We propose the geometry-informed neural operator (GINO), a highly efficient approach to learning the solution operator of large-scale partial differential equations with varying geometries. GINO uses a signed distance function and point-cloud representations of the input shape and neural operators based...
The minimization problem of the generator reduces to minimizing a Jensen Shannon divergence between the data distribution and the generated distribution. With sufficient expressive power in the neural network structures, it is guaranteed to converge to the global optimal where the data distribution is ex...
[docs]classGeometry:"""Base class for all geometries"""def__init__(self,curves,sdf,dims,bounds,parameterization=Parameterization(),interior_epsilon=1e-6,):# store attributesself.curves=curvesself.sdf=sdfself._dims=dimsself.bounds=boundsself.parameterization=parameterizationself.interior_epsilon=interio...
Informed consent was obtained from all participants, who were compensated for participation after the experiment. All participants were classified as American Society of Anesthesiologists physical status 1. Before the study, participants fasted for eight hours. An attending anesthesiologist performed a ...
We use a physics-informed neural network (PINN) to simultaneously model and optimize the flow around an airfoil to maximize its lift to drag ratio. The parameters of the airfoil shape are provided as inputs to the PINN and the multidimensional search space of shape parameters is populated with...
Using Eq. (19), the Adam optimiser performed manufacturability-informed gradient-based updates of z at each iteration to minimise Eq. (13). (19)∂Ltask2∂z=∂∂z1|V|∑v∈Vαv∂LconstraintMz∂fθ1z,v⋅fθ1z,v+Lsimilarityz+Llatentz 5.2.3. Optimisation results Two ...
Deep learning neural networks have been used to model turbulent fluid flow [16]. Unlike a “black box” solution, however, differential geometry offers a more general mathematical account of turbulent flow that can provide an understanding of the underlying physical phenomena. 5.5. Protein Folding ...
Deep learning neural networks have been used to model turbulent fluid flow [16]. Unlike a “black box” solution, however, differential geometry offers a more general mathematical account of turbulent flow that can provide an understanding of the underlying physical phenomena. 5.5. Protein Folding ...
The deep learning models then utilize this matrix ΦΦ to perform clustering tasks by feeding the matrix into a neural network. This matrix, which encapsulates the eigenvectors of the Laplace–Beltrami operator, serves as a rich, high-dimensional representation of the molecular surfaces. Through this...
They presented several case studies demonstrating the successful implementation of deep learning techniques, such as convolutional neural networks and recurrent neural networks, in detecting and classifying structural damage. This research underscores the importance of leveraging interdisciplinary methodologies and...