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Convolutional Neural Networks define an exceptionally powerful class of models, but are still limited by the lack of ability to be spatially invariant to the input data in a computationally and parameter efficient manner. In this work we…
Fourier Neural Operators (FNO) offer a principled approach to solving challenging partial differential equations (PDE) such as turbulent flows. At the core of FNO is a spectral layer that leverages a discretization-convergent representation…
Deep neural operators are recognized as an effective tool for learning solution operators of complex partial differential equations (PDEs). As compared to laborious analytical and computational tools, a single neural operator can predict…
We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks…
Neural Operators (NOs) have emerged as powerful tools for learning mappings between function spaces. Among them, the kernel integral operator has been widely used in universally approximating architectures. Following the original…
Inspired by the connectivity mechanisms in the brain, neuromorphic computing architectures model Spiking Neural Networks (SNNs) in silicon. As such, neuromorphic architectures are designed and developed with the goal of having small, low…
We present a novel application of neural networks to design improved mixing elements for single-screw extruders. Specifically, we propose to use neural networks in numerical shape optimization to parameterize geometries. Geometry…
Modelling complex multiphysics systems governed by nonlinear and strongly coupled partial differential equations (PDEs) is a cornerstone in computational science and engineering. However, it remains a formidable challenge for traditional…
Fourier neural operators (FNOs) are invariant with respect to the size of input images, and thus images with any size can be fed into FNO-based frameworks without any modification of network architectures, in contrast to traditional…
Image segmentation plays an important role in vision understanding. Recently, the emerging vision foundation models continuously achieved superior performance on various tasks. Following such success, in this paper, we prove that the…
We propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly…
Spiking Neural Networks (SNNs) currently face a critical bottleneck: while individual neurons exhibit dynamic biological properties, their macro-scopic architectures remain confined within conventional connectivity patterns that are static…
In this paper, we introduce a physics and geometry informed neural operator network with application to the forward simulation of acoustic scattering. The development of geometry informed deep learning models capable of learning a solution…
Brain morphology is shaped by genetic and mechanical factors and is linked to biological development and diseases. Its fractal-like features, regional anisotropy, and complex curvature distributions hinder quantitative insights in medical…
Neural operators have emerged as promising frameworks for learning mappings governed by partial differential equations (PDEs), serving as data-driven alternatives to traditional numerical methods. While methods such as the Fourier neural…
We propose, in this paper, a Variable Spiking Wavelet Neural Operator (VS-WNO), which aims to bridge the gap between theoretical and practical implementation of Artificial Intelligence (AI) algorithms for mechanics applications. With recent…
Shape compactness is a key geometrical property to describe interesting regions in many image segmentation tasks. In this paper, we propose two novel algorithms to solve the introduced image segmentation problem that incorporates a…
Geometric deep learning has sparked a rising interest in computer graphics to perform shape understanding tasks, such as shape classification and semantic segmentation. When the input is a polygonal surface, one has to suffer from the…
Recent research efforts in optical computing have gravitated towards developing optical neural networks that aim to benefit from the processing speed and parallelism of optics/photonics in machine learning applications. Among these…
The transfer of a robot skill between different geometric environments is non-trivial since a wide variety of environments exists, sensor observations as well as robot motions are high-dimensional, and the environment might only be…