Full trajectory optimizing operator inference for reduced-order modeling using differentiable programming

Accurate and inexpensive Reduced Order Models (ROMs) for forecasting turbulent flows can facilitate rapid design iterations and thus prove critical for predictive control in engineering problems. Galerkin projection based Reduced Order Models (GP-ROMs), derived by projecting the Navier-Stokes equations on a truncated Proper Orthogonal Decomposition (POD) basis, are popular because of their low computational costs and theoretical foundations. However, the accuracy of traditional GP-ROMs degrades over long time prediction horizons. To address this issue, we extend the recently proposed Neural Galerkin Projection (NeuralGP) data driven framework to compressibility-dominated transonic flow, considering a prototypical problem of a buffeting NACA0012 airfoil governed by the full Navier-Stokes equations. The algorithm maintains the form of the ROM-ODE obtained from the Galerkin projection; however coefficients are learned directly from the data using gradient descent facilitated by differentiable programming. This blends the strengths of the physics driven GP-ROM and purely data driven neural network-based techniques, resulting in a computationally cheaper model that is easier to interpret. We show that the NeuralGP method minimizes a more rigorous full trajectory error norm compared to a linearized error definition optimized by the calibration procedure. We also find that while both procedures stabilize the ROM by displacing the eigenvalues of the linear dynamics matrix of the ROM-ODE to the complex left half-plane, the NeuralGP algorithm adds more dissipation to the trailing POD modes resulting in its better long-term performance. The results presented highlight the superior accuracy of the NeuralGP technique compared to the traditional calibrated GP-ROM method

Design, implementation, and testing of a cryogenic loading capability on an engineering neutron diffractometer

A novel capability was designed, implemented, and tested for in situ neutron diffraction measurements during loading at cryogenic temperatures on the spectrometer for materials research at temperature and stress at Los Alamos National Laboratory. This capability allowed for the application of dynamic compressive forces of up to 250 kN on standard samples controlled at temperatures between 300 and 90 K. The approach comprised of cooling thermally isolated compression platens that in turn conductively cooled the sample in an aluminum vacuum chamber which was nominally transparent to the incident and diffracted neutrons. The cooling/heat rate and final temperature were controlled by regulating the flow of liquid nitrogen in channels inside the platens that were connected through bellows to the mechanical actuator of the load frame and by heaters placed on the platens. Various performance parameters of this system are reported here. The system was used to investigate deformation in Ni-Ti-Fe shape memory alloys at cryogenic temperatures and preliminary results are presented

Mesoscale polycrystal calculations of damage in spallation in metals

The goal of this project is to produce a damage model forspallation in metals informed by the polycrystalline grain structure at themesoscale. Earlier damage models addressed the continuum macroscale in whichthese effects were averaged out. In this work we focus on cross sectionsfrom recovered samples examined with EBSD (electron backscattereddiffraction), which reveal crystal grain orientations and voids. We seek tounderstand the loading histories of specific sample regions by meshing upthe crystal grain structure of these regions and simulating the stress,strain, and damage histories in our hydrocode, FLAG. The stresses and strainhistories are the fundamental drivers of damage and must be calculated. Thecalculated final damage structures are compared with those from therecovered samples to validate the simulations

Mesoscale polycrystal calculations of damage in spallation in metals

The goal of this project is to produce a damage model forspallation in metals informed by the polycrystalline grain structure at themesoscale. Earlier damage models addressed the continuum macroscale in whichthese effects were averaged out. In this work we focus on cross sectionsfrom recovered samples examined with EBSD (electron backscattereddiffraction), which reveal crystal grain orientations and voids. We seek tounderstand the loading histories of specific sample regions by meshing upthe crystal grain structure of these regions and simulating the stress,strain, and damage histories in our hydrocode, FLAG. The stresses and strainhistories are the fundamental drivers of damage and must be calculated. Thecalculated final damage structures are compared with those from therecovered samples to validate the simulations

Influence of sweeping detonation-wave loading on shock hardening and damage evolution during spallation loading in tantalum

Widespread research over the past five decades has provided a wealth of experimental data and insight concerning the shock hardening, damage evolution, and the spallation response of materials subjected to square-topped shock-wave loading profiles. However, fewer quantitative studies have been conducted on the effect of direct, in-contact, high explosive (HE)-driven Taylor wave (unsupported shocks) loading on the shock hardening, damage evolution, or spallation response of materials. Systematic studies quantifying the effect of sweeping-detonation wave loading are yet sparser. In this study, the shock hardening and spallation response of Ta is shown to be critically dependent on the peak shock stress and the shock obliquity during sweeping-detonation-wave shock loading. Sweeping-wave loading is observed to: a) yield a lower spall strength than previously documented for 1-D supported-shock-wave loading, b) exhibit increased shock hardening as a function of increasing obliquity, and c) lead to an increased incidence of deformation twin formation with increasing shock obliquity

Influence of sweeping detonation-wave loading on shock hardening and damage evolution during spallation loading in tantalum

Widespread research over the past five decades has provided a wealth of experimental data and insight concerning the shock hardening, damage evolution, and the spallation response of materials subjected to square-topped shock-wave loading profiles. However, fewer quantitative studies have been conducted on the effect of direct, in-contact, high explosive (HE)-driven Taylor wave (unsupported shocks) loading on the shock hardening, damage evolution, or spallation response of materials. Systematic studies quantifying the effect of sweeping-detonation wave loading are yet sparser. In this study, the shock hardening and spallation response of Ta is shown to be critically dependent on the peak shock stress and the shock obliquity during sweeping-detonation-wave shock loading. Sweeping-wave loading is observed to: a) yield a lower spall strength than previously documented for 1-D supported-shock-wave loading, b) exhibit increased shock hardening as a function of increasing obliquity, and c) lead to an increased incidence of deformation twin formation with increasing shock obliquity