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At least 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Numerical coupling of aerosol emissions, dry removal, and turbulent mixing in the E3SM Atmosphere Model version 1 (EAMv1) – Part 2: A semi-discrete error analysis framework for assessing coupling schemes

Abstract. Part 1 (Wan et al., 2024) of this study discusses the motivation and empirical evaluation of a revision to the aerosol-related numerical process coupling in the atmosphere component of the Energy Exascale Earth System Model version 1 (EAMv1) to address the previously reported issue of strong sensitivity of the simulated dust aerosol lifetime and dry removal rate to the model's vertical resolution. This paper complements that empirical justification of the revised scheme with a mathematical justification leveraging a semi-discrete analysis framework for assessing the splitting error of process coupling methods. The framework distinguishes the error due to numerical splitting from the error due to the time integration method(s) used for each individual process. Such a distinction results in a framework that provides an intuitive understanding of the causes of the splitting error. The application of this framework to the dust life cycle in EAMv1 confirms (i) that the original EAMv1 scheme artificially strengthens the effect of dry removal processes and (ii) that the revised splitting reduces that artificial strengthening. While the error analysis framework is presented in the context of the dust life cycle in EAMv1, the framework can be broadly leveraged to evaluate process coupling schemes, both in other physical problems and for any number of processes. This framework will be particularly powerful when the various process implementations support a variety of time integration approaches. Whereas traditional local truncation error approaches require separate consideration of each combination of time integration methods, this framework enables evaluation of coupling schemes independent of particular time integration approaches for each process while still allowing for the incorporation of these specific time integration errors if so desired. The framework also explains how the splitting error terms result from (i) the integration of individual processes in isolation from other processes and (ii) the choices of input state and time step size for the isolated integration of processes. Such a perspective has the potential for the rapid development of alternative coupling approaches that utilize knowledge both about the desired accuracy and about the computational costs of individual processes.

58 GEOSCIENCES↗
DOE OSTI2022

Parallel transport sweeps on two-dimensional cartesian and hexagonal grids

This paper aims to provide a proof of concept for parallel transport sweeps on two-dimensional hexagonal grids for the discrete ordinates transport equation. While the method is an extension of the popular and well-established Koch-Baker-Alcoulffe (KBA) algorithm, there are significant differences between the cartesian and hexagonal grid and thereafter sweep. The most important is the three-way connectivity of hexagons within the grid which creates greater dependencies between the elements. The KBA method in structured orthogonal grids was first implemented in the DRAGON5 code and the method is first described here. The differences in implementation for the hexagonal grid are also described. Benchmark results are also presented, showing roughly 10 times speedup in computational times with roughly 100 processors, in both cases. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

A Real-Time Testbed for Smart Inverter Cyber Security Studies

Distributed energy resources (DER) have become a popular solution to modern-day issues surrounding the efficiency and reliability of power generation, as well as climate change concerns. Energy centers are shifting towards incorporating smart inverters with embedded functionalities such as high voltage ride through (HVRT), low voltage ride through (LVRT), active and reactive power compensation. However, the integration of smart inverters leave DER systems highly vulnerable to cybersecurity threats. The distributed network protocol 3 (DNP3) is a common method of communication between grid-tied hardware. Despite its popularity, the level of security leaves all hardware connected to the grid at risk of severe cyber-attacks. Thus, it is important to study any potential cybersecurity threats towards grid-tied smart inverters to mitigate cybersecurity vulnerabilities and refine existing cyber-security protections. This report describes the proposed testbed design to study cybersecurity threats to smart inverters. The testbed utilizes a real-time simulation case in RSCAD that includes a grid-tied wind turbine (WT) topology featuring two back-to-back two-level voltage source converters (BTB,2L-VSCs) and a permanent magnet synchronous machine (PMSM). The simulated case runs within the NovaCor real time digital simulator (RTDS). This report focuses on the design and implementation of a single module of the GTNETx2 card as a distributed network protocol and the configuration of an IEEE 1518 DNP database file that includes input and output variables mapped to different connection points in the grid that transmit and receive discrete, analog, and binary signals on command. This allows realistic emulation of the communication between the smart inverter and the grid for cybersecurity studies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Embedded, Real-Time, and Distributed Traveling Wave Fault Location Method Using Graph Convolutional Neural Networks

This work proposes and develops an implementation of a fault location method to provide a fast and resilient protection scheme for power distribution systems. The method analyzes the transient dynamics of traveling waves (TWs) to generate features using the discrete wavelet transform (DWT), which are then used to train several graph convolutional network (GCN) models. Faults are simulated in the IEEE 34-node system, which is divided into three protection zones (PZs). The goal is to identify the PZ in which the fault occurs. The GCN models create a distributed protection scheme, as all nodes are able to retrieve a prediction. Given that message-passing between nodes occurs both during training and in the execution of the model, the resiliency of such schemes to communication losses was analyzed and demonstrated. One of the models, which only uses voltage measurements, was implemented on a Texas Instruments F28379D development board. The execution times were monitored to assess the speed of the protection scheme. It is shown that the proposed method can be executed in approximately a millisecond, which is comparable to existing TW protection in the transmission system. For experimental purposes, a DWT-based detection method is employed. A design of a setup to playback TWs using two development boards is also addressed.

Jiménez-Aparicio, Miguel (ORCID:000000016864461X)↗
DOE OSTI2020

Analysis of Electric Vehicle Charging Behavior Patterns with Function Principal Component Analysis Approach

This manuscript focused on analyzing electric vehicles’ (EV) charging behavior patterns with a functional data analysis (FDA) approach, with the goal of providing theoretical support to the EV infrastructure planning and regulation, as well as the power grid load management. 5-year real-world charging log data from a total of 455 charging stations in Kansas City, Missouri, was used. The focuses were placed on analyzing the daily usage occupancy variability, daily energy consumption variability, and station-level usage variability. Compared with the traditional discrete-based analysis models, the proposed FDA modeling approach had unique advantages in preserving the smooth function behavior of the data, bringing more flexibility in the modeling process with little required assumptions or background knowledge on independent variables, as well as the capability of handling time series data with different lengths or sizes. In addition to the patterns revealed in the EV charging station’s occupancy and energy consumption, the differences between EV driver’s charging time and parking time were analyzed and called for the needs for parking regulation and enforcement. The different usage patterns observed at charging stations located on different land-use types were also analyzed.

Engineering↗
DOE OSTI2023

Investigation of Best-Practices and Computationally Inexpensive Radiative Exchange Models for Discrete Element Method Modeling of Aluminosilicate Particles in Concentrating Solar Power Environments

Chemically inert, aluminosilicate based particles have been investigated as both a thermal transport and sensible energy storage medium for concentrating solar power facilities. These particles will experience a wide range of operating temperatures (300-1000 K) and handling conditions (dense to dilute falling particle curtains, dense granular flows, or dense structures), requiring specially-designed and optimized infrastructures. The relative influence of collisional and frictional interactions between particles varies based on temperature-dependent particulate properties and greatly impacts the bulk, granular flow behavior. These underlying physics are captured using discrete element method modeling tools. However, this modeling method is computationally expensive as each particle position and interaction is tracked during the simulation. These modeling methods are further complicated by introducing temperature-dependent particle properties, high-temperature radiative exchange, and directional irradiation sources experienced by granular flows in concentrating solar power environments. In this study, coupled experimental and numerical slump testing of aluminosilicate particles was performed and computationally efficient radiative exchange models were evaluated to establish best-practices for discrete element method models for concentrating solar power environments. The three particle types investigated included Carbobead HSP 30 /60, Carbobead CP 30/60, and Granusil 4030. Existing modeling limitations and computationally-efficient multi-modal heat transfer models were evaluated using Aspherix®, a commercial discrete element method software. High-temperature (< 1073 K) slump testing of aluminosilicate particles was performed to investigate the deviation between experimentally-observed and numerically-predicted angles of repose introduced by computation-time reduction practices including the relaxation of the particle elastic modulus and coarse-graining. Coarse-graining is used to use a single modeled particle that is representative of a collection of smaller particles, decreasing the computational cost at the expense of geometric accuracy. Additionally, relaxation of the elastic modulus is used to reduce computational time at the expense of an increased, modeled particle overlap. Prior studies have determined that aluminosilicate particles retain a high elastic modulus at high temperatures (< 1073 K), requiring small simulation timesteps to ensure resolved contact forces resemble appropriate solid mechanics. A parametric study was performed to evaluate the influence of computation time improvements on the deviation between experimental and modeled angle of repose across high temperatures < 1073 K. Additionally, numerical case studies were performed on candidate particle systems at varying porosities and temperatures. These studies were performed to investigate the influence of computationally-efficient radiative-exchange modeling methods coupled to Aspherix® on modeled accuracy and computation time. The recently-developed distance-based approximation was evaluated in estimating radiative exchange between particles and participating surfaces located in close proximity. The distance based approximation was developed to use tabulated estimates of the radiative distribution factor between individual particles and surfaces in close proximity (< 40 particle radii). These methods were expanded to the aluminosilicate particles of interest, including the influence of particle size distributions. To capture radiative exchange between particles and surfaces not in close proximity (> 40 particle radii) and to capture the absorption of directional irradiation from concentrating solar resources, a volumetrically-averaged radiative distribution factor was calculated between the modeled granular flow and surfaces using Monte Carlo ray-tracing for participating media. Volume-averaged absorption and scattering coefficients were predicted using a volumetric discretization of the modeled domain with monodisperse approximations based on geometric optics and experimentally-determined scattering phase functions for aluminosilicate particles.

14 SOLAR ENERGY↗
DOE OSTI2022

A reinforcement learning approach to long-horizon operations, health, and maintenance supervisory control of advanced energy systems

In this work, we develop a Reinforcement Learning (RL) approach to the supervisory control problem for advanced energy systems, such as novel nuclear reactors and other demand-driven, mission-critical, and component-health-sensitive energy plants. The inclusive problem landscape considered captures the stochastic confluence of plant performance, component health evolution, power demand from the grid, diverse maintenance actions, and operator-defined goals and constraints, all considered over meaningfully long-enough reasoning horizons. Key aspects of the proposed approach are a receding horizon control-inspired technique dictating time- or event-triggered supervisory policy (re-)constructions, as well as additional capability-enabling contributions such as timescale compression, to handle long reasoning horizons and uncertainty in parts of the problem, and practical yet demonstrably-effective handling of hybrid action spaces with continuous and discrete decision variables. The resulting algorithm consists of a simulation-based RL agent constructing stochastic supervisory control policies over nontrivial action spaces and for long horizons, applying the learned policy to the system for a much shorter interval, and perpetually repeating, to construct the next long-horizon policy. That next policy will only be applied, again, for a short interval, yet originally far-in-time events move progressively closer, their associated uncertainty decreases, and new events and aspects enter the reasoning horizon. The proposed methodology bridges fundamental receding horizon concepts with the unequivocally stronger and more scalable reasoning of contemporary RL. Numerical examples using Soft Actor–Critic Deep RL illustrate the operation and efficacy of the proposed technique for a power plant tasked with health-aware load following missions in a dynamic electricity market landscape.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Very small-scale, segregating-fluidized-bed experiments: A dataset for CFD-DEM validation and uncertainty quantification

IWe report fluidization experiments were conducted on a small scale and with a rapid response (short duration) to enable corresponding simulations at low-computational cost. Rise times are reported for four or fewer polyethylene particles (intruders) in an air-fluidized bed of ~5000 group D glass beads. Experimental inputs were completely characterized—particle properties, system dimensions and operating conditions—which is necessary for validating computational fluid mechanics (CFD)-discrete element method (DEM) including a comprehensive uncertainty quantification (UQ) analysis. Input uncertainties are reported as bounds or cumulative distribution functions of measured values. The staggering number of simulations required to complete a UQ analysis (~O[10 4 ] simulations corresponding to ~5 uncertain inputs) motivates this study. These segregating-bed experiments are designed to permit analogous CFD-DEM simulations to complete in less than a day on a single (~2.5 GHz) computational processor unit (CPU). Segregation times are reported for several operating conditions, intruder sizes, and initial configurations, providing a rich dataset for numerical model testing, validation and UQ.

42 ENGINEERING↗
DOE OSTI2022

A Comparison of Linear Solvers for Resolving Flow in Three-Dimensional Discrete Fracture Networks

We compare various methods for resolving steady flow within three-dimensional discrete fracture networks, including direct methods, Krylov subspace methods with and without preconditioning, and multi-grid methods. We compared the performance of the methods based on compute times and scaling of the solution as a function of the number of grid nodes and log-variance of the hydraulic aperture. The methods are applied to three test cases: (a) variable density of networks with a truncated power-law distribution of fracture lengths, (b) a fixed network composed of monodisperse fracture sizes but varied permeability/aperture heterogeneity, (c) and a network based on field site in Nevada, US. We chose these cases to allow us to study the impact of the mesh size and flow properties, as well as to demonstrate our conclusions on a large-scale, realistic problem (more than 40 million mesh nodes). A direct solution using Cholesky factorization outperformed other methods for every example but was closely followed in performance by some algebraic multigrid (AMG) preconditioned Krylov subspace methods. Among the Krylov methods, conjugate gradients (CG) with an AMG preconditioner performs the best. Generally, Cholesky factorization is recommended, but CG with an AMG preconditioner may be suitable for very large problems beyond 40 million nodes where the entire linear system cannot reside in memory.

58 GEOSCIENCES↗
DOE OSTI2024

Streamlined spatial and environmental expression signatures characterize the minimalist duckweed Wolffia australiana

Single-cell genomics permits a new resolution in the examination of molecular and cellular dynamics, allowing global, parallel assessments of cell types and cellular behaviors through development and in response to environmental circumstances, such as interaction with water and the light–dark cycle of the Earth. Here, we leverage the smallest, and possibly most structurally reduced, plant, the semiaquaticWolffia australiana, to understand dynamics of cell expression in these contexts at the whole-plant level. We examined single-cell-resolution RNA-sequencing data and foundWolffiacells divide into four principal clusters representing the above- and below-water-situated parenchyma and epidermis. Although these tissues share transcriptomic similarity with model plants, they display distinct adaptations thatWolffiahas made for the aquatic environment. Within this broad classification, discrete subspecializations are evident, with select cells showing unique transcriptomic signatures associated with developmental maturation and specialized physiologies. Assessing this simplified biological system temporally at two key time-of-day (TOD) transitions, we identify additional TOD-responsive genes previously overlooked in whole-plant transcriptomic approaches and demonstrate that the core circadian clock machinery and its downstream responses can vary in cell-specific manners, even in this simplified system. Distinctions between cell types and their responses to submergence and/or TOD are driven by expression changes of unexpectedly few genes, characterizingWolffiaas a highly streamlined organism with the majority of genes dedicated to fundamental cellular processes.Wolffiaprovides a unique opportunity to apply reductionist biology to elucidate signaling functions at the organismal level, for which this work provides a powerful resource.

Biochemistry & Molecular Biology↗
DOE OSTI2023

Mobiliti v1.0

Mobiliti is a software platform designed to emulate the dynamics of a regional transportation road network. It is built on open-source software that provides parallel discrete-event simulation. The software is transformative in the area of transportation network simulation because of the geospatial scale and fidelity of the network model and the computational time it takes to model a full day of travel demand. For example, it runs a simulation of the entire San Francisco Bay Area, with a network model of ~1M links and a population that completes ~19M trips in ~5 minutes. This scale of simulation has not been attempted with existing simulation models due to the complexity of the model and the computational time it would take to complete. The intent of the software is to create a digital twin capability for cities to evaluate consequences of infrastructure or policy changes on road network dynamics.

Macfarlane, Jane↗
DOE OSTI2025

Memoirs of Mass Accretion: Probing the Edges of Intracluster Light in Simulated Galaxy Clusters

The diffuse starlight extending throughout massive galaxy clusters, known as intracluster light (ICL), has the potential to be read as a memoir of mass accretion: informative, individual, and yet imperfect. Here, we combine dark-matter-only zoom-in simulations from the Symphony suite with the Nimbus “star-tagging” model of the stellar halo to assess how much information about the mass assembly of an individual galaxy cluster can be gleaned from idealized measurements of ICL outskirts. We show that the edges of a cluster’s stellar profile—the primary (R sp⋆,1 ) and secondary (R sp⋆,2 ) stellar “splashback” radii—are sensitive to both continuous mass accretion histories (MAHs) and discrete merger events, making them potentially powerful probes of a cluster’s past. We find that R sp⋆,1 strongly correlates with the cluster’s mass ∼1 dynamical time ago, while R sp⋆,2 traces more recent MAH to a slightly lesser degree. In combination, these features can further distinguish between clusters that have and have not undergone a major merger within the past dynamical time. We use both to predict realistic cluster MAHs with the MultiCAM framework. These outer ICL features are significantly more sensitive to mass accretion and merger histories than the stellar mass gap and halo concentration, and perform comparably to the commonly used X-ray-based tracer of relaxedness, x off . While our analysis is idealized, the relevant ICL features are potentially detectable in next-generation deep imaging of nearby clusters. This work highlights the promise of ICL measurements and lays the groundwork for more detailed forecasts of their power.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Optimality of Gradient-MUSIC for Spectral Estimation

We introduce the Gradient-MUSIC algorithm for estimating the unknown frequencies and amplitudes of a nonharmonic signal from noisy time samples. While the classical MUSIC algorithm performs a computationally expensive search over a fine grid, Gradient-MUSIC is significantly more efficient and eliminates the need for discretization over a fine grid by using optimization techniques. It coarsely scans the 1D landscape to find initialization simultaneously for all frequencies followed by parallelizable local refinement via gradient descent. We also analyze its performance when the noise level is sufficiently small and the signal frequencies are separated by at least 8π/m, where π/m is the standard resolution of this problem. Even though the 1D landscape is nonconvex, we prove a global convergence result for Gradient-MUSIC: coarse scanning provably finds suitable initialization and gradient descent converges at a linear rate. In addition to convergence results, we also upper bound the error between the true signal frequencies and amplitudes with those found by Gradient-MUSIC. For example, if the noise has $\ell^\infty$ norm at most ϵ, then the frequencies and amplitudes are recovered up to error at most Cϵ/m and Cϵ respectively, which are minimax optimal in m and ϵ. Our theory can also handle stochastic noise with performance guarantees under nonstationary independent Gaussian noise. Our main approach is a comprehensive geometric analysis of the landscape, a perspective that has not been explored before.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Fiber-optic diagnostic system for future accelerator magnets

The next generation high energy physics accelerators will require magnetic fields at ~20 T. HTS coils will be an essential component of future accelerator magnets and several efforts are currently dedicated on designing 20 T HTS- LTS hybrid magnets. Among the existing challenges, there is the lack of a robust quench detection system for hybrid magnet technology. Another big challenge is represented by the high number of training quenches required by Nb3Sn magnets to reach performance level. In this framework it is important to find a tool that allow local real-time monitoring of magnet strain and temperature. In this paper, we propose the use of fiber optics sensors for diagnostic and quench detection in future accelerator superconducting magnets. Discrete and distributed fiber optic sensors have demonstrated to be a promising tool. The goal is to instrument hundreds of accelerator superconducting magnets and to move beyond the proof-of-concept level. Significant developments are still needed. Here, we are going to present the most recent results and discuss the most urgent technical developments in order to make those sensors a robust and reliable diagnostic tool for accelerator superconducting magnets over the next 10 year. We foresee that discrete fiber sensors will be a stable diagnostic probe for superconducting magnets over the next 3 to 5 years. More R&D work will be necessary for distributed fibers. The most urgent needs are the increase of sample rate and sensitivity. Close collaboration with vendors will be necessary to improve mechanical properties and fabrication processes in order to produce hundreds of meters of fiber and instrument a large number of accelerator superconducting magnets. Those R&D efforts will last up to 10 years with a founding level that spans between 5-10 M$.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

Efficient Reformulation of Linear and Nonlinear Solid-Phase Diffusion in Lithium-ion Battery Models using Symmetric Polynomials: Mass Conservation and Computational Efficiency

Lithium-ion batteries are typically modeled using porous electrode theory coupled with various transport and reaction mechanisms, along with suitable discretization or approximations for the solid-phase diffusion equation. The solid-phase diffusion equation represents the main computational burden for typical pseudo-2-dimensional (p2D) models since these equations in the pseudo r -dimension must be solved at each point in the computational grid. This substantially increases the complexity of the model as well as the computational time. Traditional approaches towards simplifying solid-phase diffusion possess certain significant limitations, especially in modeling emerging electrode materials which involve phase changes and variable diffusivities. A computationally efficient representation for solid-phase diffusion is discussed in this paper based on symmetric polynomials using Orthogonal Collocation and Galerkin formulation (weak form). A systematic approach is provided to increase the accuracy of the approximation (p form in finite element methods) to enable efficient simulation with a minimal number of semi-discretized equations, ensuring mass conservation even for non-linear diffusion problems involving variable diffusivities. These methods are then demonstrated by incorporation into the full p2D model, illustrating their advantages in simulating high C-rates and short-time dynamic operation of Lithium-ion batteries.

25 ENERGY STORAGE↗
DOE OSTI2021

Multilevel Graph Partitioning for Three-Dimensional Discrete Fracture Network Flow Simulations

We present a topology-based method for mesh-partitioning in three-dimensional discrete fracture network (DFN) simulations that takes advantage of the intrinsic multi-level nature of a DFN. DFN models are used to simulate flow and transport through low-permeability fractured media in the subsurface by explicitly representing fractures as discrete entities. The governing equations for flow and transport are numerically integrated on computational meshes generated on the interconnected fracture networks. Modern high-fidelity DFN simulations require high-performance computing on multiple processors where performance and scalability depends partially on obtaining a high-quality partition of the mesh to balance work-loads and minimize communication across all processors. The discrete structure of a DFN naturally lends itself to various graph representations, which can be thought of as coarse-scale representations of the computational mesh. Using this concept, we develop two applications of the multilevel graph partitioning algorithm to partition the mesh of a DFN. In the first, we project a partition of the graph based on the DFN topology onto the mesh of the DFN and in the second, this DFN-based projection is used as the initial condition for further partitioning refinement of the mesh. We compare the performance of these methods with standard multi-level graph partitioning using graph-based metrics (cut, imbalance, partitioning time), computational-based metrics (FLOPS, iterations, solver time), and total run time. The DFN-based and the mesh-based partitioning methods are comparable in terms of the graph-based metrics, but the time required to obtain the partition is several orders of magnitude faster using the DFN-based partitions. The computation-based metrics show comparable performance between both methods so, in combination, the DFN-based partitions are several orders of magnitude faster than the mesh-based partition. Furthermore, the method which uses the DFN-partition solution as the initial condition of the mesh partition provided cut and imbalance values that were close to the mesh-based partition but in a fraction of the time. In turn, this hybrid method outperformed both of the other methods in terms of the total run time.

58 GEOSCIENCES↗
DOE OSTI2022

Fast nonlinear iterative solver for an implicit, energy-conserving, asymptotic-preserving charged-particle orbit integrator

Here recently, an asymptotic-preserving (AP) particle orbit integrator has been proposed with remarkable properties including exact energy conservation, the ability to capture of all first-order drifts (including the ∇B-drift), the ability to capture trapped-passing boundaries with parallel velocity extremely close to the critical velocity, and the ability to transition from strongly to weakly magnetized spatial regions. The new AP orbit integrator is implicit, employing a Crank-Nicolson (CN) temporal discretization to ensure exact energy conservation. This, in turn, requires a local nonlinear iteration involving particle velocities and positions, and the local electromagnetic fields, to obtain the new-time solution. Ref. [1] did not attempt to provide an efficient solver for this system, and employed a brute-force GMRES-driven Jacobian-free Newton-Krylov (JFNK) solver to invert the particle orbit equations at every timestep for expediency. While JFNK is robust and reliable, it is also expensive and very intrusive for practical implementations of the method (it requires having the JFNK machinery available and solving a 6 x 6 Jacobian system iteratively once per iteration per particle).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

CLPNets: Coupled Lie–Poisson neural networks for multi-part Hamiltonian systems with symmetries

To accurately compute data-based prediction of Hamiltonian systems, it is essential to utilize methods that preserve the structure of the equations over time. We consider a particularly challenging case of systems with interacting parts that do not reduce to pure momentum evolution. Such systems are essential in scientific computations, such as discretization of a continuum elastic rod, which can be viewed as the group of rotations and translations $SE(3)$. The evolution involves not only the momenta but also the relative positions and orientations of the particles. The presence of Lie group-valued elements, such as relative positions and orientations, poses a problem for applying previously derived methods for data-based computing. We develop a novel method of data-based computation and complete phase space learning of such systems. We follow the original framework of SympNets (Jin et al., 2020) and LPNets (Eldred et al., 2024), building the neural network from phase space mappings that preserve the Lie–Poisson structure. We derive a novel system of mappings that are built into neural networks describing the evolution of such systems. We call such networks Coupled Lie–Poisson Neural Networks, or CLPNets. We consider increasingly complex examples for the applications of CLPNets, starting with the rotation of two rigid bodies about a common axis, progressing to the free rotation of two rigid bodies, and finally to the evolution of two connected and interacting $SE(3)$ components, describing the discretization of an elastic rod into two elements. Our method preserves all Casimir invariants to machine precision, preserves energy to high accuracy, and shows good resistance to the curse of dimensionality, requiring only a few thousand data points for all cases studied (three to eighteen dimensions). Additionally, the method is highly economical in memory requirements, requiring only about 200 parameters for the most complex case considered.

Data-based modeling↗