244 research outputs found
Physics-Guided Deep Learning for Dynamical Systems: A survey
Modeling complex physical dynamics is a fundamental task in science and
engineering. Traditional physics-based models are interpretable but rely on
rigid assumptions. And the direct numerical approximation is usually
computationally intensive, requiring significant computational resources and
expertise. While deep learning (DL) provides novel alternatives for efficiently
recognizing complex patterns and emulating nonlinear dynamics, it does not
necessarily obey the governing laws of physical systems, nor do they generalize
well across different systems. Thus, the study of physics-guided DL emerged and
has gained great progress. It aims to take the best from both physics-based
modeling and state-of-the-art DL models to better solve scientific problems. In
this paper, we provide a structured overview of existing methodologies of
integrating prior physical knowledge or physics-based modeling into DL and
discuss the emerging opportunities
Enforcing statistical constraints in generative adversarial networks for modeling chaotic dynamical systems
Simulating complex physical systems often involves solving partial differential equations (PDEs) with some closures due to the presence of multi-scale physics that cannot be fully resolved. Although the advancement of high performance computing has made resolving small-scale physics possible, such simulations are still very expensive. Therefore, reliable and accurate closure models for the unresolved physics remains an important requirement for many computational physics problems, e.g., turbulence simulation. Recently, several researchers have adopted generative adversarial networks (GANs), a novel paradigm of training machine learning models, to generate solutions of PDEs-governed complex systems without having to numerically solve these PDEs. However, GANs are known to be difficult in training and likely to converge to local minima, where the generated samples do not capture the true statistics of the training data. In this work, we present a statistical constrained generative adversarial network by enforcing constraints of covariance from the training data, which results in an improved machine-learning-based emulator to capture the statistics of the training data generated by solving fully resolved PDEs. We show that such a statistical regularization leads to better performance compared to standard GANs, measured by (1) the constrained model's ability to more faithfully emulate certain physical properties of the system and (2) the significantly reduced (by up to 80%) training time to reach the solution. We exemplify this approach on the Rayleigh-BĂ©nard convection, a turbulent flow system that is an idealized model of the Earth's atmosphere. With the growth of high-fidelity simulation databases of physical systems, this work suggests great potential for being an alternative to the explicit modeling of closures or parameterizations for unresolved physics, which are known to be a major source of uncertainty in simulating multi-scale physical systems, e.g., turbulence or Earth's climate
Embed and Emulate: Learning to estimate parameters of dynamical systems with uncertainty quantification
This paper explores learning emulators for parameter estimation with
uncertainty estimation of high-dimensional dynamical systems. We assume access
to a computationally complex simulator that inputs a candidate parameter and
outputs a corresponding multichannel time series. Our task is to accurately
estimate a range of likely values of the underlying parameters. Standard
iterative approaches necessitate running the simulator many times, which is
computationally prohibitive. This paper describes a novel framework for
learning feature embeddings of observed dynamics jointly with an emulator that
can replace high-cost simulators for parameter estimation. Leveraging a
contrastive learning approach, our method exploits intrinsic data properties
within and across parameter and trajectory domains. On a coupled
396-dimensional multiscale Lorenz 96 system, our method significantly
outperforms a typical parameter estimation method based on predefined metrics
and a classical numerical simulator, and with only 1.19% of the baseline's
computation time. Ablation studies highlight the potential of explicitly
designing learned emulators for parameter estimation by leveraging contrastive
learning.Comment: Accepted at NeurIPS 202
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Statistical mechanics in climate emulation: Challenges and perspectives
Climate emulators are a powerful instrument for climate modeling, especially in terms of reducing the computational load for simulating spatiotemporal processes associated with climate systems. The most important type of emulators are statistical emulators trained on the output of an ensemble of simulations from various climate models. However, such emulators oftentimes fail to capture the “physics” of a system that can be detrimental for unveiling critical processes that lead to climate tipping points. Historically, statistical mechanics emerged as a tool to resolve the constraints on physics using statistics. We discuss how climate emulators rooted in statistical mechanics and machine learning can give rise to new climate models that are more reliable and require less observational and computational resources. Our goal is to stimulate discussion on how statistical climate emulators can further be improved with the help of statistical mechanics which, in turn, may reignite the interest of statistical community in statistical mechanics of complex systems
Physics perception in sloshing scenes with guaranteed thermodynamic consistency
Physics perception very often faces the problem that only limited data or
partial measurements on the scene are available. In this work, we propose a
strategy to learn the full state of sloshing liquids from measurements of the
free surface. Our approach is based on recurrent neural networks (RNN) that
project the limited information available to a reduced-order manifold so as to
not only reconstruct the unknown information, but also to be capable of
performing fluid reasoning about future scenarios in real time. To obtain
physically consistent predictions, we train deep neural networks on the
reduced-order manifold that, through the employ of inductive biases, ensure the
fulfillment of the principles of thermodynamics. RNNs learn from history the
required hidden information to correlate the limited information with the
latent space where the simulation occurs. Finally, a decoder returns data back
to the high-dimensional manifold, so as to provide the user with insightful
information in the form of augmented reality. This algorithm is connected to a
computer vision system to test the performance of the proposed methodology with
real information, resulting in a system capable of understanding and predicting
future states of the observed fluid in real-time.Comment: 20 pages, 11 figure
Symbiotic Ocean Modeling Using Physics-Controlled Echo State Networks
We introduce a “symbiotic” ocean modeling strategy that leverages data-driven and machine learning methods to allow high- and low-resolution dynamical models to mutually benefit from each other. In this work we mainly focus on how a low-resolution model can be enhanced within a symbiotic model configuration. The broader aim is to enhance the representation of unresolved processes in low-resolution models, while simultaneously improving the efficiency of high-resolution models. To achieve this, we use a grid-switching approach together with hybrid modeling techniques that combine linear regression-based methods with nonlinear echo state networks. The approach is applied to both the Kuramoto–Sivashinsky equation and a single-layer quasi-geostrophic ocean model, and shown to simulate short-term and long-term behavior better than either purely data-based methods or low-resolution models. By maintaining key flow characteristics, the hybrid modeling techniques are also able to provide higher quality initial conditions for high-resolution models, thereby improving their efficiency.</p
Symbiotic Ocean Modeling Using Physics-Controlled Echo State Networks
We introduce a “symbiotic” ocean modeling strategy that leverages data-driven and machine learning methods to allow high- and low-resolution dynamical models to mutually benefit from each other. In this work we mainly focus on how a low-resolution model can be enhanced within a symbiotic model configuration. The broader aim is to enhance the representation of unresolved processes in low-resolution models, while simultaneously improving the efficiency of high-resolution models. To achieve this, we use a grid-switching approach together with hybrid modeling techniques that combine linear regression-based methods with nonlinear echo state networks. The approach is applied to both the Kuramoto–Sivashinsky equation and a single-layer quasi-geostrophic ocean model, and shown to simulate short-term and long-term behavior better than either purely data-based methods or low-resolution models. By maintaining key flow characteristics, the hybrid modeling techniques are also able to provide higher quality initial conditions for high-resolution models, thereby improving their efficiency.</p
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