urban microclimate
Global urbanization has underscored the significance of urban microclimates
for human comfort, health, and building/urban energy efficiency. They
profoundly influence building design and urban planning as major environmental
impacts. Understanding local microclimates is essential for cities to prepare
for climate change and effectively implement resilience measures. However,
analyzing urban microclimates requires considering a complex array of outdoor
parameters within computational domains at the city scale over a longer period
than indoors. As a result, numerical methods like Computational Fluid Dynamics
(CFD) become computationally expensive when evaluating the impact of urban
microclimates. The rise of deep learning techniques has opened new
opportunities for accelerating the modeling of complex non-linear interactions
and system dynamics. Recently, the Fourier Neural Operator (FNO) has been shown
to be very promising in accelerating solving the Partial Differential Equations
(PDEs) and modeling fluid dynamic systems. In this work, we apply the FNO
network for real-time three-dimensional (3D) urban wind field simulation. The
training and testing data are generated from CFD simulation of the urban area,
based on the semi-Lagrangian approach and fractional stepping method to
simulate urban microclimate features for modeling large-scale urban problems.
Numerical experiments show that the FNO model can accurately reconstruct the
instantaneous spatial velocity field. We further evaluate the trained FNO model
on unseen data with different wind directions, and the results show that the
FNO model can generalize well on different wind directions. More importantly,
the FNO approach can make predictions within milliseconds on the graphics
processing unit, making real-time simulation of 3D dynamic urban microclimate
possible
Probabilistic forecast of nonlinear dynamical systems with uncertainty quantification
Data-driven modeling is useful for reconstructing nonlinear dynamical systems
when the underlying process is unknown or too expensive to compute. Having
reliable uncertainty assessment of the forecast enables tools to be deployed to
predict new scenarios unobserved before. In this work, we first extend parallel
partial Gaussian processes for predicting the vector-valued transition function
that links the observations between the current and next time points, and
quantify the uncertainty of predictions by posterior sampling. Second, we show
the equivalence between the dynamic mode decomposition and the maximum
likelihood estimator of the linear mapping matrix in the linear state space
model. The connection provides a data generating model of dynamic mode
decomposition and thus, uncertainty of predictions can be obtained.
Furthermore, we draw close connections between different data-driven models for
approximating nonlinear dynamics, through a unified view of data generating
models. We study two numerical examples, where the inputs of the dynamics are
assumed to be known in the first example and the inputs are unknown in the
second example. The examples indicate that uncertainty of forecast can be
properly quantified, whereas model or input misspecification can degrade the
accuracy of uncertainty quantification
Machine learning algorithms for fluid mechanics
Neural networks have become increasingly popular in the field of fluid dynamics due to their ability to model complex, high-dimensional flow phenomena. Their flexibility in approximating continuous functions without any preconceived notion of functional form makes them a suitable tool for studying fluid dynamics. The main uses of neural networks in fluid dynamics include turbulence modelling, flow control, prediction of flow fields, and accelerating high-fidelity simulations. This thesis focuses on the latter two applications of neural networks.
First, the application of a convolutional neural network (CNN) to accelerate the solution of the Poisson equation step in the pressure projection method for incompressible fluid flows is investigated. The CNN learns to approximate the Poisson equation solution at a lower computational cost than traditional iterative solvers, enabling faster simulations of fluid flows. Results show that the CNN approach is accurate and efficient, achieving significant speedup in the Taylor-Green Vortex problem.
Next, predicting flow fields past arbitrarily-shaped bluff bodies from point sensor and plane velocity measurements using neural networks is focused on. A novel conformal-mapping-aided method is devised to embed geometry invariance for the outputs of the neural networks, which is shown to be critical for achieving good performance for flow datasets incorporating a diverse range of geometries. Results show that the proposed methods can accurately predict the flow field, demonstrating excellent agreement with simulation data. Moreover, the flow field predictions can be used to accurately predict lift and drag coefficients, making these methods useful for optimizing the shape of bluff bodies for specific applications.Open Acces
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