Machine learning and serving of discrete field theories

Qin, Hong

doi:10.1038/s41598-020-76301-0

Cited by 28 publications

(15 citation statements)

References 69 publications

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“…[115,117], or complex models may have learned something that is not semantic for humans, e.g. [94,106]. Interpretations are needed here for a completely different objective: finding new intelligent patterns that are not yet understandable in the present.…”

Section: Remarksmentioning

confidence: 99%

Interpretable Deep Learning: Interpretation, Interpretability, Trustworthiness, and Beyond

Li¹,

Xiong²,

Li³

et al. 2021

Preprint

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Deep neural networks have been well-known for their superb performance in handling various machine learning and artificial intelligence tasks. However, due to their over-parameterized black-box nature, it is often difficult to understand the prediction results of deep models. In recent years, many interpretation tools have been proposed to explain or reveal the ways that deep models make decisions. In this paper, we review this line of research and try to make a comprehensive survey. Specifically, we introduce and clarify two basic conceptsinterpretations and interpretability-that people usually get confused. First of all, to address the research efforts in interpretations, we elaborate the design of several recent interpretation algorithms, from different perspectives, through proposing a new taxonomy. Then, to understand the results of interpretation, we also survey the performance metrics for evaluating interpretation algorithms. Further, we summarize the existing work in evaluating models' interpretability using "trustworthy" interpretation algorithms. Finally, we review and discuss the connections between deep models' interpretations and other factors, such as adversarial robustness and data augmentations, and we introduce several open-source libraries for interpretation algorithms and evaluation approaches.

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Section: Remarksmentioning

confidence: 99%

Interpretable Deep Learning: Interpretation, Interpretability, Trustworthiness, and Beyond

Li¹,

Xiong²,

Li³

et al. 2021

Preprint

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show abstract

“…The combination of deep learning and differential equations has been well known for a long time and investigated in more abstract forms (Lee and Kang 1990;Meade Jr and Fernandez 1994;Lagaris et al 1998Lagaris et al , 2000. Using this approach, various authors proposed to use the Navier-Stokes equation (Raissi et al 2017a;Chu et al 2021), Schroedinger equation (Raissi et al 2017b), Burgers Equation (Holl et al 2020), Hamilton's equation (Greydanus et al 2019;Zhong et al 2019;Chen et al 2019;Toth et al 2019) or the Euler-Lagrange equation Qin 2020;Cranmer et al 2020;Gupta et al 2019).…”

Section: Physics-inspired Deep Networkmentioning

confidence: 99%

Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models

Lutter¹,

Peters²

2021

Preprint

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Deep learning has been widely used within learning algorithms for robotics. One disadvantage of deep networks is that these networks are black-box representations. Therefore, the learned approximations ignore the existing knowledge of physics or robotics. Especially for learning dynamics models, these black-box models are not desirable as the underlying principles are well understood and the standard deep networks can learn dynamics that violate these principles. To learn dynamics models with deep networks that guarantee physically plausible dynamics, we introduce physics-inspired deep networks that combine first principles from physics with deep learning. We incorporate Lagrangian mechanics within the model learning such that all approximated models adhere to the laws of physics and conserve energy. Deep Lagrangian Networks (DeLaN) parametrize the system energy using two networks. The parameters are obtained by minimizing the squared residual of the Euler-Lagrange differential equation. Therefore, the resulting model does not require specific knowledge of the individual system, is interpretable, and can be used as a forward, inverse, and energy model. Previously these properties were only obtained when using system identification techniques that require knowledge of the kinematic structure. We apply DeLaN to learning dynamics models and apply these models to control simulated and physical rigid body systems. The results show that the proposed approach obtains dynamics models that can be applied to physical systems for real-time control. Compared to standard deep networks, the physics-inspired models learn better models and capture the underlying structure of the dynamics.

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“…Squire, Qin & Tang (2012 a , b ) first employed the methodology of discrete variational principle (Lee 1983; Veselov 1988; Marsden & West 2001; Qin & Guan 2008; Qin, Guan & Tang 2009; Qin 2020) to derive an electromagnetic PIC algorithm on an unstructured mesh. In that work, the technique of Whitney forms (Whitney 1957) was introduced for the first time to deposit charge and current and to interpolate fields.…”

Section: Introductionmentioning

confidence: 99%

Geometric electrostatic particle-in-cell algorithm on unstructured meshes

et al. 2021

Self Cite

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We present a geometric particle-in-cell (PIC) algorithm on unstructured meshes for studying electrostatic perturbations with frequency lower than electron gyrofrequency in magnetized plasmas. In this method, ions are treated as fully kinetic particles and electrons are described by the adiabatic response. The PIC method is derived from a discrete variational principle on unstructured meshes. To preserve the geometric structure of the system, the discrete variational principle requires that the electric field is interpolated using Whitney 1-forms, the charge is deposited using Whitney 0-forms and the electric field is computed by discrete exterior calculus. The algorithm has been applied to study the ion Bernstein wave (IBW) in two-dimensional magnetized plasmas. The simulated dispersion relations of the IBW in a rectangular region agree well with theoretical results. In a two-dimensional circular region with fixed boundary condition, the spectrum and eigenmode structures of the IBW are obtained from simulations. We compare the energy conservation property of the geometric PIC algorithm derived from the discrete variational principle with that of previous PIC methods on unstructured meshes. The comparison shows that the new PIC algorithm significantly improves the energy conservation property.

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Machine learning and serving of discrete field theories

Cited by 28 publications

References 69 publications

Interpretable Deep Learning: Interpretation, Interpretability, Trustworthiness, and Beyond

Interpretable Deep Learning: Interpretation, Interpretability, Trustworthiness, and Beyond

Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models

Geometric electrostatic particle-in-cell algorithm on unstructured meshes

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