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We introduce the Neural Hodge Corrective Solver (NHCS), a hybrid iterative-neural framework for partial differential equations that embeds learned corrective operators within the Discrete Exterior Calculus (DEC) formulation. The method…

Nonlinear partial differential equations (PDEs) are crucial for modeling complex fluid dynamics and are foundational to many computational fluid dynamics (CFD) applications. However, solving these nonlinear PDEs is challenging due to the…

A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, and…

Recent years have witnessed the growing popularity of domain-specific accelerators (DSAs), such as Google's TPUs, for accelerating various applications such as deep learning, search, autonomous driving, etc. To facilitate DSA designs,…

Demixing problems in many areas such as hyperspectral imaging and differential optical absorption spectroscopy (DOAS) often require finding sparse nonnegative linear combinations of dictionary elements that match observed data. We show how…

We present Unified PDE Solvers (UPS), a data- and compute-efficient approach to developing unified neural operators for diverse families of spatiotemporal PDEs from various domains, dimensions, and resolutions. UPS embeds different PDEs…

Artificial intelligence has advanced rapidly through large neural networks trained on massive datasets using thousands of GPUs or TPUs. Such training can occupy entire data centers for weeks and requires enormous computational and energy…

Hardware accelerators are key to the efficiency and performance of system-on-chip (SoC) architectures. With high-level synthesis (HLS), designers can easily obtain several performance-cost trade-off implementations for each component of a…

Polyspectral estimation is a problem of great importance in the analysis of nonlinear time series that has applications in biomedical signal processing, communications, geophysics, image, radar, sonar and speech processing, etc. Higher…

Recent years have witnessed the promise of coupling machine learning methods and physical domain-specific insights for solving scientific problems based on partial differential equations (PDEs). However, being data-intensive, these methods…

Semantic segmentation of 3D point cloud scenes is a crucial task for various applications. In real-world scenarios, training segmentation models often faces three concurrent forms of data insufficiency: scarcity of training scenes, scarcity…

In this paper, we propose a novel $hr$-adaptive finite element method, enhanced by neural networks, for parabolic equations. The main challenge of the conventional $h$-adaptive finite element method is interpolating the finite element…

Scaling deep neural network (DNN) training to more devices can reduce time-to-solution. However, it is impractical for users with limited computing resources. FOSI, as a hybrid order optimizer, converges faster than conventional optimizers…

A new generation of manycore processors is on the rise that offers dozens and more cores on a chip and, in a sense, fuses host processor and accelerator. In this paper we target the efficient training of generalized linear models on these…

In this paper we propose an efficient deep learning encoder-decoder network for performing Harmonic-Percussive Source Separation (HPSS). It is shown that we are able to greatly reduce the number of model trainable parameters by using a…

The employment of high-performance servers and GPU accelerators for training deep neural network models have greatly accelerated recent advances in deep learning (DL). DL frameworks, such as TensorFlow, MXNet, and Caffe2, have emerged to…

This study introduces the Homotopy Perturbation Sumudu Transform Method (HPSTM), a novel hybrid approach combining the Sumudu transform with homotopy perturbation to solve nonlinear fractional partial differential equations (FPDEs),…

Deep Neural Networks (DNN) applications are increasingly becoming a part of our everyday life, from medical applications to autonomous cars. Traditional validation of DNN relies on accuracy measures, however, the existence of adversarial…

In real world clinical environments, training and applying deep learning models on multi-modal medical imaging data often struggles with partially incomplete data. Standard approaches either discard missing samples, require imputation or…

Physiological signals are inherently heterogeneous: they are collected under diverse acquisition setups, differ in the number and type of modalities and channels, varying in quality, reliability, and relevance across tasks. This variability…