Efficient computation of nonlinear isogeometric elements using the adjoint method and algorithmic differentiation

Abstract. This work focuses on the numerical assessment of the accuracy of an adjoint-based gradient in the perspective of variational data assimilation and parameter identification in glaciology. Using noisy synthetic data, we quantify the ability to identify the friction coefficient for such methods with a non-linear friction law. The exact adjoint problem is solved, based on second-order numerical schemes, and a comparison with the so-called "self-adjoint" approximation, neglecting the viscosity dependence on the velocity (leading to an incorrect gradient), common in glaciology, is carried out. For data with a noise of 1%, a lower bound of identifiable wavelengths of 10 ice thicknesses in the friction coefficient is established, when using the exact adjoint method, while the "self-adjoint" method is limited, even for lower noise, to a minimum of 20 ice thickness wavelengths. The second-order exact gradient method therefore provides robustness and reliability for the parameter identification process. In another respect, the derivation of the adjoint model using algorithmic differentiation leads to the formulation of a generalization of the "self-adjoint" approximation towards an incomplete adjoint method, adjustable in precision and computational burden.

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Expansion of the Nodal-Adjoint Method for Simple and Efficient Computation of the 2D Tomographic Imaging Jacobian Matrix

Sensors ◽

10.3390/s21030729 ◽

2021 ◽

Vol 21 (3) ◽

pp. 729

Author(s):

Samar Hosseinzadegan ◽

Andreas Fhager ◽

Mikael Persson ◽

Shireen Geimer ◽

Paul Meaney

Keyword(s):

Adjoint Method ◽

Jacobian Matrix ◽

Imaging System ◽

Computational Cost ◽

Computation Time ◽

Dipole Approximation ◽

Discrete Dipole Approximation ◽

Efficient Computation ◽

Reconstruction Algorithms ◽

Reconstruction Process

This paper focuses on the construction of the Jacobian matrix required in tomographic reconstruction algorithms. In microwave tomography, computing the forward solutions during the iterative reconstruction process impacts the accuracy and computational efficiency. Towards this end, we have applied the discrete dipole approximation for the forward solutions with significant time savings. However, while we have discovered that the imaging problem configuration can dramatically impact the computation time required for the forward solver, it can be equally beneficial in constructing the Jacobian matrix calculated in iterative image reconstruction algorithms. Key to this implementation, we propose to use the same simulation grid for both the forward and imaging domain discretizations for the discrete dipole approximation solutions and report in detail the theoretical aspects for this localization. In this way, the computational cost of the nodal adjoint method decreases by several orders of magnitude. Our investigations show that this expansion is a significant enhancement compared to previous implementations and results in a rapid calculation of the Jacobian matrix with a high level of accuracy. The discrete dipole approximation and the newly efficient Jacobian matrices are effectively implemented to produce quantitative images of the simplified breast phantom from the microwave imaging system.

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Inverse design and flexible parameterization of meta-optics using algorithmic differentiation

Communications Physics ◽

10.1038/s42005-021-00568-6 ◽

2021 ◽

Vol 4 (1) ◽

Author(s):

Shane Colburn ◽

Arka Majumdar

Keyword(s):

Adjoint Method ◽

Optical Design ◽

Design Parameters ◽

Wave Analysis ◽

Algorithmic Differentiation ◽

Rigorous Coupled Wave Analysis ◽

And Topology ◽

Rigorous Coupled Wave ◽

The Cost ◽

Application Specific

AbstractUltrathin meta-optics offer unmatched, multifunctional control of light. Next-generation optical technologies, however, demand unprecedented performance. This will likely require design algorithms surpassing the capability of human intuition. For the adjoint method, this requires explicitly deriving gradients, which is sometimes challenging for certain photonics problems. Existing techniques also comprise a patchwork of application-specific algorithms, each focused in scope and scatterer type. Here, we leverage algorithmic differentiation as used in artificial neural networks, treating photonic design parameters as trainable weights, optical sources as inputs, and encapsulating device performance in the loss function. By solving a complex, degenerate eigenproblem and formulating rigorous coupled-wave analysis as a computational graph, we support both arbitrary, parameterized scatterers and topology optimization. With iteration times below the cost of two forward simulations typical of adjoint methods, we generate multilayer, multifunctional, and aperiodic meta-optics. As an open-source platform adaptable to other algorithms and problems, we enable fast and flexible meta-optical design.

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Of the gradient accuracy in Full-Stokes ice flow model: basal slipperiness inference

The Cryosphere Discussions ◽

10.5194/tcd-7-3853-2013 ◽

2013 ◽

Vol 7 (4) ◽

pp. 3853-3897 ◽

Cited By ~ 1

Author(s):

N. Martin ◽

J. Monnier

Keyword(s):

Parameter Identification ◽

Adjoint Method ◽

Adjoint Problem ◽

The Self ◽

Ice Thickness ◽

Adjoint Model ◽

Ice Flow ◽

Algorithmic Differentiation ◽

Numerical Assessment ◽

Linear Friction

Abstract. This work focuses on the numerical assessment of the accuracy of an adjoint-based gradient in the perspective of variational data assimilation and parameter identification in glaciology. We quantify the ability to identify the basal slipperiness for such methods with a non-linear friction law. The complete adjoint problem is solved and a comparison with the so called "self-adjoint" method, neglecting the viscosity dependency to the velocity, common in glaciology, is carried out. A lower bound of identifiable wavelengths of 10 ice thickness in the friction coefficient is established, when using the full adjoint method, while the "self-adjoint" method is limited to a maximum of 20 ice thickness wavelengths. In addition, the full adjoint method demonstrates a better robustness and reliability for the parameter identification process. The derivation of the adjoint model using algorithmic differentiation leads to formulate a generalization of the "self-adjoint" approximation towards an incomplete adjoint method, adjustable in precision and computational burden.

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No fear of George Kingsley Zipf

Instructed Second Language Acquisition ◽

10.1558/37291 ◽

2018 ◽

Vol 2 (2) ◽

pp. 242-263

Author(s):

Stefano Rastelli ◽

Kook-Hee Gil

Keyword(s):

Minimalist Program ◽

Classroom Research ◽

Language Design ◽

Efficient Computation ◽

Generative Linguistics ◽

The Third ◽

Factor Effect ◽

Language Classroom ◽

Recent Developments ◽

Insight Into

This paper offers a new insight into GenSLA classroom research in light of recent developments in the Minimalist Program (MP). Recent research in GenSLA has shown how generative linguistics and acquisition studies can inform the language classroom, mostly focusing on what linguistic aspects of target properties should be integrated as a part of the classroom input. Based on insights from Chomsky’s ‘three factors for language design’ – which bring together the Faculty of Language, input and general principles of economy and efficient computation (the third factor effect) for language development – we put forward a theoretical rationale for how classroom research can offer a unique environment to test the learnability in L2 through the statistical enhancement of the input to which learners are exposed.

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