Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Differentiable physics”

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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

The thermal structure of solar coronal loops and implications for physical models of coronae

EUV spectra of three active region loops observed above the solar limb with the SO55 spectrometer on Skylab are analyzed. It is noted that the lengths, peak temperatures, and pressures of the loops are typical of the X-ray coronal loops to which static models have been applied. It is found that the physical parameters of the coronal loop plasma derived from EUV spectra and raster pictures are not well represented by the static models. Although the loops also contain a significant quantity of cool plasma, no physical reason is found to differentiate them from other active region loops of similar length, pressure, and temperature. Several line ratios in the loop spectrum suggest departures from ionization equilibrium caused by rapid cooling. The source of this cooling material is discussed with reference to several models of loop dynamics.

Raymond, J. C.↗
NASA NTRS1988

The physics of parallel machines

The idea is considered that architectures for massively parallel computers must be designed to go beyond supporting a particular class of algorithms to supporting the underlying physical processes being modelled. Physical processes modelled by partial differential equations (PDEs) are discussed. Also discussed is the idea that an efficient architecture must go beyond nearest neighbor mesh interconnections and support global and hierarchical communications.

Chan, Tony F.↗
NASA NTRS1989

Coolant side heat transfer with rotation: User manual for 3D-TEACH with rotation

This program solves the governing transport equations in Reynolds average form for the flow of a 3-D, steady state, viscous, heat conducting, multiple species, single phase, Newtonian fluid with combustion. The governing partial differential equations are solved in physical variables in either a Cartesian or cylindrical coordinate system. The effects of rotation on the momentum and enthalpy calculations modeled in Cartesian coordinates are examined. The flow of the fluid should be confined and subsonic with a maximum Mach number no larger than 0.5. This manual describes the operating procedures and input details for executing a 3D-TEACH computation.

Syed, S. A.↗
NASA NTRS1992

Domain decomposition: A bridge between nature and parallel computers

Domain decomposition is an intuitive organizing principle for a partial differential equation (PDE) computation, both physically and architecturally. However, its significance extends beyond the readily apparent issues of geometry and discretization, on one hand, and of modular software and distributed hardware, on the other. Engineering and computer science aspects are bridged by an old but recently enriched mathematical theory that offers the subject not only unity, but also tools for analysis and generalization. Domain decomposition induces function-space and operator decompositions with valuable properties. Function-space bases and operator splittings that are not derived from domain decompositions generally lack one or more of these properties. The evolution of domain decomposition methods for elliptically dominated problems has linked two major algorithmic developments of the last 15 years: multilevel and Krylov methods. Domain decomposition methods may be considered descendants of both classes with an inheritance from each: they are nearly optimal and at the same time efficiently parallelizable. Many computationally driven application areas are ripe for these developments. A progression is made from a mathematically informal motivation for domain decomposition methods to a specific focus on fluid dynamics applications. To be introductory rather than comprehensive, simple examples are provided while convergence proofs and algorithmic details are left to the original references; however, an attempt is made to convey their most salient features, especially where this leads to algorithmic insight.

Keyes, David E.↗
DOE OSTI2025

The Method of Finite Averages

The Method of Finite Averages (MoFA) is a rigorous multiscale modeling methodology for efficiently modeling multi-physical phenomena in heterogeneous porous media. The code developed in this project aims to perform the numerical calculations required to formulate, implement, and verify MoFA models for Earth and Energy systems (i.e., model verification refers to performing fully-resolved simulations of the systems and comparing their results to those of the models). In general, MoFA transforms partial differential equations (PDEs) describing the fine-scale physics of a system into coupled ordinary differential equations (ODEs)---in time---that describe the coarse-scale---or "average"---physical behaviors of the system. This transformation significantly expedites system simulation, as the coarse-scale ODEs involve vastly fewer degrees of freedom than the fine-scale PDEs. The code developed under this project will allow users to 1.) generate system geometries and numerical meshes, 2.) solve the PDE and ODE systems required for MoFA model formulation and implementation, 3.) solve the PDE systems required to obtain fully-resolved simulation results for model verification, and 4.) compare and plot results (e.g., the model and fully-resolved simulation solutions, the error between the solutions, etc.).

Pietrzyk, KyleM [Lawrence Livermore National Labor↗
DOE OSTI2024

Twice upon a time: timelike-separated quantum extremal surfaces

The Python’s Lunch conjecture for the complexity of bulk reconstruction involves two types of nonminimal quantum extremal surfaces (QESs): bulges and throats, which differ by their local properties. The conjecture relies on the connection between bulk spatial geometry and quantum codes: a constricting geometry from bulge to throat encodes the bulk state nonisometrically, and so requires an exponentially complex Grover search to decode. However, thus far, the Python’s Lunch conjecture is only defined for spacetimes where all QESs are spacelike-separated from one another. Here we explicitly construct (time-reflection symmetric) spacetimes featuring both timelike-separated bulges and timelike-separated throats. Interestingly, all our examples also feature a third type of QES, locally resembling a de Sitter bifurcation surface, which we name a bounce. By analyzing the Hessian of generalized entropy at a QES, we argue that this classification into throats, bulges and bounces is exhaustive. We then propose an updated Python’s Lunch conjecture that can accommodate general timelike-separated QESs and bounces. Notably, our proposal suggests that the gravitational analogue of a tensor network is not necessarily the time-reflection symmetric slice, even when one exists.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Hutchinson Trace Estimation for high-dimensional and high-order Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) have proven effective in solving partial differential equations (PDEs), especially when some data are available by seamlessly blending data and physics. However, extending PINNs to high-dimensional and even high-order PDEs encounters significant challenges due to the computational cost associated with automatic differentiation in the residual loss function calculation. Herein, we address the limitations of PINNs in handling high-dimensional and high-order PDEs by introducing the Hutchinson Trace Estimation (HTE) method. Starting with the second-order high-dimensional PDEs, which are ubiquitous in scientific computing, HTE is applied to transform the calculation of the entire Hessian matrix into a Hessian vector product (HVP). This approach not only alleviates the computational bottleneck via Taylor-mode automatic differentiation but also significantly reduces memory consumption from the Hessian matrix to an HVP’s scalar output. We further showcase HTE’s convergence to the original PINN loss and its unbiased behavior under specific conditions. Comparisons with the Stochastic Dimension Gradient Descent (SDGD) highlight the distinct advantages of HTE, particularly in scenarios with significant variability and variance among dimensions. We further extend the application of HTE to higher-order and higher-dimensional PDEs, specifically addressing the biharmonic equation. By employing tensor-vector products (TVP), HTE efficiently computes the colossal tensor associated with the fourth-order high-dimensional biharmonic equation, saving memory and enabling rapid computation. The effectiveness of HTE is illustrated through experimental setups, demonstrating comparable convergence rates with SDGD under memory and speed constraints. Additionally, HTE proves valuable in accelerating the Gradient-Enhanced PINN (gPINN) version as well as the Biharmonic equation. Overall, HTE opens up a new capability in scientific machine learning for tackling high-order and high-dimensional PDEs.

Curse of dimensionality↗
DOE OSTI2024

Accessing bands with extended quantum metric in kagome Cs 2 Ni 3 S 4 through soft chemical processing

Flat bands that do not merely arise from weak interactions can produce exotic physical properties, such as superconductivity or correlated many-body effects. The quantum metric can differentiate whether flat bands will result in correlated physics or are merely dangling bonds. A potential avenue for achieving correlated flat bands involves leveraging geometrical constraints within specific lattice structures, such as the kagome lattice; however, materials are often more complex. In these cases, quantum geometry becomes a powerful indicator of the nature of bands with small dispersions. We present a simple, soft-chemical processing route to access a flat band with an extended quantum metric below the Fermi level. By oxidizing Ni-kagome material Cs 2 Ni 3 S 4 to CsNi 3 S 4 , we see a two orders of magnitude drop in the room temperature resistance. However, CsNi 3 S 4 is still insulating, with no evidence of a phase transition. Using experimental data, density functional theory calculations, and symmetry analysis, our results suggest the emergence of a correlated insulating state of unknown origin.

Science & Technology - Other Topics↗
NASA NTRS2006

Model Predictive Optimal Control of a Time-Delay Distributed-Parameter Systems

This paper presents an optimal control method for a class of distributed-parameter systems governed by first order, quasilinear hyperbolic partial differential equations that arise in many physical systems. Such systems are characterized by time delays since information is transported from one state to another by wave propagation. A general closed-loop hyperbolic transport model is controlled by a boundary control embedded in a periodic boundary condition. The boundary control is subject to a nonlinear differential equation constraint that models actuator dynamics of the system. The hyperbolic equation is thus coupled with the ordinary differential equation via the boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to implement a model predictive control design for a wind tunnel to eliminate a transport delay effect that causes a poor Mach number regulation.

Nguyen, Nhan↗
NASA NTRS2015

Differential Draining of Parallel-Fed Propellant Tanks in Morpheus and Apollo Flight

Parallel-fed propellant tanks are an advantageous configuration for many spacecraft. Parallel-fed tanks allow the center of gravity (cg) to be maintained over the engine(s), as opposed to serial-fed propellant tanks which result in a cg shift as propellants are drained from tank one tank first opposite another. Parallel-fed tanks also allow for tank isolation if that is needed. Parallel tanks and feed systems have been used in several past vehicles including the Apollo Lunar Module. The design of the feedsystem connecting the parallel tank is critical to maintain balance in the propellant tanks. The design must account for and minimize the effect of manufacturing variations that could cause delta-p or mass flowrate differences, which would lead to propellant imbalance. Other sources of differential draining will be discussed. Fortunately, physics provides some self-correcting behaviors that tend to equalize any initial imbalance. The question concerning whether or not active control of propellant in each tank is required or can be avoided or not is also important to answer. In order to provide data on parallel-fed tanks and differential draining in flight for cryogenic propellants (as well as any other fluid), a vertical test bed (flying lander) for terrestrial use was employed. The Morpheus vertical test bed is a parallel-fed propellant tank system that uses passive design to keep the propellant tanks balanced. The system is operated in blow down. The Morpheus vehicle was instrumented with a capacitance level sensor in each propellant tank in order to measure the draining of propellants in over 34 tethered and 12 free flights. Morpheus did experience an approximately 20 lb/m imbalance in one pair of tanks. The cause of this imbalance will be discussed. This paper discusses the analysis, design, flight simulation vehicle dynamic modeling, and flight test of the Morpheus parallel-fed propellant. The Apollo LEM data is also examined in this summary report of the flight data.

Hurlbert, Eric↗
DOE OSTI2024

Tackling the curse of dimensionality in fractional and tempered fractional PDEs with physics-informed neural networks

Fractional and tempered fractional partial differential equations (PDEs) are effective models of long-range interactions, anomalous diffusion, and non-local effects. Traditional numerical methods for these problems are mesh-based, thus struggling with the curse of dimensionality (CoD). Physics-informed neural networks (PINNs) offer a promising solution due to their universal approximation, generalization ability, and mesh-free training. In principle, Monte Carlo fractional PINN (MC-fPINN) estimates fractional derivatives using Monte Carlo methods and thus could lift CoD. However, this may cause significant variance and errors, hence affecting convergence; in addition, MC-fPINN is sensitive to hyperparameters. In general, numerical methods and specifically PINNs for tempered fractional PDEs are under-developed. Herein, we extend MC-fPINN to tempered fractional PDEs to address these issues, resulting in the Monte Carlo tempered fractional PINN (MC-tfPINN). To reduce possible high variance and errors from Monte Carlo sampling, we replace the one-dimensional (1D) Monte Carlo with 1D Gaussian quadrature, applicable to both MC-fPINN and MC-tfPINN. We validate our methods on various forward and inverse problems of fractional and tempered fractional PDEs, scaling up to 100,000 dimensions. Our improved MC-fPINN/MC-tfPINN using quadrature consistently outperforms the original versions in accuracy and convergence speed in very high dimensions.

42 ENGINEERING↗
DOE OSTI2024

Ladder symmetries and Love numbers of Reissner-Nordström black holes

It is well known that asymptotically flat black holes in general relativity have vanishing tidal Love numbers. In the case of Schwarzschild and Kerr black holes, this property has been shown to be a consequence of a hidden structure of ladder symmetries for the perturbations. In this work, we extend the ladder symmetries to non-rotating charged black holes in general relativity. As opposed to previous works in this context, we adopt a more general definition of Love numbers, including quadratic operators that mix gravitational and electromagnetic perturbations in the point-particle effective field theory. We show that the calculation of a subset of those couplings in full general relativity is affected by an ambiguity in the split between source and response, which we resolve through an analytic continuation. As a result, we derive a novel master equation that unifies scalar, electromagnetic and gravitational perturbations around Reissner-Nordström black holes. The equation is hypergeometric and can be obtained from previous formulations via nontrivial field redefinitions, which allow to systematically remove some of the singularities and make the presence of the ladder symmetries more manifest.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

jaxhps: An elliptic PDE solver built with machine learning in mind

Elliptic partial differential equations (PDEs) can model many physical phenomena, such as electrostatics, acoustics, wave propagation, and diffusion. In scientific machine learning settings, a high-throughput PDE solver may be required to generate a training dataset, run in the inner loop of an iterative algorithm, or interface directly with a deep neural network. To provide value to machine learning users, such a PDE solver must be compatible with standard automatic differentiation frameworks, scale efficiently when run on graphics processing units (GPUs), and maintain high accuracy for a large range of input parameters. We have designed the jaxhps package with these use-cases in mind by implementing a highly efficient and accurate solver for elliptic problems with native hardware acceleration and automatic differentiation support.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Recurrent convolutional neural networks for modeling nonadiabatic dynamics of quantum-classical systems

Recurrent neural networks (RNNs) have recently been extensively applied to model the time evolution in fluid dynamics, weather predictions, and even chaotic systems due to their ability to capture temporal dependencies and sequential patterns in data. Here we present an RNN model based on convolutional neural networks for modeling the nonlinear nonadiabatic dynamics of hybrid quantum-classical systems. The dynamical evolution of the hybrid systems is governed by equations of motion for classical degrees of freedom and von Neumann equation for electrons. The Physics-Aware Recurrent Convolution (PARC) neural network structure incorporates a differentiator-integrator architecture that inductively models the spatiotemporal dynamics of generic physical systems. Here, we apply our RNN approach to learn the space-time evolution of a one-dimensional semiclassical Holstein model after an interaction quench. For shallow quenches (small changes in electron-lattice coupling), the deterministic dynamics can be accurately captured using a single-CNN-based recurrent network. In contrast, deep quenches induce chaotic evolution, making long-term trajectory prediction significantly more challenging. Nonetheless, we demonstrate that the PARC-CNN architecture can effectively learn the statistical climate of the Holstein model under deep-quench conditions.

Holstein model↗
DOE OSTI2025

Harnessing the power of gradient-based simulations for multi-objective optimization in particle accelerators

Abstract Particle accelerator operation requires simultaneous optimization of multiple objectives. Multi-objective optimization (MOO) is particularly challenging due to trade-offs between the objectives. Evolutionary algorithms, such as genetic algorithms (GAs), have been leveraged for many optimization problems, however, they do not apply to complex control problems by design. This paper demonstrates the power of differentiability for solving MOO problems in particle accelerators using a deep differentiable reinforcement learning (DDRL) algorithm. We compare the DDRL algorithm with model-free reinforcement learning (MFRL), GA, and Bayesian optimization (BO) for simultaneous optimization of heat load and trip rates in the continuous electron beam accelerator facility. The underlying problem enforces strict constraints on both individual states and actions as well as cumulative (global) constraints on energy requirements of the beam. Using historical accelerator data, we develop a physics-based surrogate model which is differentiable and allows for back-propagation of gradients. The results are evaluated in the form of a Pareto-front with two objectives. We show that the DDRL outperforms MFRL, BO, and GA on high dimensional problems.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Hadamard products and BPS networks

We study examples of fourth-order Picard-Fuchs operators that are Hadamard products of two second-order Picard-Fuchs operators. Each second-order Picard-Fuchs operator is associated with a family of elliptic curves, and the Hadamard product computes period integrals on the fibred product of the two elliptic surfaces. We construct 3-cycles on this geometry as the union of 2-cycles in the fibre over contours on the base. We then use the special Lagrangian condition to constrain the contours on the base. This leads to a construction that is reminiscent of spectral networks and exponential networks that have previously appeared in string theory literature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Phospholipase D and phosphatidylinositol-4-phosphate 5-kinase 1 are involved in the regulation of oligodendrocyte morphological differentiation

Highlights: • PLD and PIP5K1 are involved in the regulation of oligodendroglial cell morphological differentiation. • Inhibition of PLD or PIP5K1 decreases differentiation or myelin marker expression. • PLD and PIP5K1 regulate differentiation of oligodendrocyte precursor cells. • Inhibition of PLD or PIP5K1 decreases differentiation marker expression of oligodendrocyte precursor cells. Oligodendroglial cells (oligodendrocytes) differentiate to form the myelin that wraps neuronal axons in the central nervous system (CNS). This myelin sheath supports the propagation of saltatory conduction and protects axons from physical stresses. When oligodendrocytes do not normally differentiate to myelinate axons, their key functions as oligodendrocytes in the CNS are severely impaired. The molecular mechanics that control differentiation still remain to be clarified. Arf6 belongs to the small GTPase family and is known to be a positive regulator of oligodendrocyte differentiation. Here, we show that the phospholipase D (PLD) and phosphatidylinositol-4-phosphate 5-kinase 1 (PIP5K1) molecules, the major effectors of Arf6, are involved in the regulation of oligodendrocyte differentiation. Knockdown of PLD1 or PIP5K type 1γ (PIP5K1C) by their respective specific siRNAs in mouse oligodendroglial FBD-102b cells inhibited morphological differentiation into structures bearing myelin-like processes; this finding is consistent with the concurrent changes in expression of differentiation and myelin marker proteins. Treatment with VU0155069 or UNC3230, specific inhibitors of PLD and PIP5K1, respectively, blunted morphological differentiation and decreased expression of myelin and differentiation marker proteins. Similar results have been obtained in studies using primary oligodendrocytes. These results suggest that the major Arf6 effector molecules PLD and PIP5K1 are among the molecules involved in the regulation of morphological differentiation in oligodendrocytes prior to myelination.

60 APPLIED LIFE SCIENCES↗