A deep learning-based hybrid approach for the solution of multiphysics problems in electrosurgery

Han, Zhongqing; Rahul, *; De, Suvranu

doi:10.1016/j.cma.2019.112603

Cited by 21 publications

(11 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As we will see, these surrogate models allow us to seamlessly integrate multimodality or multi-fidelity data. We can also use neural networks to directly map pressure and topology as input onto the deformation field as output, for example to accelerate decision making in electrosurgery [42]. Finally, natural questions that machine learning can help us answer focus on sensitivity analysis [62] and uncertainty quantification [61,146].…”

Section: Motivationmentioning

confidence: 99%

Multiscale Modeling Meets Machine Learning: What Can We Learn?

Peng

Alber

Tepole³

et al. 2020

Arch Computat Methods Eng

Self Cite

222

103

View full text Add to dashboard Cite

Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate applications in diagnostics including electrophysiology, radiology, or pathology, where we have access to massive amounts of annotated data. However, machine learning often performs poorly in prognosis, especially when dealing with sparse data. This is a field where classical physics-based simulation seems to remain irreplaceable. In this review, we identify areas in the biomedical sciences where machine learning and multiscale modeling can mutually benefit from one another: Machine learning can integrate physics-based knowledge in the form of governing equations, boundary conditions, or constraints to manage ill-posted problems and robustly handle sparse and noisy data; multiscale modeling can integrate machine learning to create surrogate models, identify system dynamics and parameters, analyze sensitivities, and quantify uncertainty to bridge the scales and understand the emergence of function. With a view towards applications in the life sciences, we discuss the state of the art of combining machine learning and multiscale modeling, identify applications and opportunities, raise open questions, and address potential challenges and limitations. This review serves as introduction to a special issue on Uncertainty Quantification, Machine Learning, and Data-Driven Modeling of Biological Systems that will help identify current roadblocks and areas where computational mechanics, as a discipline, can play a significant role. We anticipate that it will stimulate discussion within the community of computational mechanics and reach out to other disciplines including mathematics, statistics, computer science, artificial intelligence, biomedicine, systems biology, and precision medicine to join forces towards creating robust and efficient models for biological systems.

show abstract

Section: Motivationmentioning

confidence: 99%

Multiscale Modeling Meets Machine Learning: What Can We Learn?

Peng

Alber

Tepole³

et al. 2020

Arch Computat Methods Eng

Self Cite

222

103

View full text Add to dashboard Cite

show abstract

“…For instance, machine learning techniques are employed in model order reduction [2,3], and dynamic model decomposition [4]. Specifically, convolutional neural networks (CNN) are often applied in computational problems [5][6][7]. The combination of techniques from computational mathematics and ANN has resulted in interesting contributions for both fields, since the theoretical results from classical approximation theory can be used to derive results on the approximation properties of ANN [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Locally refined quad meshing for linear elasticity problems based on convolutional neural networks

Chan

Scholz

Takacs

2022

Engineering with Computers

View full text Add to dashboard Cite

In this paper we propose a method to generate suitably refined finite element meshes using neural networks. As a model problem we consider a linear elasticity problem on a planar domain (possibly with holes) having a polygonal boundary. We impose boundary conditions by fixing the position of a part of the boundary and applying a force on another part of the boundary. The resulting displacement and distribution of stresses depend on the geometry of the domain and on the boundary conditions. When applying a standard Galerkin discretization using quadrilateral finite elements, one usually has to perform adaptive refinement to properly resolve maxima of the stress distribution. Such an adaptive scheme requires a local error estimator and a corresponding local refinement strategy. The overall costs of such a strategy are high. We propose to reduce the costs of obtaining a suitable discretization by training a neural network whose evaluation replaces this adaptive refinement procedure. We set up a single network for a large class of possible domains and boundary conditions and not on a single domain of interest. The computational domain and boundary conditions are interpreted as images, which are suitable inputs for convolution neural networks. In our approach we use the U-net architecture and we devise training strategies by dividing the possible inputs into different categories based on their overall geometric complexity. Thus, we compare different training strategies based on varying geometric complexity. One of the advantages of the proposed approach is the interpretation of input and output as images, which do not depend on the underlying discretization scheme. Another is the generalizability and geometric flexibility. The network can be applied to previously unseen geometries, even with different topology and level of detail. Thus, training can easily be extended to other classes of geometries.

show abstract

“…In recent years, advances in deep learning have attracted drastic attention to the field of computational modeling and simulation of physical systems, thanks to the rich representations of deep neural networks (DNNs) for learning complex nonlinear functions. Latest studies that leverage DNNs for physical modeling branch into two streams: (1) the use of experimental or computationallygenerated data to create coarse-graining reduced-fidelity or surrogate models [3][4][5][6][7], and (2) physicsinformed neural network (PINN) for modeling the solution of partial differential equations (PDEs) that govern the behavior of physical systems [8][9][10]. The former requires rich and sufficient data to learn a reliable generative model and typically fails to satisfy physical constraints, whereas the latter relies only on small or even zero labeled datasets and enables data-scarce, physics-constrained learning.…”

Section: Introductionmentioning

confidence: 99%

Physics informed deep learning for computational elastodynamics without labeled data

Rao

Sun

Liu

2020

Preprint

View full text Add to dashboard Cite

Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical methods is how they approximate the physical fields of interest. Physics-informed deep learning (PIDL) is a novel approach developed in recent years for modeling PDE solutions and shows promise to solve computational mechanics problems without using any labeled data (e.g., measurement data is unavailable). The philosophy behind it is to approximate the quantity of interest (e.g., PDE solution variables) by a deep neural network (DNN) and embed the physical law to regularize the network. To this end, training the network is equivalent to minimization of a well-designed loss function that contains the residuals of the governing PDEs as well as initial/boundary conditions (I/BCs). In this paper, we present a physicsinformed neural network (PINN) with mixed-variable output to model elastodynamics problems without resort to the labeled data, in which the I/BCs are hardly imposed. In particular, both the displacement and stress components are taken as the DNN output, inspired by the hybrid finite element analysis, which largely improves the accuracy and the trainability of the network. Since the conventional PINN framework augments all the residual loss components in a "soft" manner with Lagrange multipliers, the weakly imposed I/BCs cannot not be well satisfied especially when complex I/BCs are present. To overcome this issue, a composite scheme of DNNs is established based on multiple single DNNs such that the I/BCs can be satisfied forcibly in a "hard" manner. The propose PINN framework is demonstrated on several numerical elasticity examples with different I/BCs, including both static and dynamic problems as well as wave propagation in truncated domains. Results show the promise of PINN in the context of computational mechanics applications.

show abstract

A deep learning-based hybrid approach for the solution of multiphysics problems in electrosurgery

Cited by 21 publications

References 27 publications

Multiscale Modeling Meets Machine Learning: What Can We Learn?

Multiscale Modeling Meets Machine Learning: What Can We Learn?

Locally refined quad meshing for linear elasticity problems based on convolutional neural networks

Physics informed deep learning for computational elastodynamics without labeled data

Contact Info

Product

Resources

About