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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.

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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

The influence of wind-tunnel walls on discrete frequency noise

This paper describes an analytical model that can be used to examine the effects of wind-tunnel walls on discrete frequency noise. First, a complete physical model of an acoustic source in a wind tunnel is described, and a simplified version is then developed. This simplified model retains the important physical processes involved, yet it is more amenable to analysis. Second, the simplified physical model is formulated as a mathematical problem. An inhomogeneous partial differential equation with mixed boundary conditions is set up and then transformed into an integral equation. The integral equation has been solved with a panel program on a computer. Preliminary results from a simple model problem will be shown and compared with the approximate analytic solution.

Mosher, M.↗
NASA NTRS1992

A multiple scales approach to sound generation by vibrating bodies

The problem of determining the acoustic field in an inviscid, isentropic fluid generated by a solid body whose surface executes prescribed vibrations is formulated and solved as a multiple scales perturbation problem, using the Mach number M based on the maximum surface velocity as the perturbation parameter. Following the idea of multiple scales, new 'slow' spacial scales are introduced, which are defined as the usual physical spacial scale multiplied by powers of M. The governing nonlinear differential equations lead to a sequence of linear problems for the perturbation coefficient functions. However, it is shown that the higher order perturbation functions obtained in this manner will dominate the lower order solutions unless their dependence on the slow spacial scales is chosen in a certain manner. In particular, it is shown that the perturbation functions must satisfy an equation similar to Burgers' equation, with a slow spacial scale playing the role of the time-like variable. The method is illustrated by a simple one-dimenstional example, as well as by three different cases of a vibrating sphere. The results are compared with solutions obtained by purely numerical methods and some insights provided by the perturbation approach are discussed.

Geer, James F.↗
NASA NTRS1996

Nonstandard Finite Difference Schemes: Relations Between Time and Space Step-Sizes in Numerical Schemes for PDE's That Follow from Positivity Condition

A large class of physical phenomena can be modeled by evolution and wave type Partial Differential Equations (PDE). Few of these equations have known explicit exact solutions. Finite-difference techniques are a popular method for constructing discrete representations of these equations for the purpose of numerical integration. However, the solutions to the difference equations often contain so called numerical instabilities; these are solutions to the difference equations that do not correspond to any solution of the PDE's. For explicit schemes, the elimination of this behavior requires functional relations to exist between the time and space steps-sizes. We show that such functional relations can be obtained for certain PDE's by use of a positivity condition. The PDE's studied are the Burgers, Fisher, and linearized Euler equations.

Mickens, Ronald E.↗
NASA NTRS1994

Postinstability Models in Dynamics

This paper is devoted to the concept of instability in dynamical systems with the main emphasis on orbital, Hadamard, and Reynolds instabilities. It demonstrates that the requirement about differentiability in dynamics in some cases is not consistent with the physical nature of motions, and may lead to unrealistic solutions. Special attention is paid to the fact that instability is not an invariant of motion: it depends upon frames of reference, the metric of configuration space, and classes of functions selected for mathematical models of physical phenomena. This leads to the possibility of elimination of certain types of instabilities (in particular, those which lead to chaos and turbulence) by enlarging the class of functions using the Reynolds-type transformation in combination with the stabilization principle: the additional terms (the so-called Reynolds stresses) are found from the conditions that they suppress the original instability. Based upon these ideas, a new approach to chaos and turbulence as well as a new mathematical formalism for nonlinear dynamics are discussed.

Zak, Michail↗
NASA NTRS1993

The use of centrifugation to study early Drosophila embryogenesis

By the end of 10th nuclear cycle, the somatic nuclei of the Drosophila embryo have migrated to the periphery of the egg. Centrifugation of embryos did not result in the displacement of these nuclei, since cytoskeletal elements anchor them to the cortex. But, mild centrifugal forces displace the centrally located, nascent yolk nuclei. If this increased sensitivity to hypergravity occurs before the beginning of nuclear differentiation during cycle 8, when the nascent yolk and somatic nuclei physically separate, then it would mark the earliest functional difference between these two lineages.

Non-NASA Center↗
NASA NTRS1992

Extracellular matrix as a solid-state regulator in angiogenesis: identification of new targets for anti-cancer therapy

Angiogenesis, the growth of blood capillaries, is regulated by soluble growth factors and insoluble extracellular matrix (ECM) molecules. Soluble angiogenic mitogens act over large distances to initiate capillary growth whereas changes in ECM govern whether individual cells will grow, differentiate, or involute in response to these stimuli in the local tissue microenvironment. Analysis of this local control mechanism has revealed that ECM molecules switch capillary endothelial cells between differentiation and growth by both binding specific transmembrane integrin receptors and physically resisting cell-generated mechanical loads that are applied to these receptors. Control of capillary endothelial cell form and function therefore may be exerted by altering the mechanical properties of the ECM as well as its chemical composition. Understanding of this mechanochemical control mechanism has led to the development of new angiogenesis inhibitors that may be useful for the treatment of cancer.

Review↗
DOE OSTI2026

Physics-aware adaptive checkpointing with shadow systems for nonlinear PDE simulations

Large-scale simulations of nonlinear partial differential equations (PDEs) that exhibit strongly transient behavior and pattern-forming dynamics produce enormous amounts of data, which, even with modern storage systems, cannot be stored for later curation. Current I/O strategies either write dense time series of snapshots, which is often prohibitive in I/O and storage, or store a few checkpoints that enable restart but incur expensive recomputation cost and provide no control over post-restart error growth, especially when lossy compression is used. Moreover, most, if not all, existing strategies take no account of the actual physical state of the system. Here, we present a simple physics-aware I/O framework in which a low-cost shadow system adaptively triggers lossy checkpoints when the shadow system deviates from the fine-scale simulation. The shadow system can be a coarsened replica of the fine-scale simulation that evolves concurrently. This means that checkpoints are taken based on the physical state of the system: fewer checkpoints are triggered when the system is quiescent while more are taken when the system undergoes a rapid change. This type of behavior is observed in many systems such as Brusselator and FitzHugh–Nagumo. We illustrate that our framework maintains stable restarts, keeps fine-scale restart errors bounded by shadow errors, and reconstructs the time history with significantly lower error and storage than interpolating fixed-interval snapshots, with low-cost shadow replay and modest online synchronization overhead.

Gong, Qian [ORNL] (ORCID:0000000235704142)↗
DOE OSTI2025

SPIKANs: separable physics-informed Kolmogorov–Arnold networks

Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving partial differential equations (PDEs) in scientific computing. While PINNs typically use multilayer perceptrons (MLPs) as their underlying architecture, recent advancements have explored alternative neural network structures. One such innovation is the Kolmogorov–Arnold Network (KAN), which has demonstrated benefits over traditional MLPs, including faster neural scaling and better interpretability. The application of KANs to physics-informed learning has led to the development of Physics-Informed KANs (PIKANs), enabling the use of KANs to solve PDEs. However, despite their advantages, KANs often suffer from slower training speeds, particularly in higher-dimensional problems where the number of collocation points grows exponentially with the dimensionality of the system. To address this challenge, we introduce Separable Physics-Informed Kolmogorov–Arnold Networks (SPIKANs). This novel architecture applies the principle of separation of variables to PIKANs, decomposing the problem such that each dimension is handled by an individual KAN. This approach drastically reduces the computational complexity of training without sacrificing accuracy, facilitating their application to higher-dimensional PDEs. Through a series of benchmark problems, we demonstrate the effectiveness of SPIKANs, showcasing their superior scalability and performance compared to PIKANs and highlighting their potential for solving complex, high-dimensional PDEs in scientific computing.

Kolmogorov-Arnold networks↗
DOE OSTI2025

Hidden zeros of the cosmological wavefunction

Motivated by the recent discovery of hidden zeros in particle and string amplitudes, we characterize zeros of individual graph contributions to the cosmological wavefunction of a scalar field theory. We demonstrate that these contributions factorize near these zeros for all tree graphs and provide evidence that this extends to loop graphs as well. We explicitly construct polytopal realizations of the relevant graph associahedra and show that the cosmological zeros have natural geometric and physical interpretations. As a byproduct, we establish an equivalence between the wavefunction coefficients of chain graphs and flat-space Tr(ϕ 3 ) amplitudes, enabling us to leverage the cosmological zeros to uncover the recently discovered hidden zeros of colored amplitudes.

Cosmological models↗
NASA NTRS2013

Extended Analytic Device Optimization Employing Asymptotic Expansion

Analytic optimization of a thermoelectric junction often introduces several simplifying assumptionsincluding constant material properties, fixed known hot and cold shoe temperatures, and thermallyinsulated leg sides. In fact all of these simplifications will have an effect on device performance,ranging from negligible to significant depending on conditions. Numerical methods, such as FiniteElement Analysis or iterative techniques, are often used to perform more detailed analysis andaccount for these simplifications. While numerical methods may stand as a suitable solution scheme,they are weak in gaining physical understanding and only serve to optimize through iterativesearching techniques. Analytic and asymptotic expansion techniques can be used to solve thegoverning system of thermoelectric differential equations with fewer or less severe assumptionsthan the classic case. Analytic methods can provide meaningful closed form solutions and generatebetter physical understanding of the conditions for when simplifying assumptions may be valid.In obtaining the analytic solutions a set of dimensionless parameters, which characterize allthermoelectric couples, is formulated and provide the limiting cases for validating assumptions.Presentation includes optimization of both classic rectangular couples as well as practically andtheoretically interesting cylindrical couples using optimization parameters physically meaningful toa cylindrical couple. Solutions incorporate the physical behavior for i) thermal resistance of hot andcold shoes, ii) variable material properties with temperature, and iii) lateral heat transfer through legsides.

Thermoelectric Generators↗
DOE OSTI2025

An attention-based neural ordinary differential equation framework for modeling inelastic processes

To preserve strictly conservative behavior as well as model the variety of dissipative behavior displayed by solid materials, we propose a significant enhancement to the internal state variable-neural ordinary differential equation (ISV-NODE) framework. In this data-driven, physics-constrained modeling framework internal states are inferred rather than prescribed. The ISV-NODE consists of: (a) a stress model dependent on observable deformation and inferred internal state, and (b) a model of the evolution of the internal states. The enhancements to ISV-NODE proposed in this work are multifold: (a) a partially input convex neural network stress potential provides polyconvexity in terms of observed strain while leaving the inferred state unconstrained, and (b) an internal state flow model uses common latent features to inform novel attention-based gating and drives the flow of internal state only in dissipative regimes. We demonstrated that this architecture can accurately model dissipative and conservative behavior across an isotropic, isothermal elastic-viscoelastic-elastoplastic spectrum with three exemplars, while maintaining fundamental principles by design.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

The cosmic ray differential diurnal variation dependences on the zenith angle and the geomagnetic disturbance

Simultaneous and continuous muon measurements in two opposite azimuthal directions under equal zenith angles demonstrated the importance of this method for cosmic ray diurnal variation investigations. Lately these measurements were extended by means of improved telescopes. The obtained cosmic ray diurnal variations were presented as intensity differential curves. Theoretical investigations connected the properties of these curves with some interplanetary spece parameters. The harmonics of these curves were interpreted physically. Some order difference curves were introduced. In earlier works some dependences between the parameters characterizing the first and the second harmonics of the differential intensity curves and the geomagnetic activity were found. Then all measurements were carried out under only one zenith angle. The results of investigations of similar dependences using data of simultaneous measurements under three different zenith angles are presented.

Kavlakov, S.↗
DOE OSTI2025

Preliminary study of auto-differentiation algorithm in beam dynamics with stochastic process

Modern particle accelerator optimization requires sophisticated computational methods to address the inherently stochastic nature of beam dynamics. This research develops a framework applying AD to SDEs that specifically addresses beam dynamics challenges in particle accelerators, focusing on accurately modeling and optimizing beam behavior in regimes dominated by stochastic processes. By incorporating key physical phenomena such as synchrotron radiation, wakefield effects, and quantum excitation, the framework aims to provide auto differentiation on the figure of merit of the phase space evolution and beam dynamics. The methodology will enable effective optimization method in a dynamic system with stochastic process.

Accelerator Physics↗
DOE OSTI2024

Designing observables for measurements with deep learning

Many analyses in particle and nuclear physics use simulations to infer fundamental, effective, or phenomenological parameters of the underlying physics models. When the inference is performed with unfolded cross sections, the observables are designed using physics intuition and heuristics. We propose to design targeted observables with machine learning. Unfolded, differential cross sections in a neural network output contain the most information about parameters of interest and can be well-measured by construction. The networks are trained using a custom loss function that rewards outputs that are sensitive to the parameter(s) of interest while simultaneously penalizing outputs that are different between particle-level and detector-level (to minimize detector distortions). We demonstrate this idea in simulation using two physics models for inclusive measurements in deep inelastic scattering. We find that the new approach is more sensitive than classical observables at distinguishing the two models and also has a reduced unfolding uncertainty due to the reduced detector distortions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2024

In-depth Analysis of LISA Pathfinder Performance Results: Time Evolution, Noise Projection, Physical Models, and Implications for LISA

We present an in-depth analysis of the LISA Pathfinder differential acceleration performance over the entire course of its science operations, spanning approximately 500 days. We find: (1) The evolution of the Brownian noise that dominates the acceleration amplitude spectral density (ASD), for frequencies f≳1 mHz, is consistent with the decaying pressure due to the outgassing of a single gaseous species. (2) Between f=36 μHz and 1 mHz, the acceleration ASD shows a 1/f tail in excess of the Brownian noise of almost constant amplitude, with ≃20% fluctuations over a period of a few days, with no particular time pattern over the course of the mission. (3) At the lowest considered frequency of f=18 μHz, the ASD significantly deviates from the 1/f behavior, because of temperature fluctuations that appear to modulate a quasistatic pressure gradient, sustained by the asymmetries of the outgassing pattern. We also present the results of a projection of the observed acceleration noise on the potential sources for which we had either a direct correlation measurement or a quantitative estimate from dedicated experiments. These sources account for approximately 40% of the noise power in the 1/f tail. Finally, we analyze the possible sources of the remaining unexplained fraction and identify the possible measures that may be taken to keep those under control in LISA.

M Armano↗
DOE OSTI2025

Renormalizing two-fermion operators in the SMEFT via supergeometry

We extend the geometric framework of field-space covariance for loop computations, thereby unifying the treatment of scalars, fermions, and gauge bosons in effective field theories. This allows us to derive a manifestly covariant formula for one-loop UV divergences that includes contributions from mixed boson-fermion graphs. The result is expressed in terms of geometric invariants of the field-space supermanifold. As a demonstration of this formula, we compute the renormalization group equations for two-fermion operators at the dimension-eight level in the Standard Model Effective Field Theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Preserving nonlinear constraints in variational flow filtering data assimilation

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems of interest obey nonlinear physical constraints, and the corresponding dynamics is confined to a certain sub-manifold of the state space. Standard data assimilation techniques applied to such systems yield posterior states lying outside the manifold, violating the physical constraints. This work focuses on particle flow filters which use stochastic differential equations to evolve state samples from a prior distribution to samples from an observation-informed posterior distribution. The variational Fokker-Planck (VFP)—a generic particle flow filtering framework—is extended to incorporate non-linear, equality state constraints in the analysis. To this end, two algorithmic approaches that modify the VFP stochastic differential equation are discussed: (i) VFPSTAB, to inexactly preserve constraints with the addition of a stabilizing drift term, and (ii) VFPDAE, to exactly preserve constraints by treating the VFP dynamics as a stochastic differential-algebraic equation (SDAE). Additionally, an implicit-explicit time integrator is developed to evolve the VFPDAE dynamics. The strength of the proposed approach for constraint preservation in data assimilation is demonstrated on three test problems: the double pendulum, Korteweg-de-Vries, and the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗