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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2023

Next-Generation Marine Energy Software Needs Assessment

Over the past decade the marine energy industry has continued to grow and evolve, with new concepts and technologies constantly being pursued. Additionally, the field of computing is vastly different today than it was five or ten years ago. By utilizing advanced software and hardware architectures, like graphics processing units as well as parallelization and high-performance computing resources, software can produce higher quality outputs and a higher volume of outputs. These software and hardware resources can enable the marine energy community to exploit computational advancements from other research fields, which can include machine learning, differentiable programming, and controls co-design. Better integration of existing software and development of potential new software is necessary to take advantage of trends in modern computing and respond to the current and future needs of the marine energy community. In order to better understand the existing marine energy software landscape and industry needs, DOE's Water Power Technologies Office (WPTO) tasked Sandia National Laboratories and the National Renewable Energy Laboratory to update the needs assessment by identifying existing software gaps and software needs, and assisting WPTO in planning the next wave of marine energy software development. The proposed effort involved cataloguing and analyzing the available data on existing software related to marine energy. The marine energy software landscape has vastly changed in the last ten years. There are now nearly 230 different software packages utilized by the marine energy sector, compared to a decade ago when the Cardinal Engineering survey identified approximately 40 software packages. In 2012, the marine energy software landscape was captured in two tables, whereas the current marine energy software landscape required development of a software database to collect and categorize software.

16 TIDAL AND WAVE POWER↗
DOE OSTI2024

Celeritas R&D Report: Accelerating Geant4

Celeritas is a new Monte Carlo (MC) detector simulation code designed for computationally intensive applications on high-performance heterogeneous architectures. In the past two years Celeritas has advanced from prototyping a Graphics Processing Unit (GPU)-based single physics model in infinite medium to implementing a full set of electromagnetic (EM) physics processes in complex geometries. The current release of Celeritas, version 0.4, has incorporated full device-based navigation, an event loop in the presence of magnetic fields, and detector hit scoring. New functionality incorporates a scheduler to offload electromagnetic physics to the GPU within a Geant4-driven simulation, enabling straightforward integration of Celeritas into the high energy physics (HEP) experimental frameworks CMSSW and ATLAS FullSimLight. On the Perlmutter supercomputer, Celeritas performs EM physics between 3× and 18× faster using the machine’s Nvidia GPUs compared to using only CPUs, corresponding to an electrical power efficiency up to a factor of 5. When running a multithreaded Geant4 ATLAS test beam application with full hadronic physics, using Celeritas to accelerate the EM physics results in an overall simulation speedup of 1.7–2.2× on GPU and 1.2× on CPU. In a CMS test application using tt¯ events and the prototype Run 4 configuration, compared to Geant4 CPU, Celeritas with a Nvidia A100 improves overall throughput up to a factor of 2.7× but cannot be efficiently shared with more than 8 cores.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Developing And Scaling an OpenFOAM Model to Study Turbulent Flow in a HFIR Coolant Channel

Improving the understanding of how computational fluid dynamics (CFD) direct numerical simulations (DNS) of flows in the High Flux Isotope Reactor (HFIR) perform when run in parallel using the high performance computing (HPC) platform Summit at the Oak Ridge Leadership Computing Facility (OLCF) is of particular importance to boost the computational tools used to support HFIR conversion to low enriched fuel (LEU). Evaluation of scaling performance was driven by the increasing importance of graphics processing unit (GPU) usage in HPC, which is becoming the standard for modern supercomputers such as Summit. The desired results are to obtain a strong positive correlation between the computational resources dedicated to a problem and the relative speed-up of the simulation in comparison to a benchmark. This capability will allow substantially improvement in HFIR flow analytical capabilities, specifically when predicting turbulence properties at high Reynolds numbers. The study leverages previous simulation results performed with code PHASTA (finite element) on HPC platforms Cori (NERSC) and Theta (ALCF) [1] with computing options provided in the computing platform OpenFOAM (finite volume) at OLCF. Transitioning from PHASTA to OpenFOAM will (1) eliminate dependence on third-party software for mesh generation and manipulation, (2) reduce resource needs by employing modern architectures, and (3) build expertise for future modeling of HFIR-specific problems like heat transfer in involute geometry, entrance effects, flow structure in channel corners, and so on—all important issues when defining the available thermal margins in the transition to LEU. CPUs and GPUs differ significantly in their architecture and utilization, as discussed in the literature [2]. The most important differences are in the approach to computations and their memory. A single GPU contains a large quantity of cores, enabling it to perform with a much higher throughput than a CPU, but execution requires a different approach. GPU codes execute instructions using the Single-Instruction Multiple-Thread (SIMT) approach in which a single instruction is used for groups of threads called warps. A warp typically consists of 32 threads which must execute the same set of instructions, although on separate threads. Alternately, a CPU has far fewer cores that are much more flexible in their operation, excelling at quickly performing more complex serial computations. This is why GPUs have greater throughput when properly utilized. The second important difference is seen when comparing their memory spaces. Limited memory allocations and CPU–GPU communications cause a significant bottleneck in GPU-accelerated programs. Further study was required to properly take advantage of GPU resources. A comprehensive analysis of code performance and the model-specific features of turbulence constitutes the core of this work. In this study, a DNS simulation of HFIR channel turbulence was performed with the finite volume CFD code OpenFOAM v2112 and CUDA v11.0 on Red Hat Enterprise Linux v8.2. The OpenFOAM installation had AMGx integrated to enable GPU acceleration and utilizes the PETSc4FOAM library. The computational resources and the problem size were scaled on CPU and CPU + GPU architectures to gain a better understanding of the performance of a DNS problem on modern computing hardware. The study aimed to analyze the scaling of the code exclusively on CPUs and then to examine the scaling of the codes with GPU acceleration enabled. Scaling studies included CPU and GPU acceleration on a mesh of varying resolution to analyze the impact of problem size relative to computational resources. In the course of preparing the GPU configuration on Summit, mainly using the AMGX solvers, difficulties were encountered stemming from constant changes resulting from extensive ongoing development activities and the changing environment. This resulted in the inability to complete the GPU portion of the work. The code was compiled and tested, but production runs to assess acceleration were not performed because the used discretional compute time allocation expired as year-end approached. The Summit HPC platform is scheduled for decommissioning in 2024, making it unattractive for future use with Nvidia-based GPUs. Therefore, the work will be moved onto NERSC machines in FY24. An application was prepared and submitted, and sufficient node-hours were awarded to continue the research in the next calendar year. This report summarizes work performed thus far, which mostly focused on CPU OpenFOAM computing.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Evaluating Operators in Deep Neural Networks for Improving Performance Portability of SYCL

SYCL is a portable programming model for heterogeneous computing, so it is important to obtain reasonable performance portability of SYCL. Towards the goal of better understanding and improving performance portability of SYCL for machine learning workloads, we have been developing benchmarks for basic operators in deep neural networks (DNNs). These operators could be offloaded to heterogeneous computing devices such as graphics processing units (GPUs) to speed up computation. In this work, we introduce the benchmarks, evaluate the performance of the operators on GPU-based systems, and describe the causes of the performance gap between the SYCL and Compute Unified Device Architecture (CUDA) kernels. We find that the causes are related to the utilization of the texture cache for read-only data, optimization of the memory accesses with strength reduction, shared local memory accesses, and register usage per thread. We hope that the efforts of developing benchmarks for studying performance portability will stimulate discussion and interactions within the community.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Celeritas Midterm SciDAC Report

Celeritas is a new Monte Carlo (MC) code that helps satisfy the increasing demand for high energy physics (HEP) detector simulation, using Graphics Processing Unit (GPU) hardware on high performance computing (HPC) systems to model Large Hadron Collider (LHC) experiments and beyond. This report details the project’s progress midway through its SciDAC funding period, highlighting the first complete implementation of standard electromagnetic (EM) physics on GPUs, initial results for performance and scalability on Leadership Computing Facilities (LCFs), and preliminary integration into the CMS and ATLAS experiments. By integrating HEP domain knowledge with expertise in MC transport, Celeritas has catalyzed a shift in the HEP community’s perception of GPU platforms as the future for HPC simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Accelerating Neutrino Event Generation in MARLEY Using CUDA-Based RNG and GPU Parallelization

MARLEY is a simulation tool that helps scientists study how low-energy neutrinos interact with matter. To work properly, MARLEY uses random numbers thousands of times in each simulation. These random numbers are important for modeling things like how neutrinos collide with atoms and what particles they produce. Right now, MARLEY runs on a regular computer processor (CPU) and uses a built-in random number generator called the Mersenne Twister. This setup works, but it can be slow, especially when trying to simulate many events. This research focuses on making MARLEY run faster by moving the random number generation and some of the repetitive calculations from the CPU to a graphics processing unit (GPU), which can handle many tasks at the same time. We use CUDA (a tool for programming NVIDIA GPUs) and cuRAND (a GPU-based random number library) to test faster alternatives to the current random number system. We compare different GPU-based generators, like curand_mtgp32, xorwow, and philox, to see which ones are the quickest and still give reliable results. Early tests show that using the GPU can make MARLEY simulations much faster. This project not only helps improve current simulation performance but also moves closer to a full simulation chain where all stages can run on modern GPU hardware.

Dunkley, Kimieka [Florida A-M]↗
DOE OSTI2025

LDRD Abbreviated report: High-Order General-Discrete-Ordinates Method Enabling Efficient Deterministic Transport in Hydrodynamic Simulations

Deterministic transport simulations for national-security and energy applications often operate in high-dimensional phase-space, where accuracy and cost both become major challenges. A common numerical artifact in such problems is the “ray-effect,” which appears as unphysical streaks. Beyond misinterpretation, these artifacts can contaminate tightly coupled physics, such as fluid dynamics, radiation-hydrodynamics, and laser-plasma interactions, eroding the predictive capability of entire multiphysics workflows. Our objective was to make high-dimension studies practical on modern hardware while mitigating the ray-effect without relying on prohibitively expensive sampling approaches such as Monte Carlo methods. We developed the Generic Discretization Library (GenDiL), a Graphics Processing Unit (GPU)-first framework that uses high-order Discontinuous Galerkin (DG) methods and matrix-free algorithms to reduce memory usage and improve computational efficiency, critical for phase-space simulations. GenDiL supports phase-space adaptivity in both mesh size and polynomial order (hp-adaptivity) to place resolution only where it is needed. A central capability is Local Dimensional Refinement (LDR), which couples lower-dimension continuum models to higher-dimension kinetic models through stable and conservative interfaces, so that high-fidelity physics is applied only in regions where it is essential. Building on the GenDiL framework, we developed the General SN (GSN) family of algorithms as a true generalization of the polar SN approach (discrete ordinates, often denoted SN). Rather than tying discrete ordinates to a specific polar change of coordinates, GSN formulates transport on an arbitrary change of coordinates chosen to reduce ray-effect. We studied two complementary variants: an analytic variant, where the coordinate map is prescribed in advance by a closed-form function; and a data-driven variant, where a quantity of interest, such as the net flux, guides the coordinate system. GenDiL provides the library infrastructure for efficient GPU execution, but the GSN concept is algorithmic and independent of any one library. Across representative high-dimension tests, including non-symmetric solutions, both variants delivered strong ray-effect mitigation at practical cost, moving four- to six-dimensional analysis toward repeatable, routine studies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

DGaaS: GPU as a Service on Distributed Computing System

In the rapidly evolving landscape of scientific computing, Graphics Processing Units (GPUs) have become indispensable for their unparalleled ability to handle parallel tasks in complex calculations, simulations, and data analysis. Their utility is further magnified in machine learning and AI applications, where they significantly accelerate model training and predictive analytics. Within this context, the Triton Inference Server emerges as a pivotal open-source tool, specializing in AI inferencing and optimizing GPU utilization across various platforms and frameworks. This paper presents an in-depth study on distributed High Throughput Computing (HTC), specifically focusing on the HTCondor framework and its resource provisioning tools, GlideinWMS and HEPCloud. These systems enable large-scale scientific experiments like CMS and DUNE to efficiently access and utilize vast computational resources. The paper explores the core architectural components of GlideinWMS, including jobs, user pools, and worker nodes, and discusses their integration with GPUs and the Triton server. The primary aim of this research is to develop a solution that optimizes GPU utilization by leveraging Glideins and containers. This approach allows computational jobs, particularly those involving AI models, to use GPUs only when essential, thereby facilitating efficient sharing of limited GPU resources. To validate this architecture, the study conducted three key tests involving custom scripts, container-based servers, and Triton server deployments. However, the study faces challenges, notably in locating the Triton server and ensuring secure remote access. To address these issues, future work will focus on developing a proxy mechanism and enhancing security protocols. In conclusion, this study offers a comprehensive roadmap for effective and efficient GPU utilization in distributed High Throughput Computing. It aims to contribute significantly to the scientific community by solving pressing problems and implementing robust solutions in collaboration with the GlideinWMS and HEPCloud teams. The research sets the stage for a more efficient, scalable, and cost-effective paradigm in scientific computing.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

FY17 MPACT Development Activities

Over the course of FY17, several improvements have been made to MPACT which effect the capability and performance of MPACT in several key areas. This report serves to document the capabilities developed at ORNL. There are four key areas of development that are highlighted here: • Externally driven source calculations to analyze reactor startup and the impact of secondary neutron sources. • Extensions to the Rhodium detector model to improve analysis of fixed core Rh detectors which are used in several cores. • Improved performance of PN scattering MOC sweeper to provide quicker reference solutions. • Implementation of an MOC kernel implemented on graphics processing units (GPU) to take advantage of advanced hardware. The next four sections discuss each of these features in detail. The final section discusses continuing work that is needed to improve these features.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

LAROMance Grade 91 Model Integration in NEML2

New reactor designs are targeting higher operating temperatures for increased thermal efficiency when compared to the current fleet of light water reactors. Designing structural components for these high temperature environments with reliable long-term operations requires material models that can accurately capture the deformation mechanisms active in these environments. The LAROMance surrogate material models are based on a database of mechanistic crystal plasticity simulations for high-temperature conditions. Inputs to the LAROMance models reflect the microstructural pedigree of the material, like dislocation densities and precipitate contents. Based on the evolution of these microstructural features, the LAROMance model provides the engineering scale constitutive model response. The LAROMance model was recently parameterized for Grade 91, a high temperature alloy. In the present work, the Grade 91 LAROMance model is implemented in the New Material Model Library, version 2 (NEML2). NEML2 provides a modular way to build material models from smaller blocks and was developed to vectorize the material update to efficiently run on modern computational architectures with graphics processing unit accelerators. NEML2 constitutive models can be used in simulations based on the multiphysics object-oriented simulation environment (MOOSE). This report provides details on the implementation of the Grade 91 LAROMance model in NEML2 and its verification of engineering scale finite element simulations in MOOSE.

42 - ENGINEERING↗
DOE OSTI2016

Large Eddy Simulation of a Supercritical Fuel Jet in Cross Flow using GPU-Acceleration

Fuel is routinely injected into combustion chambers at elevated pressures resulting in formation of supercritical fluid flow. The dispersion of fuel and the combustion processes are significantly different in high pressure conditions as the raditional liquid atomization and evaporation are replaced by diffusion-dominated mixing. Modeling supercritical flow is challenging due to the complex thermodynamics and transport properties of the fluids and in most cases high fidelity numerical simulations are prohibitively expensive. However, numerical investigations must incorporate the flow properties appropriate for the regime for accurate description of the physical processes involved. In this paper, we consider real-fluid properties and simulate the turbulent mixing of fuel jet in cross flow at high ambient pressure. In order to make efficient use of the computer resources and reduce the time to solution, without compromising the resolution requirements, the real-fluid property routines are accelerated via Graphics Processing Unit (GPU) computation. The numerical simulations performed at different resolutions suggest that the high fidelity computations with refined mesh are essential to capture the non-linear dynamics of vortex evolution downstream of the fuel jet and signifies the necessity for an accelerated code. The code is accelerated using the Kokkos C++ library and is demonstrated to be about 2 times faster than the non-accelerated version. Considerable computational cost associated with the thermodynamics routines is reduced in the accelerated version. The results also suggest the resource requirements to compute turbulent closures and the need for acceleration of the routines associated with the sub-grid scale closures.

Gottiparthi, Kalyana C.↗
DOE OSTI2019

An Adaptive Particle Tracking Algorithm for Lagrangian-Eulerian Simulations of Dispersed Multiphase Flows

The Lagrangian-Eulerian method is broadly used for simulations of dispersed multiphase flows by solving the continuous phase in the Eulerian framework while treating the dispersed phase as point particles in a Lagrangian framework. The accuracy of the Lagrangian-Eulerian method largely depends on the number of computational particles tracked for the Lagrangian phase. In this study, an adaptive Lagrangian particle tracking algorithm is proposed to balance the statistical error and the computational cost by dividing and merging the particles according to the local particle statistics in the computational domain. The computational particles are considered as weighted sampling points of the particle probability density functions (PDF) which represents a statistical equivalence of the Lagrangian phase. The algorithm is implemented as a part of a C++ library for Lagrangian particles, Grit, with performance portability to multi-core or many-core CPUs and Graphic Processing Unit (GPU) architectures. The accuracy of the proposed algorithm with two different schemes are studied through a test problem with analytical solutions for both the particle number density and momentum source term. The results are used to evaluate the proposed algorithm as well as to validate the parallel implementation.

Ge, Wenjun↗
DOE OSTI2023

Coupled cluster theory on modern heterogeneous supercomputers

This study examines the computational challenges in elucidating intricate chemical systems, particularly through ab-initio methodologies. This work highlights the Divide-Expand-Consolidate (DEC) approach for coupled cluster (CC) theory—a linear-scaling, massively parallel framework—as a viable solution. Detailed scrutiny of the DEC framework reveals its extensive applicability for large chemical systems, yet it also acknowledges inherent limitations. To mitigate these constraints, the cluster perturbation theory is presented as an effective remedy. Attention is then directed towards the CPS (D-3) model, explicitly derived from a CC singles parent and a doubles auxiliary excitation space, for computing excitation energies. The reviewed new algorithms for the CPS (D-3) method efficiently capitalize on multiple nodes and graphical processing units, expediting heavy tensor contractions. As a result, CPS (D-3) emerges as a scalable, rapid, and precise solution for computing molecular properties in large molecular systems, marking it an efficient contender to conventional CC models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Heterogeneous Reconstruction of Tracks and Primary Vertices With the CMS Pixel Tracker

The High-Luminosity upgrade of the Large Hadron Collider (LHC) will see the accelerator reach an instantaneous luminosity of 7 × 10 34 cm −2 s −1 with an average pileup of 200 proton-proton collisions. These conditions will pose an unprecedented challenge to the online and offline reconstruction software developed by the experiments. The computational complexity will exceed by far the expected increase in processing power for conventional CPUs, demanding an alternative approach. Industry and High-Performance Computing (HPC) centers are successfully using heterogeneous computing platforms to achieve higher throughput and better energy efficiency by matching each job to the most appropriate architecture. In this paper we will describe the results of a heterogeneous implementation of pixel tracks and vertices reconstruction chain on Graphics Processing Units (GPUs). The framework has been designed and developed to be integrated in the CMS reconstruction software, CMSSW. The speed up achieved by leveraging GPUs allows for more complex algorithms to be executed, obtaining better physics output and a higher throughput.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Enabling real-time adaptation of machine learning models at x-ray Free Electron Laser facilities with high-speed training optimized computational hardware

The emergence of novel computational hardware is enabling a new paradigm for rapid machine learning model training. For the Department of Energy’s major research facilities, this developing technology will enable a highly adaptive approach to experimental sciences. In this manuscript we present the per-epoch and end-to-end training times for an example of a streaming diagnostic that is planned for the upcoming high-repetition rate x-ray Free Electron Laser, the Linac Coherent Light Source-II. We explore the parameter space of batch size and data parallel training across multiple Graphics Processing Units and Reconfigurable Dataflow Units. We show the landscape of training times with a goal of full model retraining in under 15 min. Although a full from scratch retraining of a model may not be required in all cases, we nevertheless present an example of the application of emerging computational hardware for adapting machine learning models to changing environments in real-time, during streaming data acquisition, at the rates expected for the data fire hoses of accelerator-based user facilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Adiabatic Quantum Computation Applied to Deep Learning Networks

Training deep learning networks is a difficult task due to computational complexity, and this is traditionally handled by simplifying network topology to enable parallel computation on graphical processing units (GPUs). However, the emergence of quantum devices allows reconsideration of complex topologies. We illustrate a particular network topology that can be trained to classify MNIST data (an image dataset of handwritten digits) and neutrino detection data using a restricted form of adiabatic quantum computation known as quantum annealing performed by a D-Wave processor. We provide a brief description of the hardware and how it solves Ising models, how we translate our data into the corresponding Ising models, and how we use available expanded topology options to explore potential performance improvements. Although we focus on the application of quantum annealing in this article, the work discussed here is just one of three approaches we explored as part of a larger project that considers alternative means for training deep learning networks. The other approaches involve using a high performance computing (HPC) environment to automatically find network topologies with good performance and using neuromorphic computing to find a low-power solution for training deep learning networks. Our results show that our quantum approach can find good network parameters in a reasonable time despite increased network topology complexity; that HPC can find good parameters for traditional, simplified network topologies; and that neuromorphic computers can use low power memristive hardware to represent complex topologies and parameters derived from other architecture choices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Adaptive Fault Detection Based on Neural Networks and Multiple Sampling Points for Distribution Networks and Microgrids

Smart networks such as microgrid (MG) and active distribution networks (ADN) have been recently playing an important role in power system operation. The design and implementation of appropriate protection systems for such networks must be addressed, which imposes new technical challenges. This paper presents the implementation and validation aspects of an adaptive fault detection strategy based on neural networks (NNs) and multiple sampling points for ADN and MG. The solution is implemented on an edge device. Artificial NNs are used to derive a data-driven model that uses only local measurements to detect fault states of the network without the need for communication infrastructure. Multiple sampling points are used to derive a data-driven model, which allows the generalization considering the implementation in physical systems. The adaptive fault detector model is implemented on a Jetson Nano system, which is a single-board computer (SBC) with a small Graphic Processing Unit (GPU) intended to run machine learning loads at the edge. The proposed method is tested in a physical, real-life, low-voltage network located at Universidad del Norte, Colombia. This testing network is based on the IEEE-13 Node Test Feeder scaled down to 220 V. The validation in a simulation environment shows the accuracy and dependability above 99.6%, while the real-time tests show the accuracy and dependability of 95.5% and 100%, respectively. Without hard-to-derive parameters, the easy-to-implement embedded model highlights the potential for real-life applications.

42 ENGINEERING↗
DOE OSTI2016

THOR: A NEW AND FLEXIBLE GLOBAL CIRCULATION MODEL TO EXPLORE PLANETARY ATMOSPHERES

We have designed and developed, from scratch, a global circulation model (GCM) named THOR that solves the three-dimensional nonhydrostatic Euler equations. Our general approach lifts the commonly used assumptions of a shallow atmosphere and hydrostatic equilibrium. We solve the “pole problem” (where converging meridians on a sphere lead to increasingly smaller time steps near the poles) by implementing an icosahedral grid. Irregularities in the grid, which lead to grid imprinting, are smoothed using the “spring dynamics” technique. We validate our implementation of spring dynamics by examining calculations of the divergence and gradient of test functions. To prevent the computational time step from being bottlenecked by having to resolve sound waves, we implement a split-explicit method together with a horizontally explicit and vertically implicit integration. We validate our GCM by reproducing the Earth and hot-Jupiter-like benchmark tests. THOR was designed to run on graphics processing units (GPUs), which allows for physics modules (radiative transfer, clouds, chemistry) to be added in the future, and is part of the open-source Exoclimes Simulation Platform (www.exoclime.org).

79 ASTRONOMY AND ASTROPHYSICS↗