Numerical analysis of nonlinear pneumatic structures

Numerical analysis of nonlinear behavior of inflatable structure

Corrector Operator to Enhance Accuracy and Reliability of Neural Operator Surrogates of Nonlinear Variational Boundary-Value Problems

This work focuses on developing methods for approximating the solution operators of a class of parametric partial differential equations via neural operators. Neural operators have several challenges, including the issue of generating appropriate training data, cost-accuracy trade-offs, and nontrivial hyperparameter tuning. The unpredictability of the accuracy of neural operators impacts their applications in downstream problems of inference, optimization, and control. A framework is proposed based on the linear variational problem that gives the correction to the prediction furnished by neural operators. The operator associated with the corrector problem is referred to as the corrector operator. Numerical results involving a nonlinear diffusion model in two dimensions with PCANet-type neural operators show almost two orders of increase in the accuracy of approximations when neural operators are corrected using the proposed scheme. Further, topology optimization involving a nonlinear diffusion model is considered to highlight the limitations of neural operators and the efficacy of the correction scheme. Optimizers with neural operator surrogates are seen to make significant errors (as high as 80 percent). However, the errors are much lower (below 7 percent) when neural operators are corrected following the proposed method.Comment: 34 pages, 14 figure

A dual weighted residual method applied to complex periodic gratings

An extension of the dual weighted residual (DWR) method to the analysis of electromagnetic waves in a periodic diffraction grating is presented. Using the α,0-quasi-periodic transformation, an upper bound for the a posteriori error estimate is derived. This is then used to solve adaptively the associated Helmholtz problem. The goal is to achieve an acceptable accuracy in the computed diffraction efficiency while keeping the computational mesh relatively coarse. Numerical results are presented to illustrate the advantage of using DWR over the global a posteriori error estimate approach. The application of the method in biomimetic, to address the complex diffraction geometry of the Morpho butterfly wing is also discussed

Experimental Validation of Contact Dynamics for In-Hand Manipulation

This paper evaluates state-of-the-art contact models at predicting the motions and forces involved in simple in-hand robotic manipulations. In particular it focuses on three primitive actions --linear sliding, pivoting, and rolling-- that involve contacts between a gripper, a rigid object, and their environment. The evaluation is done through thousands of controlled experiments designed to capture the motion of object and gripper, and all contact forces and torques at 250Hz. We demonstrate that a contact modeling approach based on Coulomb's friction law and maximum energy principle is effective at reasoning about interaction to first order, but limited for making accurate predictions. We attribute the major limitations to 1) the non-uniqueness of force resolution inherent to grasps with multiple hard contacts of complex geometries, 2) unmodeled dynamics due to contact compliance, and 3) unmodeled geometries dueto manufacturing defects.Comment: International Symposium on Experimental Robotics, ISER 2016, Tokyo, Japa

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, which is to correct 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

A weighted reduced basis method for parabolic PDEs with random data

This work considers a weighted POD-greedy method to estimate statistical outputs parabolic PDE problems with parametrized random data. The key idea of weighted reduced basis methods is to weight the parameter-dependent error estimate according to a probability measure in the set-up of the reduced space. The error of stochastic finite element solutions is usually measured in a root mean square sense regarding their dependence on the stochastic input parameters. An orthogonal projection of a snapshot set onto a corresponding POD basis defines an optimum reduced approximation in terms of a Monte Carlo discretization of the root mean square error. The errors of a weighted POD-greedy Galerkin solution are compared against an orthogonal projection of the underlying snapshots onto a POD basis for a numerical example involving thermal conduction. In particular, it is assessed whether a weighted POD-greedy solutions is able to come significantly closer to the optimum than a non-weighted equivalent. Additionally, the performance of a weighted POD-greedy Galerkin solution is considered with respect to the mean absolute error of an adjoint-corrected functional of the reduced solution.Comment: 15 pages, 4 figure

NSTAR Ion Thruster Plume Impact Assessments

Tests were performed to establish 30-cm ion thruster plume impacts, including plume characterizations via near and farfield ion current measurements, contamination, and sputtering assessments. Current density measurements show that 95% of the beam was enclosed within a 22 deg half-angle and that the thrust vector shifted by less than 0.3 deg during throttling from 2.3 to 0.5 kW. The beam flatness parameter was found to be 0.47, and the ratio of doubly charged to singly charged ion current density decreased from 15% at 2.3 kW to 5% at 0.5 kW. Quartz sample erosion measurements showed that the samples eroded at a rate of between 11 and 13 pm/khr at 25 deg from the thruster axis, and that the rate dropped by a factor of four at 40 deg. Good agreement was obtained between extrapolated current densities and those calculated from tantalum target erosion measurements. Quartz crystal microbalance and witness plate measurements showed that ion beam sputtering of the tank resulted in a facility material backflux rate of -10 A/hr in a large space simulation chamber

Ability of tropical forest soils of French Guiana and Reunion to depollute woods impregnated with biocides

Our study sought to fine-tune knowledge about those microorganisms, particularly wood-decaying fungi degrading pollutants in situ. With a view to the depollution or bioremediation of treated woods, wood-decaying microorganisms from tropical forest soils in French Guiana and the island of Reunion were assessed for their ability to degrade toxic biocides such as pentachlorophenol (PCP) or copper chromium arsenic compounds (CCA). The degradation of red pine (Pinus resinosa) test pieces was monitored and it was found that the soil from French Guiana was more efficient than the soil from Reunion in terms of microbial activity in relation to these two biocides. A significant difference in weight loss was found for the red pinetest pieces treated with CCA and PCP, varying in a ratio of one to two (18% and 30%, respectively). In addition, a study of wood and soil fungus communities using D-HPLC and CE-SSCP, then analysed by a PCA, showed that biocide products leached into the soil had an impact on the fungus communities, which differed depending on the sampling time and on the wood treatment. Lastly, these results confirmed that CCA was less leachable and less degradable by microorganisms in these soils than PCP. (Résumé d'auteur