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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Demonstrating Computational Equivalence Between Continuous and Discrete Adjoint Methods by Calculating Time-Dependent Adjoint Solutions with Neutron Diffusion Models

The continuous adjoint method and the discrete adjoint method are two alternative approaches used to calculate adjoint solutions for adjoint systems. The continuous adjoint method derives adjoint equations analytically from continuous forward equations and then solves the adjoint equations either analytically or numerically in a discretized form whereas the discrete adjoint method calculates the adjoint solutions directly from the discretized forward equations. With regard to the methodology development and calculation procedure, distinct differences are well recognized between the two methods. For certain reasons, both methods are exclusively preferred and commonly used by different computational communities, but limited studies clarify the connections between the two adjoint methods from either of the communities. Herein, this paper demonstrates the computational equivalence between the continuous and discrete adjoint methods by investigating time-dependent adjoint solutions to the two-group neutron diffusion model in nuclear reactor analysis problems using both methods. Adjoint solutions can be used to estimate system parameters for reactor safety analysis. Appropriate final state conditions for the adjoint systems are specified in both of the methods, and the conditions are clarified with proper physical explanations. With the help of an event-based case study on neutron diffusion models, the accuracy of the time-dependent adjoint fluxes obtained from both methods is verified, and the pros and cons of both adjoint methods are examined. More importantly, the computational equivalence of both methods is demonstrated when they are applied to multigroup neutron diffusion systems. The advantage of calculating time-dependent adjoint fluxes by directly solving time-dependent adjoint systems rather than taking steady-state approximations as in common practice is also demonstrated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Dataset from: "Adjoint methods for quasisymmetry of vacuum fields on a surface"

Adjoint methods can speed up stellarator optimisation by providing gradient information more efficiently compared to finite-difference evaluations. Adjoint methods are herein applied to vacuum magnetic fields, with objective functions targeting quasisymmetry and a rotational transform value on a surface. To measure quasisymmetry, a novel way of evaluating approximate flux coordinates on a single flux surface without the assumption of a neighbourhood of flux surfaces is proposed. The shape gradients obtained from the adjoint formalism are evaluated numerically and verified against finite-difference evaluations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Adjoint methods for quasi-symmetry of vacuum fields on a surface

Adjoint methods can speed up stellarator optimisation by providing gradient information more efficiently compared with finite-difference evaluations. Adjoint methods are herein applied to vacuum magnetic fields, with objective functions targeting quasi-symmetry and a rotational transform value on a surface. Here to measure quasi-symmetry, a novel way of evaluating approximate flux coordinates on a single flux surface without the assumption of a neighbourhood of flux surfaces is proposed. The shape gradients obtained from the adjoint formalism are evaluated numerically and verified against finite-difference evaluations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Simulation of Channel Flow with Square Ribs for Blanket First-Wall Cooling: Geometry-Specific Tuning of k-ω Model Using Adjoint Method

Cooling of the plasma-facing first wall is challenging in the design of blanket components because of the high heat flux (on the order of 𝑀𝑊/𝑚2) from the plasma, especially when a low thermal mass medium like helium is chosen as the coolant. Therefore, heat transfer enhancement in which the convective heat transfer rate is augmented by the addition of turbulence-promoting structures becomes a key initiative for providing sufficient cooling capability with helium. Previously, computational fluid dynamics simulations had been performed on pipe flows with different transverse and longitudinal ribbed geometries at Oak Ridge National Laboratory to compare the enhancement performance among different ribbed geometries. Rib shape morphing had been conducted to obtain an optimized rib profile. In the work presented here, the adjoint method is adopted in the ANSYS Fluent solver for turbulence model augmentation, and the Generalized k-ω (GEKO) turbulence model is employed because of its ability of tuning the turbulence model. The Nusselt number and pressure drop obtained from the channel flow with bottom ribbed wall experiments are used as the targets. Sensitivity analysis provides information as guidance to improve the turbulence model accuracy. The augmented GEKO model is tuned for the studied ribbed channel geometry and flow conditions, providing improved predictive accuracy within this context. Extension to other configurations offers potential but may require additional tuning and validation.

Xu, Tracy [ORNL] (ORCID:0009000193700887)↗
DOE OSTI2023

An adjoint-based method for optimising MHD equilibria against the infinite- n , ideal ballooning mode

We demonstrate a fast adjoint-based method to optimise tokamak and stellarator equilibria against a pressure-driven instability known as the infinite-n ideal ballooning mode. We present three finite-β (the ratio of thermal to magnetic pressure) equilibria: one tokamak equilibrium and two stellarator equilibria that are unstable against the ballooning mode. Using the self-adjoint property of ideal magnetohydrodynamics, we construct a technique to rapidly calculate the change in the eigenvalue, a measure of ideal ballooning instability. Using the SIMSOPT optimisation framework, we then implement our fast adjoint gradient-based optimiser to minimise the eigenvalue and find stable equilibria for each of the three originally unstable equilibria.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Minimum feature size control in level set topology optimization via density fields

A level set topology optimization approach that uses an auxiliary density field to nucleate holes during the optimization process and achieves minimum feature size control in optimized designs is explored. The level set field determines the solid-void interface and the density field describes the distribution of a fictitious porous material using the solid isotropic material with penalization. These fields are governed by two sets of independent optimization variables which are initially coupled using a penalty for hole nucleation. The strength of the density field penalization and projection is gradually increased during the optimization process to promote a 0-1 density distribution. In addition, a second penalty regulates the evolution of the density field in the void phase. The treatment of the density field combined with the second penalty mitigate the appearance of small design features. The minimum feature size of optimized designs is controlled by the radius of the linear filter applied to the density optimization variables. The structural response is predicted by the extended finite element method, the sensitivities by the adjoint method, and the optimization variables are updated by a gradient-based optimization algorithm. Numerical examples investigate the robustness of this approach with respect to algorithmic parameters and mesh refinement. The results show the applicability of the combined density level set topology optimization approach for both optimal hole nucleation and for minimum feature size control in 2D and 3D. This comes, however, at the cost of a more complex problem formulation and additional computational cost due to an increased number of optimization variables.

42 ENGINEERING↗
DOE OSTI2022

Dynamic Parameter Estimation with Physics-based Neural Ordinary Differential Equations

Accurate estimation of dynamic parameters of gen-erators is crucial to building a reliable model for dynamical studies and reliable operation of the power system. This paper develops a physics-based neural ordinary differential equations (ODE) approach to learn the parameters of generator dynamic model using phasor measurement units (PMU) data. We design a physics-based neural network to represent the swing equations of the power system dynamics. A loss function is defined as the difference between dynamic simulation results from the physics-based neural networks and pseudo PMU measurements. The parameters of generator dynamic model are iteratively updated using the neural ODEs and the adjoint method. By exploiting the mini-batch scheme in neural ODE training, the parameter estimation performance is significantly improved. Numerical study results on a 3-machine 9-bus system show that the proposed algorithm outperforms state-of-the-art baseline method in both computation time and dynamic parameter estimation accuracy.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

New Time Integrators and Capabilities in SUNDIALS Versions 6.2.0-7.4.0

SUNDIALS is a well-established numerical library that provides robust and efficient time integrators and nonlinear solvers. This article overviews several significant improvements and new features added over the last 3 years to support scientific simulations run on high-performance computing systems. Notably, three new classes of one-step methods have been implemented: low storage Runge–Kutta, symplectic partitioned Runge–Kutta, and operator splitting. In addition, we describe new timestep adaptivity support for multirate methods, adjoint sensitivity analysis capabilities for explicit Runge–Kutta methods, additional options for Anderson acceleration in nonlinear solvers, and improved error handling and logging.

Computer science↗
DOE OSTI2024

Development of a Method for Shape Optimization for a Gas Turbine Fuel Injector Design Using Metal-Additive Manufacturing

Adjoint shape optimization has enabled physics-based optimal designs for aerodynamic surfaces. Additive manufacturing (AM) makes it possible to manufacture complex shapes. However, there has been a gap between optimal and manufacturable surfaces due to the inherent limitations of commercial computational fluid dynamics (CFD) codes to implement geometric constraints during adjoint computation. In such cases, the design sensitivities are exported and used to perform constrained shape modifications using parametric information stored in computer aided design (CAD) files to satisfy manufacturability constraints. However, modifying the design using adjoint methods in CFD solvers and performing constrained shape modification in CAD can lead to inconsistencies due to different shape parameterization schemes. This paper describes a method to enable the simultaneous optimization of the fluid domain and impose AM manufacturability constraints, resolving one of the key issues of geometry definition for isogeometric analysis. Similar to a grid convergence study, the proposed method verifies the consistencies between shape parameterization techniques present within commercial CAD and CFD software during mesh movement as a part of the adjoint shape optimization routine. By identifying the appropriate parameters essential to a shape optimization study, the error metric between the different parameterization techniques converges to demonstrate sufficient consistencies for justifiable exchange of data between CAD and CFD. For the identified shape optimization parameters, the error metric to measure the deviation between the two parameterization schemes lies within the AM laser-powder bed fusion (L-PBF) process tolerance. Additionally, comparison for subsequent objective function calculations between iterations of the optimization loop showed acceptable differences within 1% variation between the modified geometries obtained using the two parameterization schemes. This method provides justification for the use of multiphysics guided adjoint design sensitivities computed in CFD software to perform shape modifications in CAD to incorporate AM manufacturability constraints during the shape optimization loop such that optimal designs are also additively manufacturable.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling

Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur numerical errors whose impacts on models' representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a “discretize-then-optimize” adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrological modeling. The adjoint model demonstrates comprehensively improved performance, with Kling–Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model's ability to represent hydrological dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model's success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology.

58 GEOSCIENCES↗
DOE OSTI2022

A mixed, unified forward/inverse framework for earthquake problems: fault implementation and coseismic slip estimate

SUMMARY We introduce a new finite-element (FE) based computational framework to solve forward and inverse elastic deformation problems for earthquake faulting via the adjoint method. Based on two advanced computational libraries, FEniCS and hIPPYlib for the forward and inverse problems, respectively, this framework is flexible, transparent and easily extensible. We represent a fault discontinuity through a mixed FE elasticity formulation, which approximates the stress with higher order accuracy and exposes the prescribed slip explicitly in the variational form without using conventional split node and decomposition discrete approaches. This also allows the first order optimality condition, that is the vanishing of the gradient, to be expressed in continuous form, which leads to consistent discretizations of all field variables, including the slip. We show comparisons with the standard, pure displacement formulation and a model containing an in-plane mode II crack, whose slip is prescribed via the split node technique. We demonstrate the potential of this new computational framework by performing a linear coseismic slip inversion through adjoint-based optimization methods, without requiring computation of elastic Green’s functions. Specifically, we consider a penalized least squares formulation, which in a Bayesian setting—under the assumption of Gaussian noise and prior—reflects the negative log of the posterior distribution. The comparison of the inversion results with a standard, linear inverse theory approach based on Okada’s solutions shows analogous results. Preliminary uncertainties are estimated via eigenvalue analysis of the Hessian of the penalized least squares objective function. Our implementation is fully open-source and Jupyter notebooks to reproduce our results are provided. The extension to a fully Bayesian framework for detailed uncertainty quantification and non-linear inversions, including for heterogeneous media earthquake problems, will be analysed in a forthcoming paper.

58 GEOSCIENCES↗
DOE OSTI2024

Simultaneous shape and topology optimization of inflatable soft robots

Simultaneous shape and topology optimization is used to design pressure-activated inflatable soft robots. The pressure loaded boundary is meshed conformingly and shape optimized, while the morphology of the robot is topology optimized. The design objective is to exert maximum force on an object, i.e. to produce soft “grippers”. The robot’s motion is modeled using nearly incompressible finite deformation hyperelasticity. To ensure stability of the robot, the buckling load factors obtained via linearized buckling analyses are constrained. The finite element method is used to evaluate the optimization cost and constraint functions and the adjoint method is employed to compute their sensitivities. The numerical examples produce pressure-driven soft robots with varying complexity. We also compare our simultaneous optimization results to those obtained via sequential topology and then shape optimization.

42 ENGINEERING↗
DOE OSTI2025

Technical Report on Subsurface Monitoring of the Brady Hot Spring Geothermal Site, Nevada, based upon Full Waveform Inversion

Abilities to accurately characterize the subsurface in a geothermal setting is key to assess and support production. An important element of geothermal reservoir monitoring is also the ability to investigate fluid transport within fracture network. This report focuses on improving subsurface imaging and monitoring in geothermal settings using full waveform inversion based on the adjoint method and time-lapse imaging. To assess our method, we rely on a dense seismic dataset collected in 2016 at the Brady Hot Springs geothermal site in Nevada for the DOE-funded project Poroelastic Tomography by Adjoint Inverse Modeling of Data from Seismology, Geodesy, and Hydrology. This dataset captures subsurface changes across four stages of geothermal power plant operations, which involve varying rates of fluid injection and extraction. Two velocity models were previously derived from this dataset using different methods: one based on travel times and another on sweep interferometry. Our first step is to refine these models using adjoint tomography, which has been applied successfully at global and regional-scales but is less common at the reservoir-scale. Two approaches are then explored for time-lapse analysis: directly comparing refined tomographic models from different stages or backpropagating waveform differences relative to a baseline tomographic model. The main take away is that both approaches highlight similar reservoir behaviors, but the latter approach is more computationally effective in capturing small-scale changes in subsurface properties. For this work, we leverage the use of Salvus (www.mondaic.com), an end-to-end seismic imaging solution, relying on the spectral element method to compute forward and adjoint simulations, and developed by Mondaic Ltd. It includes integrated workflow management that handles waveform and metadata, launches simulations, computes waveform misfits and adjoint sources, and iterates for model updates by nonlinear optimization.

15 GEOTHERMAL ENERGY↗
DOE OSTI2023

Adjoint DSMC for nonlinear spatially-homogeneous Boltzmann equation with a general collision model

We derive an adjoint method for the Direct Simulation Monte Carlo (DSMC) method for the spatially homogeneous Boltzmann equation with a general collision law. This generalizes our previous results in Caflisch et al., which was restricted to the case of Maxwell molecules, for which the collision rate is constant. The main difficulty in generalizing the previous results is that a rejection sampling step is required in the DSMC algorithm in order to handle the variable collision rate. We find a new term corresponding to the so-called score function in the adjoint equation and a new adjoint Jacobian matrix capturing the dependence of the collision parameter on the velocities. The new formula works for a much more general class of collision models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

An autoencoder compression approach for accelerating large-scale inverse problems

Abstract Partial differential equation (PDE)-constrained inverse problems are some of the most challenging and computationally demanding problems in computational science today. Fine meshes required to accurately compute the PDE solution introduce an enormous number of parameters and require large-scale computing resources such as more processors and more memory to solve such systems in a reasonable time. For inverse problems constrained by time-dependent PDEs, the adjoint method often employed to compute gradients and higher order derivatives efficiently requires solving a time-reversed, so-called adjoint PDE that depends on the forward PDE solution at each timestep. This necessitates the storage of a high-dimensional forward solution vector at every timestep. Such a procedure quickly exhausts the available memory resources. Several approaches that trade additional computation for reduced memory footprint have been proposed to mitigate the memory bottleneck, including checkpointing and compression strategies. In this work, we propose a close-to-ideal scalable compression approach using autoencoders to eliminate the need for checkpointing and substantial memory storage, thereby reducing the time-to-solution and memory requirements. We compare our approach with checkpointing and an off-the-shelf compression approach on an earth-scale ill-posed seismic inverse problem. The results verify the expected close-to-ideal speedup for the gradient and Hessian-vector product using the proposed autoencoder compression approach. To highlight the usefulness of the proposed approach, we combine the autoencoder compression with the data-informed active subspace (DIAS) prior showing how the DIAS method can be affordably extended to large-scale problems without the need for checkpointing and large memory.

Mathematics↗
DOE OSTI2022

Differential methods for assessing sensitivity in biological models

Differential sensitivity analysis is indispensable in fitting parameters, understanding uncertainty, and forecasting the results of both thought and lab experiments. Although there are many methods currently available for performing differential sensitivity analysis of biological models, it can be difficult to determine which method is best suited for a particular model. In this paper, we explain a variety of differential sensitivity methods and assess their value in some typical biological models. First, we explain the mathematical basis for three numerical methods: adjoint sensitivity analysis, complex perturbation sensitivity analysis, and forward mode sensitivity analysis. We then carry out four instructive case studies. (a) The CARRGO model for tumor-immune interaction highlights the additional information that differential sensitivity analysis provides beyond traditional naive sensitivity methods, (b) the deterministic SIR model demonstrates the value of using second-order sensitivity in refining model predictions, (c) the stochastic SIR model shows how differential sensitivity can be attacked in stochastic modeling, and (d) a discrete birth-death-migration model illustrates how the complex perturbation method of differential sensitivity can be generalized to a broader range of biological models. Finally, we compare the speed, accuracy, and ease of use of these methods. We find that forward mode automatic differentiation has the quickest computational time, while the complex perturbation method is the simplest to implement and the most generalizable.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Lossy checkpoint compression in full waveform inversion: a case study with ZFPv0.5.5 and the overthrust model

This paper proposes a new method that combines checkpointing methods with error-controlled lossy compression for large-scale high-performance full-waveform inversion (FWI), an inverse problem commonly used in geophysical exploration. This combination can significantly reduce data movement, allowing a reduction in run time as well as peak memory. In the exascale computing era, frequent data transfer (e.g., memory bandwidth, PCIe bandwidth for GPUs, or network) is the performance bottleneck rather than the peak FLOPS of the processing unit. Like many other adjoint-based optimization problems, FWI is costly in terms of the number of floating-point operations, large memory footprint during backpropagation, and data transfer overheads. Past work for adjoint methods has developed checkpointing methods that reduce the peak memory requirements during backpropagation at the cost of additional floating-point computations. Combining this traditional checkpointing with error-controlled lossy compression, we explore the three-way tradeoff between memory, precision, and time to solution. We investigate how approximation errors introduced by lossy compression of the forward solution impact the objective function gradient and final inverted solution. Empirical results from these numerical experiments indicate that high lossy-compression rates (compression factors ranging up to 100) have a relatively minor impact on convergence rates and the quality of the final solution.

58 GEOSCIENCES↗