Latent Space Physics: Towards Learning the Temporal Evolution of Fluid Flow

Wiewel, Steffen; Becher, Moritz; Thuerey, Nils

doi:10.1111/cgf.13620

Cited by 204 publications

(174 citation statements)

References 51 publications

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“…Complete replacement of equations with ML algorithms for gaining computational efficiency when generalization is not a necessity (e.g., we refer to [318]- [325] and references cited therein for speeding up numerical solvers for real-time applications) can be used in the context of digital twin when the same process is to be monitored time and again. However, this approach will fail in unexpected situation because the model only learns to interpolate and not extrapolate.…”

Section: Nonintrusive Data-driven Modelingmentioning

confidence: 99%

Digital Twin: Values, Challenges and Enablers From a Modeling Perspective

2020

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A digital twin can be defined as an adaptive model of a complex physical system. Recent advances in computational pipelines, multiphysics solvers, artificial intelligence, big data cybernetics, data processing and management tools bring the promise of digital twins and their impact on society closer to reality. Digital twinning is now an important and emerging trend in many applications. Also referred to as a computational megamodel, device shadow, mirrored system, avatar or a synchronized virtual prototype, there can be no doubt that a digital twin plays a transformative role not only in how we design and operate cyber-physical intelligent systems, but also in how we advance the modularity of multi-disciplinary systems to tackle fundamental barriers not addressed by the current, evolutionary modeling practices. In this work, we review the recent status of methodologies and techniques related to the construction of digital twins. Our aim is to provide a detailed coverage of the current challenges and enabling technologies along with recommendations and reflections for various stakeholders.

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Section: Nonintrusive Data-driven Modelingmentioning

confidence: 99%

Digital Twin: Values, Challenges and Enablers From a Modeling Perspective

2020

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“…Given sufficient amounts of training data, such models, or regression neural networks, are capable of learning complex, non-linear mappings from a high-dimensional feature vector to a desired output. This property makes these models useful to solve novel kinds of problems also in fields such as physics and materials science [7][8][9][10][11][12][13] , and related activities have very recently gained significant momentum 14 .…”

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confidence: 99%

Machine learning plastic deformation of crystals

2018

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Plastic deformation of micron-scale crystalline solids exhibits stress-strain curves with significant sample-to-sample variations. It is a pertinent question if this variability is purely random or to some extent predictable. Here we show, by employing machine learning techniques such as regression neural networks and support vector machines that deformation predictability evolves with strain and crystal size. Using data from discrete dislocations dynamics simulations, the machine learning models are trained to infer the mapping from features of the pre-existing dislocation configuration to the stress-strain curves. The predictability vs strain relation is non-monotonic and exhibits a system size effect: larger systems are more predictable. Stochastic deformation avalanches give rise to fundamental limits of deformation predictability for intermediate strains. However, the large-strain deformation dynamics of the samples can be predicted surprisingly well.

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“…LSTM is a variant of recurrent neural networks capable of learning and predicting the temporal dependencies between the given data sequence based on the input information and previously acquired information. Recurrent neural networks have been used successfully in ROM community to enhance standard projection ROMs [89] and build fully non-intrusive ROMs [90][91][92][93][94][95]. In the present study, we use LSTMs to augment the standard physics-informed ROM by introducing closure as well as super-resolution data-driven models.…”

Section: Long Short-term Memory Embeddingmentioning

confidence: 99%

A long short-term memory embedding for hybrid uplifted reduced order models

Ahmed

San

Rasheed

et al. 2020

Physica D: Nonlinear Phenomena

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In this paper, we introduce an uplifted reduced order modeling (UROM) approach through the integration of standard projection based methods with long short-term memory (LSTM) embedding. Our approach has three modeling layers or components. In the first layer, we utilize an intrusive projection approach to model dynamics represented by the largest modes. The second layer consists of an LSTM model to account for residuals beyond this truncation. This closure layer refers to the process of including the residual effect of the discarded modes into the dynamics of the largest scales. However, the feasibility of generating a low rank approximation tails off for higher Kolmogorov n-width systems due to the underlying nonlinear processes. The third uplifting layer, called superresolution, addresses this limited representation issue by expanding the span into a larger number of modes utilizing the versatility of LSTM. Therefore, our model integrates a physics-based projection model with a memory embedded LSTM closure and an LSTM based super-resolution model. In several applications, we exploit the use of Grassmann manifold to construct UROM for unseen conditions. We performed numerical experiments by using the Burgers and Navier-Stokes equations with quadratic nonlinearity. Our results show robustness of the proposed approach in building reduced order models for parameterized systems and confirm the improved trade-off between accuracy and efficiency.Keywords Hybrid analysis and modeling · Supervised machine learning · Long short-term memory · Model reduction · Galerkin projection · Grassmann manifold.Reduced order models (ROMs) have shown great success for prototypical problems in different fields. In particular, Galerkin projection (GP) coupled with proper orthogonal decomposition (POD) capability to extract the most energetic modes has been used to build ROMs for linear and nonlinear systems [22][23][24][25][26][27][28][29]. These ROMs preserve sufficient arXiv:1912.06756v1 [physics.flu-dyn]

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Latent Space Physics: Towards Learning the Temporal Evolution of Fluid Flow

Cited by 204 publications

References 51 publications

Digital Twin: Values, Challenges and Enablers From a Modeling Perspective

Digital Twin: Values, Challenges and Enablers From a Modeling Perspective

Machine learning plastic deformation of crystals

A long short-term memory embedding for hybrid uplifted reduced order models

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