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At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

NH-PINN: Neural homogenization-based physics-informed neural network for multiscale problems

Physics-informed neural network (PINN) is a data-driven approach to solving equations. It is successful in many applications; however, the accuracy of the PINN is not satisfactory when it is used to solve multiscale equations. Homogenization approximates a multiscale equation by a homogenized equation without multiscale property; it includes solving cell problems and the homogenized equation. The cell problems are periodic, and we propose an oversampling strategy that significantly improves the PINN accuracy on periodic problems. The homogenized equation has a constant or slow dependency coefficient and can also be solved by PINN accurately. We hence proposed a 3-step method, neural homogenization based PINN (NH-PINN), to improve the PINN accuracy for solving multiscale problems with the help of homogenization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A low-rank power iteration scheme for neutron transport criticality problems

Computing effective eigenvalues for neutron transport often requires a fine numerical resolution. Here, the main challenge of such computations is the high memory effort of classical solvers, which limits the accuracy of chosen discretizations. In this work, we derive a method for the computation of effective eigenvalues when the underlying solution has a low-rank structure. This is accomplished by utilizing dynamical low-rank approximation (DLRA), which is an efficient strategy to derive time evolution equations for low-rank solution representations. The main idea is to interpret the iterates of the classical inverse power iteration as pseudo-time steps and apply the DLRA concepts in this framework. In our numerical experiment, we demonstrate that our method significantly reduces memory requirements while achieving the desired accuracy. Analytic investigations show that the proposed iteration scheme inherits the convergence speed of the inverse power iteration, at least for a simplified setting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Integrating a ponderomotive guiding center algorithm into a quasi-static particle-in-cell code based on azimuthal mode decomposition

High fidelity modeling of plasma based acceleration (PBA) requires the use of three dimensional, fully nonlinear, and kinetic descriptions based on the particle-in-cell (PIC) method. In PBA an intense particle beam or laser (driver) propagates through a tenuous plasma whereby it excites a plasma wave wake. Three-dimensional PIC algorithms based on the quasi-static approximation (QSA) have been successfully applied to efficiently model the interaction between relativistic charged particle beams and plasma. In a QSA PIC algorithm, the plasma response to a charged particle beam or laser driver is calculated based on forces from the driver and self-consistent forces from the QSA form of Maxwell's equations. These fields are then used to advance the charged particle beam or laser forward by a large time step. Since the time step is not limited by the regular Courant-Friedrichs-Lewy (CFL) condition that constrains a standard 3D fully electromagnetic PIC code, a 3D QSA PIC code can achieve orders of magnitude speedup in performance. Recently, a new hybrid QSA PIC algorithm that combines another speedup technique known as an azimuthal Fourier decomposition has been proposed and implemented. This hybrid algorithm decomposes the electromagnetic fields, charge and current density into azimuthal harmonics and only the Fourier coefficients need to be updated, which can reduce the algorithmic complexity of a 3D code to that of a 2D code. Modeling the laser-plasma interaction in a full 3D electromagnetic PIC algorithm is very computationally expensive due the enormous disparity of physical scales to be resolved. In the QSA the laser is modeled using the ponderomotive guiding center (PGC) approach. We describe how to implement a PGC algorithm compatible for the QSA PIC algorithms based on the azimuthal mode expansion. Here this algorithm permits time steps orders of magnitude larger than the cell size and it can be asynchronously parallelized. Details on how this is implemented into the QSA PIC code that utilizes an azimuthal mode expansion, QPAD, are also described. Benchmarks and comparisons between a fully 3D explicit PIC code (OSIRIS), as well as a few examples related to laser wakefield acceleration, are presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Jacobian-free Newton–Krylov method for the simulation of non-thermal plasma discharges with high-order time integration and physics-based preconditioning

A preconditioning framework for the numerical simulation of non-thermal streamer discharges is developed using the Jacobian-free Newton-Krylov (JFNK) method. A reduced plasma fluid model is considered, consisting of electrons, one positive ion, one negative ion, and the electrostatic potential. Here, the plasma kinetics model includes ionization, electron-ion recombination, electron attachment, electron detachment, and ion-ion recombination. The governing equations are made dimensionless, discretized in space with finite differences, and integrated in time with a fully implicit method based on high-order backward differentiation formulas. The preconditioning framework is based on a linearized form of the governing equations and physics-based operator splitting. The efficiency of the preconditioning strategy is assessed through two test cases: streamer propagation between parallel plates and an axisymmetric pin-to-pin discharge. The fully implicit approach overcomes traditional restrictions in the time step size due to processes such as electron drift, electron diffusion, and dielectric relaxation. Excellent performance is observed through relevant statistics of the JFNK solver, although the number of linear iterations increases for the pin-to-pin discharge when nonlinear numerical boundary conditions are imposed at the electrodes. Performance studies show scalability with O(100-1000) processors for O(10M) unknowns with ample room for optimization.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems

We explore using neural operators, or neural network representations of nonlinear maps between function spaces, to accelerate infinite-dimensional Bayesian inverse problems (BIPs) with models governed by nonlinear parametric partial differential equations (PDEs). Neural operators have gained significant attention in recent years for their ability to approximate the parameter-to-solution maps defined by PDEs using as training data solutions of PDEs at a limited number of parameter samples. The computational cost of BIPs can be drastically reduced if the large number of PDE solves required for posterior characterization are replaced with evaluations of trained neural operators. However, reducing error in the resulting BIP solutions via reducing the approximation error of the neural operators in training can be challenging and unreliable. We provide an a priori error bound result that implies certain BIPs can be ill-conditioned to the approximation error of neural operators, thus leading to inaccessible accuracy requirements in training. To reliably deploy neural operators in BIPs, we consider a strategy for enhancing the performance of neural operators: correcting the prediction of a trained neural operator by solving a linear variational problem based on the PDE residual. We show that a trained neural operator with error correction can achieve a quadratic reduction of its approximation error, all while retaining substantial computational speedups of posterior sampling when models are governed by highly nonlinear PDEs. The strategy is applied to two numerical examples of BIPs based on a nonlinear reaction–diffusion problem and deformation of hyperelastic materials. We demonstrate that posterior representations of the two BIPs produced using trained neural operators are greatly and consistently enhanced by error correction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

This paper introduces a sharp-interface approach to simulating fluid-structure interaction (FSI) involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) scheme extends our prior work on integrating partitioned and immersed approaches to rigid-body FSI. Our numerical approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. As in earlier work, we use approximate Lagrange multiplier forces to treat the kinematic interface conditions along the fluid-structure interface. This penalty approach simplifies the linear solvers needed by our formulation by introducing two representations of the fluid-structure interface, one that moves with the fluid and another that moves with the structure, that are connected by stiff springs. This approach also enables the use of multi-rate time stepping, which allows us to use different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces to impose stress jump conditions along complex interfaces while enabling the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures with a constant total volume, and it can handle fully compressible solid structures for cases in which at least part of the solid boundary does not contact the incompressible fluid. Selected grid convergence studies demonstrate second-order convergence in volume conservation and in the pointwise discrepancies between corresponding positions of the two interface representations as well as between first and second-order convergence in the structural displacements. The time stepping scheme is also demonstrated to yield second-order convergence. To assess and validate the robustness and accuracy of the new algorithm, comparisons are made with computational and experimental FSI benchmarks. Test cases include both smooth and sharp geometries in various flow conditions. Furthermore, we also demonstrate the capabilities of this methodology by applying it to model the transport and capture of a geometrically realistic, deformable blood clot in an inferior vena cava filter.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Fast GPU 3D diffeomorphic image registration

3D image registration is one of the most fundamental and computationally expensive operations in medical image analysis. Here, we present a mixed-precision, Gauss–Newton–Krylov solver for diffeomorphic registration of two images. Our work extends the publicly available CLAIRE library to GPU architectures. Despite the importance of image registration, only a few implementations of large deformation diffeomorphic registration packages support GPUs. Our contributions are new algorithms to significantly reduce the run time of the two main computational kernels in CLAIRE: calculation of derivatives and scattered-data interpolation. Additionally, we deploy (i) highly-optimized, mixed-precision GPU-kernels for the evaluation of scattered-data interpolation, (ii) replace Fast-Fourier-Transform (FFT)-based first-order derivatives with optimized 8th-order finite differences, and (iii) compare with state-of-the-art CPU and GPU implementations. As a highlight, we demonstrate that we can register clinical images in less than 6 s on a single NVIDIA Tesla V100. This amounts to over 20 speed-up over the current version of CLAIRE and over 30 speed-up over existing GPU implementations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Structural conserved moiety splitting of a stoichiometric matrix

Characterising biochemical reaction network structure in mathematical terms enables the inference of functional biochemical consequences from network structure with existing mathematical techniques and spurs the development of new mathematics that exploits the peculiarities of biochemical network structure. The structure of a biochemical network may be specified by reaction stoichiometry, that is, the relative quantities of each molecule produced and consumed in each reaction of the network. A biochemical network may also be specified at a higher level of resolution in terms of the internal structure of each molecule and how molecular structures are transformed by each reaction in a network. The stoichiometry for a set of reactions can be compiled into a stoichiometric matrix N ϵ Z mxn where each row corresponds to a molecule and each column corresponds to a reaction. We demonstrate that a stoichiometric matrix may be split into the sum of m - rank(N) moiety transition matrices, each of which corresponds to a subnetwork accessible to a structurally identifiable conserved moiety. The existence of this moiety matrix splitting is a property that distinguishes a stoichiometric matrix from an arbitrary rectangular matrix.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Evaluating adaptive and predictive power management strategies for optimizing visualization performance on supercomputers

Power is becoming an increasingly scarce resource on the next generation of supercomputers, and should be used wisely to improve overall performance. One strategy for improving power usage is hardware overprovisioning, i.e., systems with more nodes than can be run at full power simultaneously without exceeding the system-wide power limit. With this study, we compare two strategies for allocating power throughout an overprovisioned system – adaptation and prediction – in the context of visualization workloads. While adaptation has been suitable for workloads with more regular execution behaviors, it may not be as suitable on visualization workloads, since they can have variable execution behaviors. This study considers a total of 104 experiments, which vary the rendering workload, power budget, allocation strategy, and node concurrency, including tests processing data sets up to 1 billion cells and using up to 18,432 cores across 512 nodes. Overall, we find that prediction is a superior strategy for this use case, improving performance up to 27% compared to an adaptive strategy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Design-time performance modeling of compositional parallel programs

Performance models are powerful instruments for understanding the performance of parallel systems and uncovering their bottlenecks. Already during system design, performance models can help ponder alternative development options. However, creating a performance model – whether theoretically or empirically – for an entire application that does not exist yet is challenging. In this paper, we propose to generate performance models of full programs from performance models of their components using formal composition operators derived from parallel design patterns. As long as the design of the overall system follows such a pattern, its performance model can be predicted with reasonable accuracy without an actual implementation. In conclusion, we demonstrate our approach with design patterns of varying complexity, including pipeline, task pool, and eventually MapReduce, which is representative of a broad class of data-analytics applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Towards real-time forecasting of natural gas production by harnessing graph theory for stochastic discrete fracture networks

In this work, we compare hydrocarbon production curves obtained from a graph-based reduced-order model with the high-fidelity Discrete Fracture Network (DFN) predictions for a fracture network created using data from a real shale site. We observe that the bounds for the high fidelity DFN model lie within the bounds for the reduced order model, implying that the reduced-order model provides a conservative estimate. Moreover, we found that except for first-passage times and late arriving mass, the production curves from the reduced-order model predict transport accurately. However, it is to be noted that the results are inspite of trading a three-dimensional geometry for a reduced system in the form of a graph, one that is 500–1000 times faster in terms of computational efficiency (for this particular application). In addition, we also compare the production curves for large drawdown and small drawdown using our graph approach. The reduced-order model is successful in showing that the long term productivity is higher in case of small drawdown although the initial productivity is higher for large drawdown. Thus, this reduced-order model offers great potential in uncertainty quantification for production, as well as in providing operators with information to make real-time decisions for optimal production.

03 NATURAL GAS↗
DOE OSTI2020

Time-series learning of latent-space dynamics for reduced-order model closure

In this work, we study the performance of long short-term memory networks (LSTMs) and neural ordinary differential equations (NODEs) in learning latent-space representations of dynamical equations for an advection-dominated problem given by the viscous Burgers equation. Our formulation is devised in a nonintrusive manner with an equation-free evolution of dynamics in a reduced space with the latter being obtained through a proper orthogonal decomposition. In addition, we leverage the sequential nature of learning for both LSTMs and NODEs to demonstrate their capability for closure in systems that are not completely resolved in the reduced space. We assess our hypothesis for two advection-dominated problems given by the viscous Burgers equation. We observe that both LSTMs and NODEs are able to reproduce the effects of the absent scales for our test cases more effectively than does intrusive dynamics evolution through a Galerkin projection. This result empirically suggests that time-series learning techniques implicitly leverage a memory kernel for coarse-grained system closure as is suggested through the Mori–Zwanzig formalism.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Version [OpenIPSL 2.0.0] - [iTesla Power Systems Library (iPSL): A Modelica library for phasor time-domain simulations]

This paper describes Open-Instance Power System Library (OpenIPSL) version 2.0.0 and its most recent enhancements. This new version brings upgrades that include more robust models that are better documented, and example systems that illustrate certain functionalities to users. Repository and library documentations have been enhanced and expanded, and the library is now released under a new license. Changes are meant to foster user and developer communities, while providing more attractive frameworks for collaborative work to be carried out with the library.

97 MATHEMATICS AND COMPUTING↗