DiffPD: Differentiable Projective Dynamics

We present a novel, fast differentiable simulator for soft-body learning and control applications. Existing differentiable soft-body simulators can be classified into two categories based on their time integration methods: Simulators using explicit timestepping schemes require tiny timesteps to avoid numerical instabilities in gradient computation, and simulators using implicit time integration typically compute gradients by employing the adjoint method and solving the expensive linearized dynamics. Inspired by Projective Dynamics ( PD ), we present Differentiable Projective Dynamics ( DiffPD ), an efficient differentiable soft-body simulator based on PD with implicit time integration. The key idea in DiffPD is to speed up backpropagation by exploiting the prefactorized Cholesky decomposition in forward PD simulation. In terms of contact handling, DiffPD supports two types of contacts: a penalty-based model describing contact and friction forces and a complementarity-based model enforcing non-penetration conditions and static friction. We evaluate the performance of DiffPD and observe it is 4–19 times faster compared with the standard Newton’s method in various applications including system identification, inverse design problems, trajectory optimization, and closed-loop control. We also apply DiffPD in a reality-to-simulation ( real-to-sim ) example with contact and collisions and show its capability of reconstructing a digital twin of real-world scenes.

Fast and numerically stable Mie solution of EM near field and absorption for stratified spheres

Purpose The purpose of this paper is the development of an analytic computational model for electromagnetic (EM) wave scattering from spherical objects. The main application field is the modeling of electrically large objects, where the standard numerical techniques require huge computational resources. An example is full-wave modeling of the human head in the millimeter-wave regime. Hence, an approximate model or analytical approach is used. Design/methodology/approach The Mie–Debye theorem is used for calculating the EM scattering from a layered dielectric sphere. The evaluation of the analytical expressions involved in the infinite sum has several numerical instabilities, which makes the precise calculation a challenge. The model is validated through an application example with comparing results to numerical calculations (finite element method). The human head model is used with the approximation of a two-layer sphere, where the brain tissues and the cranial bones are represented by homogeneous materials. Findings A significant improvement is introduced for the stable calculation of the Mie coefficients of a core–shell stratified sphere illuminated by a linearly polarized EM plane wave. Using this technique, a semi-analytical expression is derived for the power loss in the sphere resulting in quick and accurate calculations. Originality/value Two methods are introduced in this work with the main objective of estimating the final precision of the results. This is an important aspect for potentially unstable calculations, and the existing implementations have not included this feature so far.

A technique for non-intrusive greedy piecewise-rational model reduction of frequency response problems over wide frequency bands

In the field of model order reduction for frequency response problems, the minimal rational interpolation (MRI) method has been shown to be quite effective. However, in some cases, numerical instabilities may arise when applying MRI to build a surrogate model over a large frequency range, spanning several orders of magnitude. We propose a strategy to overcome these instabilities, replacing an unstable global MRI surrogate with a union of stable local rational models. The partitioning of the frequency range into local frequency sub-ranges is performed automatically and adaptively, and is complemented by a (greedy) adaptive selection of the sampled frequencies over each sub-range. We verify the effectiveness of our proposed method with two numerical examples.

Regularization of the Factorization Method applied to diffuse optical tomography

In this paper, we develop a new regularized version of the Factorization Method for positive operators mapping a complex Hilbert Space into it’s dual space. The Factorization Method uses Picard’s Criteria to define an indicator function to image an unknown region. In most applications the data operator is compact which gives that the singular values can tend to zero rapidly which can cause numerical instabilities. The regularization of the Factorization Method presented here seeks to avoid the numerical instabilities in applying Picard’s Criteria. This method allows one to image the interior structure of an object with little a priori information in a computationally simple and analytically rigorous way. Here we will focus on an application of this method to diffuse optical tomography where will prove that this method can be used to recover an unknown subregion from the Dirichlet-to-Neumann mapping. Numerical examples will be presented in two dimensions.

Photoionization and Electron-Ion Recombination of n = 1 to Very High n-Values of Hydrogenic Ions

Single electron hydrogen or hydrogenic ions have analytical forms to evaluate the atomic parameters for the inverse processes of photoionization and electron-ion recombination (H I + hν↔ H II + e) where H is hydrogen. Studies of these processes have continued until the present day (i) as the computations are restricted to lower principle quantum number n and (ii) to improve the accuracy. The analytical expressions have many terms and there are numerical instabilities arising from cancellations of terms. Strategies for fast convergence of contributions were developed but precise computations are still limited to lower n. This report gives a brief review of the earlier precise methodologies for hydrogen, and presents numerical tables of photoionization cross sections (σPI), and electron-ion recombination rate coefficients (αRC) obtained from recombination cross sections (σRC) for all n values going to a very high value of 800. σPI was obtained using the precise formalism of Burgess and Seaton, and Burgess. αRC was obtained through a finite integration that converge recombination exactly as implemented in the unified method of recombination of Nahar and Pradhan. Since the total electron-ion recombination includes all levels for n = 1 −∞, the total asymptotic contribution of n=801−∞, called the top-up, is obtained through a n−3 formula. A FORTRAN program “hpxrrc.f” is provided to compute photoionization cross sections, recombination cross sections and rate coefficients for any nl. The results on hydrogen atom can be used to obtain those for any hydrogenic ion of charge z through z-scaling relations provided in the theory section. The present results are of high precision and complete for astrophysical modelings.

Volume Preserving Simulation of Soft Tissue with Skin

Simulation of human soft tissues in contact with their environment is essential in many fields, including visual effects and apparel design. Biological tissues are nearly incompressible. However, standard methods employ compressible elasticity models and achieve incompressibility indirectly by setting Poisson's ratio to be close to 0.5. This approach can produce results that are plausible qualitatively but inaccurate quantatively. This approach also causes numerical instabilities and locking in coarse discretizations or otherwise poses a prohibitive restriction on the size of the time step. We propose a novel approach to alleviate these issues by replacing indirect volume preservation using Poisson's ratios with direct enforcement of zonal volume constraints, while controlling fine-scale volumetric deformation through a cell-wise compression penalty. To increase realism, we propose an epidermis model to mimic the dramatically higher surface stiffness on real skinned bodies. We demonstrate that our method produces stable realistic deformations with precise volume preservation but without locking artifacts. Due to the volume preservation not being tied to mesh discretization, our method also allows a resolution consistent simulation of incompressible materials. Our method improves the stability of the standard neo-Hookean model and the general compression recovery in the Stable neo-Hookean model.

Performance comparison of r2SCAN and SCAN metaGGA density functionals for solid materials via an automated, high-throughput computational workflow

Computational materials discovery efforts utilize hundreds or thousands of density functional theory (DFT) calculations to predict material properties. Historically, such efforts have performed calculations at the generalized gradient approximation (GGA) level of theory due to its efficient compromise between accuracy and computational reliability. However, high-throughput calculations at the higher metaGGA level of theory are becoming feasible. The Strongly Constrainted and Appropriately Normed (SCAN) metaGGA functional offers superior accuracy to GGA across much of chemical space, making it appealing as a general-purpose metaGGA functional, but it suffers from numerical instabilities that impede it's use in high-throughput workflows. The recently-developed r2SCAN metaGGA functional promises accuracy similar to SCAN in addition to more robust numerical performance. However, its performance compared to SCAN has yet to be evaluated over a large group of solid materials. In this work, we compared r2SCAN and SCAN predictions for key properties of approximately 6,000 solid materials using a newly-developed high-throughput computational workflow. We find that r2SCAN predicts formation energies more accurately than SCAN and PBEsol for both strongly- and weakly-bound materials and that r2SCAN predicts systematically larger lattice constants than SCAN. We also find that r2SCAN requires modestly fewer computational resources than SCAN and offers significantly more reliable convergence. Thus, our large-scale benchmark confirms that r2SCAN has delivered on its promises of numerical efficiency and accuracy, making it a preferred choice for high-throughput metaGGA calculations.

Performance comparison of r2SCAN and SCAN metaGGA density functionals for solid materials via an automated, high-throughput computational workflow

Computational materials discovery efforts utilize hundreds or thousands of density functional theory (DFT) calculations to predict material properties. Historically, such efforts have performed calculations at the generalized gradient approximation (GGA) level of theory due to its efficient compromise between accuracy and computational reliability. However, high-throughput calculations at the higher metaGGA level of theory are becoming feasible. The Strongly Constrainted and Appropriately Normed (SCAN) metaGGA functional offers superior accuracy to GGA across much of chemical space, making it appealing as a general-purpose metaGGA functional, but it suffers from numerical instabilities that impede it's use in high-throughput workflows. The recently-developed r2SCAN metaGGA functional promises accuracy similar to SCAN in addition to more robust numerical performance. However, its performance compared to SCAN has yet to be evaluated over a large group of solid materials. In this work, we compared r2SCAN and SCAN predictions for key properties of approximately 6,000 solid materials using a newly-developed high-throughput computational workflow. We find that r2SCAN predicts formation energies more accurately than SCAN and PBEsol for both strongly- and weakly-bound materials and that r2SCAN predicts systematically larger lattice constants than SCAN. We also find that r2SCAN requires modestly fewer computational resources than SCAN and offers much more reliable convergence. Thus, our large-scale benchmark confirms that r2SCAN has delivered on its promises of numerical efficiency and accuracy, making it an ideal choice for high-throughput metaGGA calculations.