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DOE OSTI2024

Material Model Parameters Optimization in Liquid Mercury Target Dynamics Simulation With Machine Learning Surrogates

A pulsed spallation target is subjected to very short (∼0.7μs) but intense loads (23.3 kJ) from repeated proton pulses, which knock away neutrons from the mercury atoms’ nuclei for a wide range application in physics, engineering, medicine, petroleum exploration, biology, chemistry, etc. The effect of this pulsed loading on the stainless-steel target module which contains the flowing mercury target material is difficult to predict not only due to its short but intense explosive-like physical reaction, but also the nonlinear material behavior of the liquid mercury in the structure. Injecting small helium bubbles in the mercury has been an efficient method of mitigating the pressure wave at high power level stage. However, prediction of the resultant loading on the target is more difficult when helium gas is intentionally injected into the mercury. A 2-phase material model that incorporates the Rayleigh-Plesset (R-P) model is expected to address this complex multi-physics dynamics problem by including the bubble dynamics in the liquid mercury. A parameter sensitivity study was firstly employed to understand their impact on the simulation strains. The investigated parameters included E, μ, γ, σ, n, VFgas, and gas cumulative volume curve control parameters a and b. Verification and validation results from sparse polynomial expansions (SPE) method and directional Gaussian smoothing (DGS) optimization show that the surrogate model had training error of ∼7% and validation error of ∼15%, indicating that machine learning methods and surrogate models can help optimize the uncertain parameters in the complex 2-phase material model. This approach is expected to fill the knowledge gap between unknown liquid-gas mixture material model and measured vessel strain responses.

Lin, Lianshan↗
DOE OSTI2014

WE-G-18C-06: Is Diaphragm Motion a Good Surrogate for Liver Tumor Motion?

Purpose: To investigate whether diaphragm motion is a good surrogate for liver tumor motion by comparing their motion trajectories obtained from cine-MRI. Methods: Fourteen patients with hepatocellular carcinoma (10/14) or liver metastases (4/14) undergoing radiation therapy were included in this study. All patients underwent single-slice 2D cine-MRI simulations across the center of the tumor in three orthogonal planes. Tumor and diaphragm motion trajectories in the superior-inferior (SI), anteriorposterior (AP), and medial-lateral (ML) directions were obtained using the normalized cross-correlation based tracking technique. Agreement between tumor and diaphragm motions was assessed by calculating the phase difference percentage (PDP), intra-class correlation coefficient (ICC), Bland-Altman analysis (Diffs) and paired t-test. The distance (D) between tumor and tracked diaphragm area was analyzed to understand its impact on the correlation between tumor and diaphragm motions. Results: Of all patients, the means (±standard deviations) of PDP were 7.1 (±1.1)%, 4.5 (±0.5)% and 17.5 (±4.5)% in the SI, AP and ML directions, respectively. The means of ICC were 0.98 (±0.02), 0.97 (±0.02), and 0.08 (±0.06) in the SI, AP and ML directions, respectively. The Diffs were 2.8 (±1.4) mm, 2.4 (±1.1) mm, and 2.2 (±0.5) mm in the SI, AP and ML directions, respectively. The p-values derived from the paired t-test were < 0.02 in SI and AP directions, whereas were > 0.58 in ML direction primarily due to the small motion in ML direction. Tumor and diaphragmatic motion had high concordance when the distance between the tumor and tracked diaphragm areas was small. Conclusion: Preliminary results showed that liver tumor motion had good correlations with diaphragm motion in the SI and AP directions, indicating diaphragm motion in the SI and AP directions could potentially be a reliable surrogate for liver tumor motion. NIH (1R21CA165384-01A1), Golfers Against Cancer (GAC) Foundation, The China Scholarship Council (CSC)

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

TH-E-17A-08: Estimation of Image Quality of 4-Dimensional Computed Tomography (4DCT) Via Fourier Analysis of Corresponding 1D Breathing Surrogate

Purpose: Motion artifacts are common in patient 4DCT, leading to an illdefined tumor volume with variation up to 110% or setting up a poor foundation with low imaging fidelity for tumor motion study. We developed a method to estimate 4DCT image quality by establishing a correlation between the severity of motion artifacts in 4DCT images and the periodicity of corresponding 1D respiratory wave-function (1DRW) surrogate used for 4DCT reconstruction. Methods: Fast Fourier Transformation (FFT) was applied to analyze 1DRW periodicity, defined as the sum of the 5 largest Fourier coefficients, ranging in 0–1. Distortional motion artifacts of cine-scan 4DCT at the junctions of adjacent couchposition scans around the diaphragm were identified in 3 categories: incomplete, overlapping and duplicate. To quantify these artifacts, the discontinuity of the diaphragm at the junctions was measured in distance and averaged along 6 directions in 3 orthogonal views. Mean and sum artifacts per junction (APJ) across the entire diaphragm were calculated in each breathing phase. To make the APJ inter-patient comparable, patientspecific motion was removed from APJ by dividing patient-specific diaphragmatic velocity (displacement divided by the mean period, from FFT analysis of the 1DRW) and the normalized APJ was defined as motion artifact severity (MAS). Twenty-five patients with free-breathing 10-phase 4DCT and corresponding 1DRW surrogate datasets were studied. Results: A mild correlation of 0.56 was found between 1DRW periodicity and 4DCT artifact severity. Higher MAS tends to appear around mid inhalation and mid exhalation and the lowest MAS tends to be around full exhalation. The breathing periodicity of >0.8 possesses minimal motion artifacts. Conclusion: The 1D-4D correlation provides a fast means to estimate 4DCT image quality. Using 1DRW signal, we can retrospectively screen out high-quality 4DCT images for clinical research (periodicity>0.8) and prospectively identify poor breathers as candidates of breath coaching prior to 4DCT scan. This research is in part supported by NIH (U54CA137788/132378). MC would like to thank MSKCC summer medical student research program supported by National Cancer Institute and hosted by Department of Medical Physics at MSKCC.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

MO-FG-BRA-02: A Feasibility Study of Integrating Breathing Audio Signal with Surface Surrogates for Respiratory Motion Management

Purpose: Tracking the surrogate placed on patient skin surface sometimes leads to problematic signals for certain patients, such as shallow breathers. This in turn impairs the 4D CT image quality and dosimetric accuracy. In this pilot study, we explored the feasibility of monitoring human breathing motion by integrating breathing sound signal with surface surrogates. Methods: The breathing sound signals were acquired though a microphone attached adjacently to volunteer’s nostrils, and breathing curve were analyzed using a low pass filter. Simultaneously, the Real-time Position Management™ (RPM) system from Varian were employed on a volunteer to monitor respiratory motion including both shallow and deep breath modes. The similar experiment was performed by using Calypso system, and three beacons taped on volunteer abdominal region to capture breath motion. The period of each breathing curves were calculated with autocorrelation functions. The coherence and consistency between breathing signals using different acquisition methods were examined. Results: Clear breathing patterns were revealed by the sound signal which was coherent with the signal obtained from both the RPM system and Calypso system. For shallow breathing, the periods of breathing cycle were 3.00±0.19 sec (sound) and 3.00±0.21 sec (RPM); For deep breathing, the periods were 3.49± 0.11 sec (sound) and 3.49±0.12 sec (RPM). Compared with 4.54±0.66 sec period recorded by the calypso system, the sound measured 4.64±0.54 sec. The additional signal from sound could be supplement to the surface monitoring, and provide new parameters to model the hysteresis lung motion. Conclusion: Our preliminary study shows that the breathing sound signal can provide a comparable way as the RPM system to evaluate the respiratory motion. It’s instantaneous and robust characteristics facilitate it possibly to be a either independently or as auxiliary methods to manage respiratory motion in radiotherapy.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

WE-FG-206-12: Enhanced Laws Textures: A Potential MRI Surrogate Marker of Hepatic Fibrosis in a Murine Model

Purpose: To compare enhanced Laws texture derived from parametric proton density (PD) maps to other MRI-based surrogate markers (T2, PD, ADC) in assessing degrees of liver fibrosis in a murine model of hepatic fibrosis using 11.7T scanner. Methods: This animal study was IACUC approved. Fourteen mice were divided into control (n=1) and experimental (n=13). The latter were fed a DDC-supplemented diet to induce hepatic fibrosis. Liver specimens were imaged using an 11.7T scanner; the parametric PD, T2, and ADC maps were generated from spin-echo pulsed field gradient and multi-echo spin-echo acquisitions. Enhanced Laws texture analysis was applied to the PD maps: first, hepatic blood vessels and liver margins were segmented/removed using an automated dual-clustering algorithm; secondly, an optimal thresholding algorithm was applied to reduce the partial volume artifact; next, mean and stdev were corrected to minimize grayscale variation across images; finally, Laws texture was extracted. Degrees of fibrosis was assessed by an experienced pathologist and digital image analysis (%Area Fibrosis). Scatterplots comparing enhanced Laws texture, T2, PD, and ADC values to degrees of fibrosis were generated and correlation coefficients were calculated. Unenhanced Laws texture was also compared to assess the effectiveness of the proposed enhancements. Results: Hepatic fibrosis and the enhanced Laws texture were strongly correlated with higher %Area Fibrosis associated with higher Laws texture (r=0.89). Only a moderate correlation was detected between %Area Fibrosis and unenhanced Laws texture (r=0.70). Strong correlation also existed between ADC and %Area Fibrosis (r=0.86). Moderate correlations were seen between %Area Fibrosis and PD (r=0.65) and T2 (r=0.66). Conclusions: Higher degrees of hepatic fibrosis are associated with increased Laws texture. The proposed enhancements improve the accuracy of Laws texture. Enhanced Laws texture features are more accurate than PD and T2 in assessing fibrosis, and can potentially serve as an accurate surrogate marker for hepatic fibrosis.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

TH-CD-207A-05: Lung Surface Deformation Vector Fields Prediction by Monitoring Respiratory Surrogate Signals

Purpose: In this study, we developed and evaluated a method for predicting lung surface deformation vector fields (SDVFs) based on surrogate signals such as chest and abdomen motion at selected locations and spirometry measurements. Methods: A Patient-specific 3D triangular surface mesh of the lung region at end-expiration (EE) phase was obtained by threshold-based segmentation method. For each patient, a spirometer recorded the flow volume changes of the lungs; and 192 selected points at a regular spacing of 2cm X 2cm matrix points over a total area of 34cm X 24cm on the surface of chest and abdomen was used to detect chest wall motions. Preprocessing techniques such as QR factorization with column pivoting (QRCP) were employed to remove redundant observations of the chest and abdominal area. To create a statistical model between the lung surface and the corresponding surrogate signals, we developed a predictive model based on canonical ridge regression (CRR). Two unique weighting vectors were selected for each vertex on the surface of the lung, and they were optimized during the training process using the all other phases of 4D-CT except the end-inspiration (EI) phase. These parameters were employed to predict the vertices locations of a testing data set, which was the EI phase of 4D-CT. Results: For ten lung cancer patients, the deformation vector field of each vertex of lung surface mesh was estimated from the external motion at selected positions on the chest wall surface plus spirometry measurements. The average estimation of 98th percentile of error was less than 1 mm (AP= 0.85, RL= 0.61, and SI= 0.82). Conclusion: The developed predictive model provides a non-invasive approach to derive lung boundary condition. Together with personalized biomechanical respiration modelling, the proposed model can be used to derive the lung tumor motion during radiation therapy accurately from non-invasive measurements.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

Towards Generalizable and Efficient Circuit Topology Design: A Graph-Transformer-based Surrogate Model with Curriculum Learning

Unlike circuit parameter and sizing optimizations, the automated design of analog circuit topologies poses significant challenges for learning-based approaches. One challenge arises from the combinatorial growth of the topology space with circuit size, which limits the topology optimization efficiency. Moreover, traditional circuit evaluation methods are time-consuming, while the presence of data discontinuity in the topology space makes the accurate prediction of circuit performance exceptionally difficult for unseen topologies. To tackle these challenges, we design a novel Graph-Transformer-based Network (GTN) as the surrogate model for circuit evaluation, offering a substantial acceleration in the speed of circuit topology optimization without sacrificing performance. Our GTN model architecture is designed to embed voltage changes in circuit loops and current flows in connected devices, enabling accurate performance predictions for circuits with unseen topologies. To address the cold start problem when scaling GTN to large-scale circuits, we further introduce a curriculum learning strategy that progressively trains GTN from small-scale to large-scale circuits. This approach enables the model to first learn fundamental physical principles from simpler topologies and gradually adapt to complex configurations, effectively bridging the circuit complexity gap and improving prediction accuracy. Taking the power converter circuit design as an experimental task, our GTN model significantly outperforms an analytical approach and baseline methods directly utilizing graph neural networks. Furthermore, GTN achieves less than 5% relative error and 196× speed-up compared with high-fidelity simulation. Notably, our GTN surrogate model empowers an automatic circuit design framework to discover circuits of comparable quality to those identified through high-fidelity simulation while reducing the time required by up to 98.2%. With curriculum learning, the enhanced GTN achieves a 51% improvement for performance prediction of large-scale circuits compared to the GTN model without this strategy. These advancements establish GTN as a scalable framework for automated analog circuit design across varying circuit complexity levels.

Lu, Haoshu [New Jersey Institute of Technology (NJ↗
DOE OSTI2026

wa-hls4ml: A Benchmark and Surrogate Models for hls4ml Resource and Latency Estimation

As machine learning (ML) is increasingly implemented in hardware to address real-time challenges in scientific applications, the development of advanced toolchains has significantly reduced the time required to iterate on various designs. These advancements have solved major obstacles, but also exposed new challenges. For example, processes that were not previously considered bottlenecks, such as hardware synthesis, are becoming limiting factors in the rapid iteration of designs. To mitigate these emerging constraints, multiple efforts have been undertaken to develop an ML-based surrogate model that estimates resource usage of ML accelerator architectures. We introduce wa-hls4ml, a benchmark for ML accelerator resource and latency estimation, and its corresponding initial dataset of over 680,000 fully connected and convolutional neural networks, all synthesized using hls4ml and targeting Xilinx FPGAs. The benchmark evaluates the performance of resource and latency predictors against several common ML model architectures, primarily originating from scientific domains, as exemplar models, and the average performance across a subset of the dataset. Additionally, we introduce GNN- and transformer-based surrogate models that predict latency and resources for ML accelerators. We present the architecture and performance of the models and find that the models generally predict latency and resources for the 75% percentile within several percent of the synthesized resources on the synthetic test dataset.

Hawks, Benjamin [Fermilab] (ORCID:0000000157000288↗
DOE OSTI2019

Surrogate Optimization of Computationally Expensive Black-Box Problems with Hidden Constraints (SHEBO) v1.0

SHEBO (surrogate optimization of problems with hidden constraints and expensive black-box objectives) is an efficient optimization algorithm that employs surrogate models to solve computationally expensive black-box simulation optimization problems that have hidden constraints. Hidden constraints are encountered when the objective function evaluation does not return a value for a parameter vector. These constraints are often encountered in optimization problems in which the objective function is computed by a black-box simulation code. SHEBO uses a combination of local and global search strategies together with an evaluability prediction function and a dynamically adjusted evaluability threshold to iteratively select new sample points.

Mueller, Juliane↗
DOE OSTI2022

ROMNet: Neural-Network-Based Surrogates for Reduced-Order Model Dynamics

SAND2023-05829O ROMNet is a toolbox built on the Tensorflow library for training reduced-order, neural operator surrogate models. The software is used for training reduced order neural operator surrogate models for dynamical systems applications. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗
DOE OSTI2024

soogo (Surrogate-based 0-th Order Global Optimization) [SWR-24-57]

Surrogate-based 0-th Order Global Optimization for black-box problems. This software is comprised of active learning algorithms based on surrogate models to solve black-box optimization problems and other scientific applications. See also: https://pypi.org/project/soogo/

da Silva Pereira, Weslley↗
DOE OSTI2024

SysCaps (Language Interfaces for Simulation Surrogates of Complex Systems) [SWR-24-97]

You've found the official code repository for the paper "SysCaps: Language Interfaces for Simulation Surrogates of Complex Systems," presented at the Foundation Models for Science: Progress, Opportunities, and Challenges workshop at NeurIPS 2024. Our paper conjectures that interfaces (both text templates as well as conversational) makes interacting with simulation surrogate models for complex systems more intuitive and accessible for both non-experts and experts. "System captions", or SysCaps, are text-based descriptions of systems based on information contained in simulation metadata. Our paper's goal is to train multimodal regression models that take text inputs (SysCaps) and timeseries inputs (exogenous system conditions such as hourly weather) and regress timeseries simulation outputs (e.g. hourly building energy consumption). The experiments in our paper with building and wind farm simulators, which can be reproduced using this codebase, aim to help us understand whether a) accurate regression in this setting is possible and b) if so, how well can we do it. Paper: https://arxiv.org/abs/2405.19653

Emami, Patrick↗
DOE OSTI2026

GP Cosmology Surrogate v1.0

GP Cosmology Surrogate is a Python library for building and training a generalized multi-output Gaussian process (GP) framework of @takhtaganov2021cosmic. In this approach, the surrogate is constructed sequentially, guided by a Bayesian optimization acquisition function that targets reduction of emulation error in the regions most consistent with the observational data. This adaptive design concentrates computational resources where they have the greatest impact on inference accuracy. The library supports efficient training for separable GP kernels, which allows the use of Kronecker algebra to handle high-dimensional input spaces and large numbers of correlated outputs. This makes it well suited for applications such as modeling cosmological power spectra, large-scale physical simulations, and multi-output hyperparameter tuning. By combining scalable multi-output GP modeling with data-driven adaptive sampling, GPsurrogate enables parameter inference and optimization with substantially fewer simulations than conventional space-filling designs.

Lukic, Zarija [Lawrence Berkeley National Laborato↗
DOE OSTI2024

Spatially Local Surrogate Modeling of Subgrid-Scale Effects in Idealized Atmospheric Flows: A Deep Learned Approach Using High-Resolution Simulation Data

Abstract We introduce a machine learned surrogate model from high-resolution simulation data to capture the subgrid-scale effects in dry, stratified atmospheric flows. We use deep neural networks (NNs) to model the spatially local state differences between a coarse-resolution simulation and a high-resolution simulation. The setup enables the capture of both dissipative and antidissipative effects in the state differences. The NN model is able to accurately capture the state differences in offline tests outside the training regime. In online tests intended for production use, the NN-coupled coarse simulation has higher accuracy over a significant period of time compared to the coarse-resolution simulation without any correction. We provide evidence of the capability of the NN model to accurately capture high-gradient regions in the flow field. With the accumulation of the errors, the NN-coupled simulation becomes computationally unstable after approximately 90 coarse simulation time steps. Insights gained from these surrogate models further pave the way for formulating stable, complex, physics-based spatially local NN models which are driven by traditional subgrid-scale turbulence closure models. Significance Statement Flows in the atmosphere are highly chaotic and turbulent, comprising flow structures of broad scales. For effective computational modeling of atmospheric flows, the effects of the small- and large-scale structures need to be captured by the simulations. Capturing the small-scale structures requires fine-resolution simulations. Even with the current state-of-the-art supercomputers, it can be prohibitively expensive to simulate these flows when computed for the entire earth over climate time scales. Thus, it is necessary to focus on the larger-scale structures using a coarse-resolution simulation while capturing the effects of the smaller-scale structures using some parameterization (approximation) scheme and incorporating it into the coarse-resolution simulation. We use machine learning to model the effects of the small-scale structures (subgrid-scale effects) in atmospheric flows. Data from a fine-resolution simulation is used to compute the missing subgrid-scale effects in coarse-resolution simulations. We then use machine learning models to approximate these differences between the coarse- and fine-resolution simulations. We see improved accuracy for the coarse-resolution simulations when corrected using these machine learned models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Assessment of an E10 gasoline surrogate: Qualitative and quantitative comparisons of in-cylinder spray morphology

A minimum-component gasoline fuel surrogate that captures both chemical and physical behaviors of a full-distillate fuel is needed for high-fidelity CFD simulations. This study evaluates gasoline spray characteristics in a direct-injection spark-ignition engine under motored operation. Two fuels are compared; PACE-20, which is a 9-component surrogate formulation of RD5-87, is compared with its target fuel RD5-87, which is a full-boiling range research grade E10 gasoline. The spray morphologies of both fuels are recorded for a centrally-located direct-injection 8-hole spray subject to intake air cross-flow during the early part of the intake stroke. High-speed imaging recorded scattered light of the side and axial projections of the liquid spray. Quantitative metrics were developed and employed to facilitate comparison of spray morphologies as well as to identify the transition in spray morphology due to flash boiling. This paper builds on a previous study of RD5-87 where coolant temperature (20°C–100°C), in-cylinder pressure (40–110 kPa), engine speed (650–1950 rpm), and injection pressure (60–180 bar) were systematically changed to span operating conditions with and without flash boiling. Images of the PACE-20 morphology are selected for a sub-set of operating conditions from the previous study where distinctive morphology changes occurred. Visual inspection of the images and quantitative metrics demonstrate that the PACE-20 spray morphology is equivalent to that of the RD5-87 in most cases. The exception was for changes in the ambient-gas pressure where the flash-boiling transition occurred at ∼5 kPa higher in-cylinder pressure for PACE-20. Three empirical metrics, Merging Index, Asymmetry, and Flash Index are proposed here and they were found to be useful both as quantitative comparisons of the fuel morphologies, and for identifying the transition in spray morphology due to flash boiling.

Kim, Namho↗
DOE OSTI2023

Solving multiphysics-based inverse problems with learned surrogates and constraints

Abstract Solving multiphysics-based inverse problems for geological carbon storage monitoring can be challenging when multimodal time-lapse data are expensive to collect and costly to simulate numerically. We overcome these challenges by combining computationally cheap learned surrogates with learned constraints. Not only does this combination lead to vastly improved inversions for the important fluid-flow property, permeability, it also provides a natural platform for inverting multimodal data including well measurements and active-source time-lapse seismic data. By adding a learned constraint, we arrive at a computationally feasible inversion approach that remains accurate. This is accomplished by including a trained deep neural network, known as a normalizing flow, which forces the model iterates to remain in-distribution, thereby safeguarding the accuracy of trained Fourier neural operators that act as surrogates for the computationally expensive multiphase flow simulations involving partial differential equation solves. By means of carefully selected experiments, centered around the problem of geological carbon storage, we demonstrate the efficacy of the proposed constrained optimization method on two different data modalities, namely time-lapse well and time-lapse seismic data. While permeability inversions from both these two modalities have their pluses and minuses, their joint inversion benefits from either, yielding valuable superior permeability inversions and CO 2 plume predictions near, and far away, from the monitoring wells.

Yin, Ziyi (ORCID:0000000250248771)↗
DOE OSTI2025

Prediction of cccDNA dynamics in hepatitis B patients by a combination of serum surrogate markers

Quantification of intrahepatic covalently closed circular DNA (cccDNA) is a key for evaluating an elimination of hepatitis B virus (HBV) in infected patients. However, quantifying cccDNA requires invasive methods such as a liver biopsy, which makes it impractical to access the dynamics of cccDNA in patients. Although HBV RNA and HBV core-related antigens (HBcrAg) have been proposed as surrogate markers for evaluating cccDNA activity, they do not necessarily estimate the amount of cccDNA. Here, we employed a recently developed multiscale mathematical model describing intra- and intercellular viral propagation and applied it in HBV-infected patients under treatment. We developed a model that can predict intracellular HBV dynamics by use of extracellular viral markers, including HBsAg, HBV DNA, and HBcrAg in peripheral blood. Importantly, the model prediction of the amount of cccDNA in patients over time was confirmed to be well correlated with the data for quantified cccDNA by paired liver biopsy. Thus, our method combining classic and emerging surrogate markers enables us to predict the decay dynamics of cccDNA in patients undergoing treatment.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Fiats: Functional inference and training for surrogates

Fiats provides a platform for research on the training and deployment of neural-network surrogate models for computational science. Fiats also supports exploring, advancing, and combining functional, object-oriented, and parallel programming patterns in Fortran 2023. As such, the Fiats name has dual expansions: “Functional Inference And Training for Surrogates” or “Fortran Inference And Training for Science.” Fiats inference and training procedures are pure and therefore satisfy a language constraint imposed on procedure invocations inside Fortran’s parallel loop construct: do concurrent. Furthermore, the Fiats training procedures are built around a do concurrent parallel reduction. Several compilers can automatically parallelize do concurrent on Central Processing Units (CPUs) or Graphics Processing Units (GPUs). Fiats thus aims to achieve performance portability through standard language mechanisms.

Rouson, Damian [Lawrence Berkeley National Laborat↗