H-Analysis and data-parallel physics-informed neural networks

Most Computational Fluid Dynamics (CFD) applications solve the Naiver-Stokes equations using various discretization methods like Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), etc. The most compute-intensive process in CFD algorithms is the pressure Poisson solver. Solving the pressure Poisson equation requires the solution of a set of linear simultaneous equations. As the problem size/complexity increases, so does the effort and time invested in solving the equations. This study presents fast and robust iterative solvers and the acceleration of the same using the Graphics Processing Unit (GPU) architecture. Serial versions of the codes are implemented in the C language and the parallelization on GPU is achieved using Compute Unified Device Architecture (CUDA). For this study, a two-dimensional heat conduction problem is considered. FDM is used for discretization. Iterative solvers Conjugate Gradient and Multi Grid methods have been implemented in serial and parallel. The performance enhancement with single GPU and CPU system over a single CPU in terms of computing time is reported. It is seen that multigrid algorithms are superior in convergence and nearly 13 times speed-up has been obtained through GPU acceleration using CUDA, for a grid size of 2048 X 2048. The tests have been done on a cluster with Intel(R) Xeon(R) CPU E5-2670 CPU and NVIDIA K10 GPU.

A direct simulation Monte Carlo (DSMC) method is implemented on graphical processing unit (GPU) architecture to simulate the deposition phenomena that occur on a glass panel during modern organic light emitting diodes (OLED) manufacturing processes with a huge number of simulated particles because a fully three-dimensional (3D) particle simulation is required to accurately predict deposition thickness and uniformity on the substrate in a low-pressure environment. To examine the accuracy and efficiency of the newly developed DSMC code running on GPU architecture, verification and validation tests were performed by solving several benchmarking problems. Under three conditions which have been applied in previous OLED deposition process test experiments, the new DSMC model successfully simulates the transport of organic material evaporated from the heated nozzle array and its deposition onto a glass panel inside a low-pressure chamber. The uniformity and normalized thickness between the DSMC and experimental results for the three test cases are then compared. The normalized thickness of the organic material deposited to the large glass panel calculated from the DSMC is found to have an error of less than 4%, and the uniformity values calculated from the absolute deposition thickness show good agreement with those obtained from experimental data in all test cases.

Self-induced stochastic resonance (SISR) is the emergence of coherent oscillations in slow-fast excitable systems driven solely by noise, without external periodic forcing or proximity to a bifurcation. This work presents a physics-informed machine learning framework for modeling and predicting SISR in the stochastic FitzHugh–Nagumo neuron. We embed the governing stochastic differential equations and SISR-asymptotic timescale-matching constraints directly into a Physics-Informed Neural Network (PINN) based on a Noise-Augmented State Predictor architecture. The composite loss integrates data fidelity, dynamical residuals, and barrier-based physical constraints derived from Kramers’ escape theory. The trained PINN accurately predicts the dependence of spike-train coherence on noise intensity, excitability, and timescale separation, matching results from direct stochastic simulations with substantial improvements in accuracy and generalization compared with purely data-driven methods, requiring significantly less computation. The framework provides a data-efficient and interpretable surrogate model for simulating and analyzing noise-induced coherence in multiscale stochastic systems. • A physics-informed neural network that learns stochastic dynamics directly. • Noise-Augmented State Predictor (NASP) for data-efficient multiscale modeling. • Predicts noise-driven oscillations and coherence from short trajectory data. • Shown on self-induced stochastic resonance in FitzHugh–Nagumo neuron model.

We present a spectral crystal plasticity (CP) solver for graphics processing unit (GPU) architectures that achieves a tenfold increase in efficiency over prior GPU solvers. The approach makes use of a database containing a spectral decomposition of CP simulations performed using a conventional iterative solver over a parameter space of crystal orientations and applied velocity gradients. The key improvements in efficiency come from reducing global memory transactions, exposing more instruction-level parallelism, reducing integer instructions and performing fast range reductions on trigonometric arguments. The scheme also makes more efficient use of memory than prior work, allowing for larger problems to be solved on a single GPU. We illustrate these improvements with a simulation of 390 million crystal grains on a consumer-grade GPU, which executes at a rate of 2.72 s per strain step.

This study presents a comprehensive nowcasting and forecasting approach for ionospheric peak parameters, including foF2, NmF2, and TEC, using a Physics Informed Neural Network (PINN). This approach integrates multiple datasets, utilizing extensive ground-based ionosonde station measurements and COSMIC satellite observations to model and predict these parameters in relation to ionospheric conditions and space weather dynamics.Our work also explores the response of ionospheric peak parameters to extreme solar eruptions and geomagnetic storms, providing critical insights into the behaviour of the ionosphere under these challenging conditions. The PINN incorporates fundamental physical laws as constraints, including the Chapman function, continuity equation, ion production rates as a function of F10.7, recombination reactions, geomagnetic and electric fields, and Abel inversion effects. Our model utilizes a comprehensive set of input features, including COSMIC satellite foF2, NmF2, TEC measurements, temporal and spatial parameters, and various solar and geomagnetic indices. Data normalization and a deep neural network architecture with multiple dense layers and batch normalization were employed to capture complex, non-linear relationships in the ionospheric data. These constraints enable highly accurate predictions  achieving a high average correlation of 0.92 between COSMIC satellite and ionosonde measurements.A detailed random forest parameter importance analysis identified key contributors to ionospheric variability, revealing that atmospheric dynamics (meridional and zonal winds) and solar activity (notably F10.7) play dominant roles. Spatial and temporal factors were also considered critical compared to other space weather parameters.These findings highlight the potential of physics-informed machine learning as a robust tool for advancing our understanding of ionospheric behaviour and improving predictive capabilities for space weather applications. Furthermore, this study underscores the value of integrating ground- and space-based observations with physical principles to achieve accurate and reliable forecasts of ionospheric peak parameters.

The architecture of the latest Graphic Processing Unit (GPU) has surpassed the previous application-specific stream architecture. This has led to an architecture consisting of a number of uniform programmable units integrated on the same chip which facilitate the general-purpose computing beyond the graphic processing. With the multiple programmable units executing in parallel, the latest GPU shows superior performance. Furthermore, programmers can have a direct control on the GPU pipeline using easy-to-use parallel programming environments, whereas they had to rely on specific graphics API's in the past. These advances in hardware and software make General-Purpose GPU (GPGPU) computing widespread. In this paper, using the latest GPU and its software environment, we parallelize a computationally demanding financial application and optimize its performance. We also analyze the performance results compared with those obtained using CPU only. Experimental results show that GPU can achieve a superior performance, greater than 190x, compared with the CPU-only case.

Physics-informed machine learning models for ship speed prediction

Direct numerical simulations of supersonic compression-expansion slope with a multi-GPU parallel algorithm

Humans have main senses: sight, hearing, touch, smell, and taste. Most of them combine several aspects. For example vision addresses at least three perceptual modalities: motion, color, and luminance. Extraction of these modalities begins in the human eye in the retinal network and the preprocessed signals enter the brain as streams of spatio-temporal patterns. As vision is our main sense, particularly for the perception of the three dimensional structure of the world around us, major eorts have been made to understand and simulate the visual system based on the knowledge collected to date. The research done over the last decades in elds of image processing and computer vision coupled with a tremendous step forward in hardware for parallel computing opened the door to building of so-called cognitive vision systems and for their incorporation into robots. The goal of any cognitive vision system is to transform visual input information into more descriptive representations than just color, motion, or luminance. Furthermore, in most robotic systems \live" interactions of robots with the environment are required, greatly increasing demands on the system. In such systems all pre-computations of the visual data need to be performed in real-time in order to be able to use the output data in the perception-action loop. Thus, a central goal of this thesis is to provide techniques which are strictly compatible with real-time computation. In the first part of this thesis we investigate possibilities for the powerful compression of the initial visual input data into symbol-like descriptors, upon which abstract logic or learning schemes can be applied. We introduce a new real-time video segmentation framework performing automatic decomposition of monocular and stereo video streams without use of prior knowledge on data and considering only preceding information. All entities in the scene, representing objects or their parts, are uniquely identied. In the second part of the thesis we make additional use of stereoscopic visual information and address the problem of establishing correspondences between two views of the scene solved with apparent ease in the human visual system (for images acquired with left and right eye). We exploit these correspondences in the stereo image pairs for the estimation of depth (distance) by proposing a novel disparity measurement technique based on extracted stereo-segments. This technique approximates shape and computes depth information for all entities found in the scene. The most important and novel achievement of this approach is that it produces reliable depth information for objects with weak texture where performance of traditional stereo techniques is very poor. In the third part of this thesis we employ an active sensor, producing indoors much more precise depth information encoded as range-data than any passive stereo technique. We perform fusion of image and range data for video segmentation which results in better results. By this we can now even handle fast moving objects, which was not possible so far. To address the real-time constraint, the proposed segmentation framework was accelerated on a Graphics Processing Unit (GPU) architecture using the parallel programming model of Compute Uni ed Device Architecture (CUDA). All introduced methods: segmentation of single images, segmentation of monocular and stereo video streams, depth-supported video segmentation, and disparity computation from stereosegment correspondences run in real-time for middle-size images and close to real-time for higher resolutions. In summary: The main result of this thesis is a framework which can produce a compact representation of any visual scene where all meaningful entities are uniquely identied, tracked, and important descriptors, such as shape and depth information, are extracted. The ability of the framework was successfully demonstrated in the context of several European projects (PACO-PLUS, Garnics, IntellAct, and Xperience). The developed real-time system is now employed as a robust visual front-end in various real-time robotic systems.

Parallelizing software applications through the use of existing optimized primitives is a common trend that mediates the complexity of manual parallelization and the use of less efficient directivebased programming models. Parallel primitive libraries allow software engineers to map any sequential code to a target many-core architecture by identifying the most computational intensive code sections and mapping them into one or more existing primitives. On the other hand, the spreading of such a primitivebased programming model and the different graphic processing unit (GPU) architectures has led to a large and increasing number of third-party libraries, which often provide different implementations of the same primitive, each one optimized for a specific architecture. From the developer point of view, this moves the actual problem of parallelizing the software application to selecting, among the several implementations, the most efficient primitives for the target platform. This paper presents Pro++, a profiling framework for GPU primitives that allows measuring the implementation quality of a given primitive by considering the target architecture characteristics. The framework collects the information provided by a standard GPU profiler and combines them into optimization criteria. The criteria evaluations are weighed to distinguish the impact of each optimization on the overall quality of the primitive implementation. This paper shows how the tuning of the different weights has been conducted through the analysis of five of the most widespread existing primitive libraries and how the framework has been eventually applied to improve the implementation performance of two standard and widespread primitives.

Passive bistatic radar is a novel radar technology that passively detects targets without actively emitting signals. Since passive bistatic radar entails larger data volumes and computations compared to traditional active radiation radar, the development of hardware and software platforms capable of efficiently processing signals from passive bistatic radar has emerged as a research focus in this field. This research investigates the signal processing flow of passive bistatic radar based on its characteristics and devises a parallel signal processing scheme under graphic processing unit (GPU) architecture for computation-intensive tasks. The proposed scheme utilizes high-computing-power GPU as the hardware platform and compute unified device architecture (CUDA) as the software platform and optimizes the extensive cancellation algorithm batches (ECA-B), range Doppler and constant false alarm detection algorithms. The detection and tracking of a single target are realized on the passive bistatic radar dataset of natural scenarios, and experiments show that the design of this algorithm can achieve a maximum acceleration ratio of 113.13. Comparative experiments conducted with varying data volumes revealed that this method significantly enhances the signal processing rate for passive bistatic radar.

Introduction: The evolution of precision oncology will demand the integration of multi-omics, clinical data, demographics and outcomes, which is a complex and computationally intensive endeavor. Accurate and robust molecular characterization of pediatric leukemias require a comprehensive approach involving longitudinal sample collection across a large cohort. Genomic alterations, both germline and somatic, need to be efficiently captured and annotated to identify clinically meaningful trends. Algorithms developed for conducting genomic analysis typically leverage a central processing unit (CPU) environment for data processing and traditional statistical approach, such as Bayes' theorem, for variant detection. More recently, algorithms have been developed that can leverage a graphics processing unit (GPU) architecture and machine learning (ML) technology. In this study we benchmarked these techniques and applied them sequencing data generated from pediatric AML subjects enrolled on the Children's Oncology Group AAML1031 trial (951 samples). Methods: Whole genome sequencing was conducted using the Illumina platform (2X150) and sequenced between 30x-60x coverage. Genome alignment files were generated and subjected to germline and somatic variant calling (NVIDIA's Selene DGXA100 cluster; Parabricks Pipelines). Germline variants were called using Haplotype caller and DeepVariant (Parabricks v3.0). HG002 genome in a bottle sample was used as a positive control to determine precision, recall and F1 score. Somatic variant calling was completed using somatic sniper, VarScan2, Muse, MuTect2, and Strelka (Parabricks v3.5) and SEQCII data was used to assess somatic variant calling performance. Results: Control sample HG002 was used for benchmarking the algorithms tested. At all depths analyzed, 50X, 30X, 15X, and 5X, GoogleDeep Variant had the highest F1 score, precision, and recall compared to Haplotyper for SNPs and InDels. For somatic SNV detection using SEQCII dataset, Strelka2 had the highest F1 score, precision, and recall (0.9435, 0.9445, 0.9425), followed by MuTect2, MUSE, VarScan2, and SomaticSniper. For somatic InDel detection, MuTect2 and Strelka2 performed similar with MuTect2 higher precision, but Strelka2 had higher recall. These pipelines were utilized to analyze 951 pediatric AML samples, and demonstrated superior processing time and identification of variants, both germline and somatic. Discussion: ML algorithms integrated into a GPU computing environment demonstrated greater precision and accuracy for germline variant detection compared to traditional statistical approaches for variant detection. Ongoing efforts are focused at integration of multiple data sources correlated with outcomes and analyzed via ML tools in order to improve future risk stratification and therapeutic selection for superior outcomes. Citation Format: Erin L. Crowgey, Pankaj Vats, Karl Franke, Gary Burnett, Ankit Sethia, Timothy Harkins, Todd E. Druley. Enhanced processing of genomic sequencing data for pediatric cancers: GPUs and machine learning techniques for variant detection [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2021; 2021 Apr 10-15 and May 17-21. Philadelphia (PA): AACR; Cancer Res 2021;81(13_Suppl):Abstract nr 165.

This paper proposes a novel imaging approach for damage identification in structural components. Improvements to conventional Synthetic Aperture Focus (SAF) algorithms are introduced by exploiting multiple wave propagation modes (longitudinal and shear) in the bulk of the material. Significant reduction of artifacts is achieved through the application of adaptive weights based on the wave mode structure and the coherent compounding of longitudinal and shear waves. Further improvement can be achieved by introducing various signal processing techniques, such as baseline subtraction and deconvolution of the point spread function. Finally, utilizing the massively parallel processing structure of a Graphical Processing Unit (GPU) architecture, a considerable increase in speed can be achieved compared to a traditional serial processing technique based on a Central Processing Unit (CPU). A 64-element linear array connected to a data acquisition system was used for experimental validation of the proposed tomographic algorithm steps. Results will be shown from tests performed on rail sections with simulated and natural flaws acquired from the Federal Railroad Administration (FRA) rail defect library. Considerable reduction of side lobes and improvement of image contrast are demonstrated. Future extensions of this work are also investigated, including guided wave inspection in a multi-mode environment and high-speed inspections.

We implemented the fast Gaussian gridding (FGG) based nonuniform fast Fourier transform (NUFFT) and complex OCT processing on the graphics processing unit (GPU) architecture for high-speed, real-time Fourier-domain optical coherence tomography (FD-OCT). The Vander monde matrix based non-uniform discrete Fourier transform (NUDFT) as well as the linear/cubic interpolation with fast Fourier transform (InFFT) methods are also implemented on GPU to compare their performance in terms of image quality and processing speed. The GPU accelerated NUDFT/NUFFT are applied to process both the standard half-range FDOCT and complex full-range FD-OCT (C-FD-OCT). GPU-NUFFT provides a very close approximation to GPU-NUDFT in terms of image quality but offers >10 times higher processing speed. Compared with the GPU-InFFT methods, GPU-NUFFT has improved sensitivity fall-off, higher local signal-to-noise ratio and immunity to side lobe artifacts caused by the interpolation error. Using a high speed CMOS line-scan camera, we demonstrated the real-time processing and display of GPU-NUFFT based C-FD-OCT at a camera-limited rate of 122 k line/s (1024 pixel/A-scan).

Nowadays the need for powerful hardware architectures, which allow for high throughput data analysis and calculus, is fundamental especially for biological applications. We have been focused on utilizing the Graphic Processing Unit (GPU) architectures of NVIDIA for accelerating a lipid bilayer simulation tool for biomembranes. ©2010 IEEE.