Search NASA⌕ Search

SEARCH · Search NASA

Results for “meshing framework”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 523 records · Page 29

Causality-respecting adaptive refinement for PINNs: enabling precise interface evolution in phase field modeling

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp moving boundaries with complex initial morphologies, remains a challenge. Here, this study introduces an approach combining residual-based adaptive refinement (RBAR) with causality-informed training to enhance the performance of PINNs in solving spatio-temporal PDEs. Our method employs a three-step iterative process: initial causality-based training, RBAR-guided domain refinement, and subsequent causality training on the refined mesh. Applied to the Allen-Cahn equation, a widely-used model in phase field simulations, our approach demonstrates significant improvements in solution accuracy and computational efficiency over traditional PINNs. Notably, we observe an ‘overshoot and relocate’ phenomenon in dynamic cases with complex morphologies, showcasing the method’s adaptive error correction capabilities. This synergistic interaction between RBAR and causality training enables accurate capture of interface evolution, even in challenging scenarios where traditional PINNs fail. Our framework not only resolves the limitations of uniform refinement strategies but also provides a generalizable methodology for solving a broad range of spatio-temporal PDEs. The enhanced performance of the RBAR–causality combined framework demonstrates its strong potential for advancing PINN-based modeling of physical systems characterized by complex, evolving interfaces.

Allen-Cahn equations↗

Steady RANS methodology for calculating pressure drop in an in-line molten salt compact crossflow heat exchanger

We report the development of molten salt cooled reactors (MSR) and fluoride-salt cooled high temperature reactors (FHR) requires the use of advanced design tools for the primary heat exchanger design. Due to geometric and flow characteristics, compact (pitch to diameter ratios equal to or less than 1.25) heat exchangers with a crossflow flow arrangement can become desirable for these reactors. Unfortunately, the available experimental data is limited for compact tube bundles or banks in crossflow. Computational Fluid Dynamics can be used to alleviate the lack of experimental data in these tube banks. Previous computational efforts have been primarily focused on large S/D ratios (larger than 1.4) using unsteady Reynolds averaged Navier-Stokes and Large Eddy Simulation frameworks. These approaches are useful, but have large computational requirements that make comprehensive design studies impractical. A CFD study was conducted with steady RANS in an effort to provide a starting point for future design work. The study was performed for an in-line tube bank geometry with FLiBe (LiF-BeF2), a frequently selected molten salt, as the working fluid. Based on the estimated pressure drops, the pressure and velocity distributions in the domain, an appropriate meshing strategy was determined and presented. Periodic boundaries in the spanwise direction transverse flow were determined to be an appropriate boundary condition for reduced computational domains. The domain size was investigated and a minimum of 2-flow channels for a domain is recommended to ensure the behavior is accounted for. Finally, the standard low Re κ-ε (Lien) turbulence model was determined to be the most appropriate for steady RANS of this case at the time of writing.

42 ENGINEERING↗

Unstructured Adaptive Grid Computations on an Array of SMPs

Dynamic load balancing is necessary for parallel adaptive methods to solve unsteady CFD problems on unstructured grids. We have presented such a dynamic load balancing framework called JOVE, in this paper. Results on a four-POWERnode POWER CHALLENGEarray demonstrated that load balancing gives significant performance improvements over no load balancing for such adaptive computations. The parallel speedup of JOVE, implemented using MPI on the POWER CHALLENCEarray, was significant, being as high as 31 for 32 processors. An implementation of JOVE that exploits 'an array of SMPS' architecture was also studied; this hybrid JOVE outperformed flat JOVE by up to 28% on the meshes and adaption models tested. With large, realistic meshes and actual flow-solver and adaption phases incorporated into JOVE, hybrid JOVE can be expected to yield significant advantage over flat JOVE, especially as the number of processors is increased, thus demonstrating the scalability of an array of SMPs architecture.

Biswas, Rupak↗

Subject-specific modeling framework for particle deposition using computational fluid dynamics

Quantifying particle deposition and dose in the respiratory tract requires a physiologically realistic representation and reproducible computational workflows. However, existing modeling frameworks, such as the International Commission on Radiological Protection (ICRP) compartmental models and the Multiple Path Particle Dosimetry (MPPD) tool, lack detailed deposition profiles and subject-specific capabilities. The combination of advances in computer vision algorithms applied to the respiratory tract and Computational Fluid and Particle Dynamics (CFPD) allows high-fidelity simulations of particle behavior in anatomically accurate geometries derived from individual CT scans. The segmentation, preprocessing, and file preparation task for a CFPD simulation was often time-consuming, and no prior studies to-date have yet presented a fully automated framework. This work presents a fully automated workflow to obtain individualized particle deposition profiles in the human respiratory tract. The pipeline starts with segmenting upper and lower airway geometries using morphological and deep learning-based methods, generating three-dimensional (3D) models from CT imaging data. Next, a series of algorithms are presented to quality check and prepare the 3D geometry for a CFD or CFPD simulation. The preprocessing step includes correcting geometric artifacts, enforcing a physically consistent mesh, and automatically identifying and capping multiple outlets, which is required for CFD/CFPD simulations. These processed models are then input into open-source (OpenFOAM) or commercial (StarCCM+) CFD solvers, where flow and transient particle transport equations — including turbulence and particle–wall interactions are solved under realistic breathing conditions. Finally, the resulting particle deposition profiles can be integrated with Monte Carlo radiation transport codes and state-of-the-art computational phantoms to assess organ-specific absorbed doses in scenarios of radioactive aerosol inhalation. The presented work streamlines respiratory tract segmentation, preprocessing for CFD/CFPD simulations, and integration with dose assessment workflows, reducing manual intervention and improving access to high-fidelity, subject-specific modeling. The high precision in predicted particle deposition and dose distributions can improve personalized treatment strategies in respiratory medicine and refine dose estimates for radiation protection.

AI↗

CHEQUP v0.1

CHEQUP (Castro-based Hofi Expansion with QUasineutral Plasma) is a simulation code for modeling the formation of hydrodynamic optical-field-ionized (HOFI) plasma channels, which are used as waveguides in laser-plasma acceleration experiments. This includes experiments performed at LBNL's BELLA facility as well as other laser facilities across the world. CHEQUP extends the open-source Castro hydrodynamics framework with physics modules tailored for modeling HOFI plasma channels -- including multi-species ionization and three-body recombination for mixtures of hydrogen, nitrogen, helium, and argon ; a two-temperature model tracking electron and heavy-species temperatures separately ; and coupling with other codes of the BLAST ecosystem (https://blast.lbl.gov/) such as WarpX, via the openPMD standard. CHEQUP inherits from Castro the ability to run on modern GPU architectures (NVIDIA CUDA, AMD HIP) and supports adaptive mesh refinement (AMR) for efficient multi-scale resolution. Compared to existing tools, CHEQUP would be, to our knowledge, the first open-source code implementing the full HOFI channel formation physics, and the first implementation capable of running on GPUs. This enables significantly faster, large-scale parameter scans critical for the design of next-generation LPA-based accelerators and light sources.

Lehe, Remi [Lawrence Berkeley National Laboratory ↗

A conservative, interface-resolved, compressible framework for the modeling and simulation of liquid/gas phase change

This paper presents a method for simulating evaporation in a compressible, interface-resolved framework appropriate for modeling problems of engineering interest. In order to achieve robustness and broad applicability, the method has been designed to discretely enforce consistent mass and thermal energy transport at the phase interface, to globally conserve mass, momentum, and energy, and to be capable of modeling compressible and incompressible systems. Verification is performed via the Sod-shock test, one-dimensional heat conduction, evaporation from a planar interface, and evaporation of three-dimensional droplets. Convergence with increasing mesh resolution is demonstrated in all tested configurations, and conservation is maintained near machine precision for a translating droplet. Conservation and accurate phase change rates are preserved at the low numerical resolutions commonly encountered in engineering calculations. Following verification, the method is validated by comparison to an empirical correlation for evaporating droplets in high temperature crossflow, and the presentation concludes with the simulation of an iso-octane spray at conditions representative of gasoline direct injection. In conclusion, successful verification, validation, and demonstrated practical utility suggest the method to be an accurate, efficient, and robust approach for the study of phase change in engineering systems.

97 MATHEMATICS AND COMPUTING↗

Establishing Best Practices for X-57 Maxwell CFD Database Generation

The X-57 Maxwell is NASA’s latest electric airplane concept that has been simulated for aerodynamic performance using the structured overset and unstructured grid solvers within the Launch Ascent and Vehicle Aerodynamics (LAVA) solver framework as well as the unstructured polyhedral grid solver in Star-CCM+ for code-to-code comparison. In order to validate the predictions, comparisons were made between the CFD solutions and experimental data collected in the 12-foot Low-Speed Wind Tunnel at NASA Langley Research Center. The simulations are in preparation for the development of a comprehensive aerodynamic database which will assess aircraft performance at a variety of conditions. The findings from these simulations will establish the best practices for mesh resolution, numerical discretization, and turbulence modeling to be used for this database. Preliminary database results have shown that best-practices learned from the initial validation simulations will potentially reduce error in X-57 aerodynamic loads and moments relative to experiment by up to 14%.

Duensing, Jared C.↗

Hail Storm Risk Assessment Using Space-Borne Remote Sensing Observations and Reanalyses

Much of the world is impacted by severe thunderstorms, but whether they become disasters depends upon resilience--our capacity to prepare, mitigate, respond, and recover. Hail is the costliest severe weather hazard for the insurance industry, generating ~70% of severe convective storm losses due to damage to assets such as homes, businesses, agriculture, and infrastructure. Most insurance companies do not reserve enough capital to cover catastrophes, so they acquire reinsurance. The reinsurance industry uses catastrophe models (CatModels) to statistically estimate risk to an insurer’s portfolio. Hail CatModels are developed with climatologies that define hailstorm frequency and severity. Hail-prone areas can be defined using hail reports from trained spotters, the media, and the general public. Extremely severe hail (2+ inch diameter) occurs nearly every day across the world. Weather radars can detect hail because hailstones strongly reflect microwave signals that they emit. However, hail climatologies are difficult to derive because hail covers small areas and there are neither hail reporting mechanisms (e.g. website or mobile app) nor radar networks in most places outside the US and Europe. This lack of ground truth on severe hail puts society and economies at risk. Hail is generated within storms by strong updrafts. These updrafts exhibit unique signatures in NASA and other agency satellite observations, offering new opportunities for hailstorm analysis. Geostationary (GEO) visible and infrared imagery has been collected for ~15-25 years across the world (region dependent) and methods have been developed at NASA Langley Research Center (LaRC) to detect hailstorm updrafts using GEO imagery. Climatological GEO updraft data has been used by Willis Towers Watson (WTW), a leader in catastrophe risk assessment for the insurance industry, and Karlsruhe Institute of Technology to develop CatModels over Europe and Australia. Hail can also be inferred with passive microwave imagery collected by low-Earth-orbiting sensors such as the GPM GMI, TRMM TMI, AMSR-E, AMSR-2, SSM/I, and SSMIS over the last 20+ years using methods developed at the Marshall Space Flight Center (MSFC). Hailstorms generate enhanced lightning flash rates that can be tracked using new GOES-R series GEO Lightning Mapping (GLM) imagery. Atmospheric reanalyses can be used to define favorable hailstorm environments for combination with the satellite-based storm detections. This presentation will describe a framework for developing continental to global hail climatologies and CatModels based on NASA satellite data and capabilities. This is a collaboration between LaRC and MSFC, WTW, and partners in Brazil, Argentina, and South Africa. This project seeks to mitigate hail disasters by aiding development of new satellite-based severe storm nowcasting tools by regional partners and developing climatologies to improve societal understanding of hail frequency. GEOO visible and infrared metrics of storm intensity, environmental conditions based on reanalyses, spotter hail reports and radar MESH observations are intercompared to quantify the detectability of hailstorms, and our ability to discriminate hailstorms from other severe storms. We are also maturing methods using land surface imaging satellite data (e.g. MODIS, Landsat, Sentinel 1 and 2) to identify hail damage to agriculture. Work with WTW will improve socioeconomic resilience through development of new CatModels. Southern Brazil, Uruguay, Paraguay, and Argentina feature some of the most intense thunderstorms on Earth. South America and South Africa are developing insurance markets of interest to WTW clients, and is similar to other regions routinely impacted by hail that do not have comprehensive hail reporting or radars to assess hailstorm frequency. Project datasets will be made available via online GIS-enabled tools developed at the LaRC Atmospheric Science Data Center (ASDC) which will visualize data and provide it in multiple formats for use in a wide range of open source and commercial tools.

Kristopher Michael Bedka↗

Mortar-based Cohesive Zone Model with Application to TRISO Particle Debonding

The U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel cycle systems. This program has been providing engineering-scale support for the development of BISON, a high-fidelity and high-resolution fuel performance tool. This report outlines work towards the development of an integrated, mortar-based cohesive zone framework with mechanical contact. We model debonding of tri-structural isotropic (TRISO) layers using a mortar approach, extending the framework used for mechanical contact, using weighted quantities. A bilinear mixed mode traction approach, already used in Jiang et al. (2021), is applied analogously herein to model debonding between TRISO particle layers. The examples include the debonding of the inner pyrolytic carbon (IPyC) from the silicon carbide (SiC) layers, as well as partial and full debonding of the buffer from the IPyC layers. Both 2D and 3D examples are utilized to demonstrate the superior numerical performance of the new mortar approach, which allows for modeling arbitrarily meshed interfaces (i.e., non-matching discretizations).

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Meso-scale framework for modeling granular material using computed tomography

Numerical modeling of unconsolidated granular materials is comprised of multiple nonlinear phenomena. Accurately capturing these phenomena, including grain deformation and intergranular forces depends on resolving contact regions several orders of magnitude smaller than the grain size. Here, we investigate a method for capturing the morphology of the individual particles using computed X-ray and neutron tomography, which allows for accurate characterization of the interaction between grains. The ability of these numerical approaches to determine stress concentrations at grain contacts is important in order to capture catastrophic splitting of individual grains, which has been shown to play a key role in the plastic behavior of the granular material on the continuum level. Discretization approaches, including mesh refinement and finite element type selection are presented to capture high stress concentrations at contact points between grains. The effect of a grain’s coordination number on the stress concentrations is also investigated.

36 MATERIALS SCIENCE↗

Unstructured mesh-based multi-physics reactor transient simulation with iMC code

In this study, we present a time-dependent Monte Carlo simulation result about a complex fuel-loaded light water reactor system with thermal-hydraulic feedback using the KAIST iMC code. The intra-pin temperature distribution is calculated based on Monte Carlo-tallied detailed power distribution and the finite element heat transfer method. The temperature effect of fuel, absorber, and coolant are adequately reflected into the dynamic response by the on-the-fly Doppler broadened cross-section correction. For the time-dependent Monte Carlo transport simulation, the predictor-corrector quasi-static Monte Carlo method is used for this study. We tested the coupled analysis framework with a 17-by-17 fuel assembly loaded with the centrally-shielded burnable absorber (CSBA) fuel element. The temperature feedback effect on the material cross-section and the moderator density incurred negative reactivity in response to the external positive reactivity insertion, showing the inherent stability of the reactor system. The pin-wise power and temperature change during the system transient are presented and discussed. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Computational diagnostics for flame acceleration and transition to detonation in a hydrogen/air mixture

A new computational diagnostic method for pressure-induced compressibility is proposed by projecting its local contribution to the chemical explosive mode (CEM) in the chemical explosive mode analysis (CEMA) framework. The new method is validated for the study of detonation development during the deflagration-to-detonation transition (DDT) process. The flame characteristics are identified through the quantification of individual CEM contributions of chemical reaction, diffusion, and pressure-induced compressibility. Numerical simulations are performed to investigate the DDT processes in a stoichiometric hydrogen-air mixture. A Godunov algorithm, fifth-order in space, and third-order in time are used to solve the fully compressible Navier-Stokes equations on a dynamically adapting mesh. A single-step, calibrated chemical diffusive model (CDM) described by Arrhenius kinetics is used for energy release and conservation between the fuel and the product. The new diagnostic method is first applied to onedimensional (1D) canonical flame configurations followed by two-dimensional (2D) simulations of DDT in an obstructed channel where different detonation initiation scenarios are examined using the new CEMA projection formulation. Detailed examinations of the idealized configuration of detonation initiation through shock focusing mechanism at a flame front are also studied using the new formulation. A comparison of the currently proposed CEMA projection and the original formulation by the authors suggests that including the pressure-induced compressibility is essential for the use of CEMA in DDT process. The results also show that the new formulation of CEMA projection can successively capture the detonation initiation through either a gradient mechanism or a direct initiation mechanism, and therefore can be used as an effective local analytical tool for the computational diagnostics of detonation initiation in a DDT process. It was found that detonation development is characterized by a strong contribution of chemistry role to the CEM which is pivotal to the initiation of detonation. The role of compressibility is found enhanced at the edge of the detonation front where diffusion was found to have minimal effects on detonation development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Generator coordinate method for transition-state dynamics in nuclear fission

Since its beginnings, fission theory has assumed that low-energy induced fission takes place through transition-state channels at the barrier tops. Nevertheless, up to now there is no microscopic theory applicable to those conditions. We suggest that modern reaction theory is suitable for this purpose, and propose a methodology based on a configuration-interaction framework using the generator coordinate method (GCM). Simple reaction-theoretic models are constructed with the Gaussian overlap approximation to parametrize both the dynamics within the channels and their incoherent couplings to states outside the barrier. The physical characteristics of the channels examined here are their effective bandwidths and the quality of the coupling to compound-nucleus states as measured by the transmission factor T. We also investigate the spacing of GCM states with respect to their degree of overlap. We find that a rather coarse mesh provides an acceptable accuracy for estimating the bandwidths and transmission factors. The common numerical stability problem in using the GCM is avoided due to the choice of meshes and the finite bandwidths of the channels. Here, the bandwidths of the channels are largely controlled by the zero-point energy with respect to the collective coordinate in the GCM configurations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Frameworks, Algorithms, and Scalable Technologies for Mathematics (FASTMath) SciDAC Institute

The FASTMath SciDAC Institute addressed two key challenges that application scientists faced at the beginning of SciDAC-3. First, FASTMath helped them continue to improve the quality of their simulations by increasing accuracy and reliability of both their software and algorithms. Second, FASTMath helped them adapt their computations to make effective use of high-end computing facilities acquired by DOE over the past five years. This required the development of new mathematical algorithms that were appropriate for the physics problems being solved, implementations that scaled to million-way parallelism, and software that effectively leveraged both distributed memory and on-node parallelism. The Rensselaer Polytechnic Institute team’s efforts focused on the unstructured mesh technologies developed by FASTMath.

97 MATHEMATICS AND COMPUTING↗

Gateway Element and Payload Materials Outgassing Analyses: HALO, HERMES, and ERSA

Gateway was intended to be humanity’s first space station around the Moon, but its development has been paused as the National Aeronautics and Space Administration (NASA) shifts focus to achieving the United States’ National Space Policy goals. Instead of an orbiting lunar outpost, NASA will now pursue the development of a lunar surface base to support a sustained human presence on the Moon. Before the program’s pause, Gateway’s Induced Environments team worked to ensure payloads and elements (i.e., modules) complied with induced environment requirements. Methods developed and insights gained from this work will have applicability to NASA’s Moon Base and the potential repurposing of Gateway elements and payloads, as well as to induced environments modeling for future space stations. The Gateway program’s induced environment included molecular contamination, electric thruster plume sputter and redeposition, and lunar dust transfer from the Human Landing System (HLS). Primary sources of external molecular contamination included materials outgassing, chemical thruster plume contamination, and vacuum venting. The focus of this paper will be on element- and payload-level materials outgassing analyses performed for Gateway Configuration 1, extending the previously-developed framework for Gateway system-level external molecular contamination modeling. Gateway Configuration 1 consisted of the Power and Propulsion Element (PPE) and the Habitation and Logistics Outpost (HALO). It also included payloads like the European Radiation Sensor Array (ERSA) attached to PPE and the Heliophysics Environmental and Radiation Measurement Experiment Suite (HERMES) attached to HALO. The element- and payload-level analyses to be introduced in this paper for HALO, HERMES, and ERSA enabled high-fidelity descriptions of Gateway’s external molecular contamination environment. Approaches to geometric modeling, meshing, outgassing rate assignment, molecular transport modeling, and analysis methodology will be presented. Element and payload contaminant deposition onto sensitive Gateway receiver surfaces will be summarized and results compared to induced environment requirements. While these results incorporate refinements made over the course of the program, they were not intended to be final. Therefore, modeling assumptions and inputs, potential improvements, and lessons-learned will be documented to inform future work on Moon Base, repurposed elements and payloads, and other space stations.

Gateway↗

System monitoring and diagnosis with qualitative models

A substantial foundation of tools for model-based reasoning with incomplete knowledge was developed: QSIM (a qualitative simulation program) and its extensions for qualitative simulation; Q2, Q3 and their successors for quantitative reasoning on a qualitative framework; and the CC (component-connection) and QPC (Qualitative Process Theory) model compilers for building QSIM QDE (qualitative differential equation) models starting from different ontological assumptions. Other model-compilers for QDE's, e.g., using bond graphs or compartmental models, have been developed elsewhere. These model-building tools will support automatic construction of qualitative models from physical specifications, and further research into selection of appropriate modeling viewpoints. For monitoring and diagnosis, plausible hypotheses are unified against observations to strengthen or refute the predicted behaviors. In MIMIC (Model Integration via Mesh Interpolation Coefficients), multiple hypothesized models of the system are tracked in parallel in order to reduce the 'missing model' problem. Each model begins as a qualitative model, and is unified with a priori quantitative knowledge and with the stream of incoming observational data. When the model/data unification yields a contradiction, the model is refuted. When there is no contradiction, the predictions of the model are progressively strengthened, for use in procedure planning and differential diagnosis. Only under a qualitative level of description can a finite set of models guarantee the complete coverage necessary for this performance. The results of this research are presented in several publications. Abstracts of these published papers are presented along with abtracts of papers representing work that was synergistic with the NASA grant but funded otherwise. These 28 papers include but are not limited to: 'Combined qualitative and numerical simulation with Q3'; 'Comparative analysis and qualitative integral representations'; 'Model-based monitoring of dynamic systems'; 'Numerical behavior envelopes for qualitative models'; 'Higher-order derivative constraints in qualitative simulation'; and 'Non-intersection of trajectories in qualitative phase space: a global constraint for qualitative simulation.'

Kuipers, Benjamin↗

An implicit-in-time DPG formulation of the 1D1V Vlasov-Poisson equations

Efficient solution of the Vlasov equation, which can be up to six-dimensional, is key to the simulation of many difficult problems in plasma physics. The discontinuous Petrov-Galerkin (DPG) finite element methodology provides a framework for the development of stable (in the sense of Ladyzhenskaya–Babuška–Brezzi conditions) finite element formulations, with built-in mechanisms for adaptivity. While DPG has been studied extensively in the context of steady-state problems and to a lesser extent with space-time discretizations of transient problems, relatively little attention has been paid to time-marching approaches. In the present work, we study a first application of time-marching DPG to the Vlasov equation, using backward Euler for a Vlasov-Poisson discretization. We demonstrate adaptive mesh refinement for two problems: the two-stream instability problem, and a cold diode problem. Furthermore, we believe the present work is novel both in its application of unstructured adaptive mesh refinement (as opposed to block-structured adaptivity, which has been studied previously) in the context of Vlasov-Poisson, as well as in its application of DPG to the Vlasov-Poisson system. We also discuss extensive additions to the Camellia library in support of both the present formulation as well as extensions to higher dimensions, Maxwell equations, and space-time formulations.

97 MATHEMATICS AND COMPUTING↗

Learning effective physical laws for generating cosmological hydrodynamics with Lagrangian deep learning

The goal of generative models is to learn the intricate relations between the data to create new simulated data, but current approaches fail in very high dimensions. When the true data-generating process is based on physical processes, these impose symmetries and constraints, and the generative model can be created by learning an effective description of the underlying physics, which enables scaling of the generative model to very high dimensions. In this work, we propose Lagrangian deep learning (LDL) for this purpose, applying it to learn outputs of cosmological hydrodynamical simulations. The model uses layers of Lagrangian displacements of particles describing the observables to learn the effective physical laws. The displacements are modeled as the gradient of an effective potential, which explicitly satisfies the translational and rotational invariance. The total number of learned parameters is only of order 10, and they can be viewed as effective theory parameters. Further, we combine N-body solver fast particle mesh (FastPM) with LDL and apply it to a wide range of cosmological outputs, from the dark matter to the stellar maps, gas density, and temperature. The computational cost of LDL is nearly four orders of magnitude lower than that of the full hydrodynamical simulations, yet it outperforms them at the same resolution. We achieve this with only of order 10 layers from the initial conditions to the final output, in contrast to typical cosmological simulations with thousands of time steps. This opens up the possibility of analyzing cosmological observations entirely within this framework, without the need for large dark-matter simulations.

79 ASTRONOMY AND ASTROPHYSICS↗