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.

Full-field Electroretinography Changes Associated with Age-related Macular Degeneration: A Systematic Review with Meta-Analyses

Background: To systematically review the literature and to perform meta-analyses on full-field electroretinography (ffERG) between healthy controls and age-related macular degeneration (AMD) to map the extent of retinal dysfunction. Summary: We systematically searched 11 databases on 3 March 2021. Eligible studies had to measure retinal function using ffERG in eyes with AMD and in healthy controls. We extracted data on a-wave and b-wave function in dark- and light-adapted ffERG, and calculated summary estimates on differences between eyes with AMD and controls using weighted mean differences (WMD). Subgroup analyses were made for early and late AMD. Six studies (n=481 eyes) were eligible for review (301 with any AMD, 180 controls). For dark-adapted data, any AMD was associated with reduced a-wave amplitude (WMD: -17.16 µV; 95% CI: -31.79 to -2.52 µV; P=0.02) and b-wave amplitude (WMD: -28.70 µV; 95% CI: -51.40 to -6.01 µV; P=0.01). For light-adapted data, any AMD was associated with longer a-wave implicit time (WMD: 0.92 ms; 95% CI: 0.12 to 1.72 ms; P=0.02), reduced b-wave amplitude (WMD: -13.26 µV; 95% CI: -18.64 to -7.88 µV; P<0.0001), and longer b-wave implicit time (WMD: 0.69 ms; 95% CI: 0.30 to 1.08 ms; P=0.0006). Subgroup analyses found that these changes were only statistically significant in eyes with late AMD, not early AMD. Key messages: Reduced retinal function on ffERG is present in eyes with AMD, in particular those with late AMD. These findings suggest that AMD is a pan-retinal disease with AMD-associated photoreceptor dysfunction beyond the macula.

On Parameter Identification for Reaction-Dominated Pore-Scale Reactive Transport Using Modified Bee Colony Algorithm

Parameter identification is an important research topic with a variety of applications in industrial and environmental problems. Usually, a functional has to be minimized in conjunction with parameter identification; thus, there is a certain similarity between the parameter identification and optimization. A number of rigorous and efficient algorithms for optimization problems were developed in recent decades for the case of a convex functional. In the case of a non-convex functional, the metaheuristic algorithms dominate. This paper discusses an optimization method called modified bee colony algorithm (MBC), which is a modification of the standard bees algorithm (SBA). The SBA is inspired by a particular intelligent behavior of honeybee swarms. The algorithm is adapted for the parameter identification of reaction-dominated pore-scale transport when a non-convex functional has to be minimized. The algorithm is first checked by solving a few benchmark problems, namely finding the minima for Shekel, Rosenbrock, Himmelblau and Rastrigin functions. A statistical analysis was carried out to compare the performance of MBC with the SBA and the artificial bee colony (ABC) algorithm. Next, MBC is applied to identify the three parameters in the Langmuir isotherm, which is used to describe the considered reaction. Here, 2D periodic porous media were considered. The simulation results show that the MBC algorithm can be successfully used for identifying admissible sets for the reaction parameters in reaction-dominated transport characterized by low Pecklet and high Damkholer numbers. Finite element approximation in space and implicit time discretization are exploited to solve the direct problem.

Evaluation of Macular Function after Vitrectomy in Diabetic Macular Edema

Purpose: To document the effects of successful vitrectomy on retinal function and anatomy in diabetic patients. Methods: Three-port pars plana vitrectomy with detachment of posterior vitrous face was performed in 30 eyes of 25 patients with diabetic macular oedema DME (11 male, 14 Female).For each patients, visual acuity (VA) examination, measurement of retinal thickness using optical coherence tomography (OCT), full field electro-retinogram (ERG) and multifocal eletroretinogram (MF-ERG) were performed before and 1week,1month and 3months after vitrectomy. Results: Mean postoperative visual acuity was significantly improved (P<0.05); mean retinal thickness was significantly (P=0.001 ) decreased after 3monthes of surgery (from 450±150 into 220±50 micron ) .b-wave amplitudes of all cone and rod responses of ERG were significantly decreased in all vitrectomized eyes after 1 week. At one month, rod response was still unimproved but improved after 3months. Reduction in foveal Function as well as in para-foveal areas detected in the MF-ERG within 1st month. Then, mean P1 wave amplitude of MF-ERG of central ring increased and mean P1 wave implicit time decreased. These changes of MF-ERG parameters observed 3 months after vitrectomy. Conclusion: Multifocal electroretinogram can be useful to provide objective criteria for functional evaluation before and after vitrectomy in diabetic oedema.

Performance of a Three-Substep Time Integration Method on Structural Nonlinear Seismic Analysis

In this work, a study of a three substeps’ implicit time integration method called the Wen method for nonlinear finite element analysis is conducted. The calculation procedure of the Wen method for nonlinear analysis is proposed. The basic algorithmic property analysis shows that the Wen method has good performance on numerical dissipation, amplitude decay, and period elongation. Three nonlinear dynamic problems are analyzed by the Wen method and other competitive methods. The result comparison indicates that the Wen method is feasible and efficient in the calculation of nonlinear dynamic problems. Theoretical analysis and numerical simulation illustrate that the Wen method has desirable solution accuracy and can be a good candidate for nonlinear dynamic problems.

Electroretinogram Analysis In Patients With Non-Proliferative Diabetic Retinopathy

Purpose: Non-proliferative diabetic retinopathy (NPDR) is the earliest stage of diabetic eye disease. Microscopic changes occur in the blood vessels of the eye in NPDR. The changes typically do not produce symptoms and are not visible to the naked eye. This paper aims to investigate a method for distinguishing NPDR based on Electroretinogram (ERG).Method: The ERG responses were recorded in 20 eyes from 14 patients with NPDR and 20 eyes from 20 healthy subjects as the control group. The responses of three standard stimuli were collected for both groups. Time-domain parameters, including amplitudes and implicit time, and a nonlinear criterion, were used to differentiate the groups. Results: This study showed that implicit time and amplitude of b-wave in dark-adapted 10.0 ERG and amplitude and implicit time of light-adapted flicker 30 Hz could distinguish between controls and NPDR groups. Theta values obtained for dark-adapted 10.0 ERG (p=0.0019), light-adapted 3.0 ERG (p=0.0021), and light-adapted flicker 30 Hz (p=0.0023) had significant differences between the groups. Conclusion: The proposed features have made it possible to distinguish between healthy and NPDR eyes. Choosing an appropriate method can effectively evaluate inner retinal dysfunction, especially in diabetic retinopathy.

Nonlinearly Preconditioned FETI Solver for Substructured Formulations of Nonlinear Problems

We consider the finite element approximation of the solution to elliptic partial differential equations such as the ones encountered in (quasi)-static mechanics, in transient mechanics with implicit time integration, or in thermal diffusion. We propose a new nonlinear version of preconditioning, dedicated to nonlinear substructured and condensed formulations with dual approach, i.e., nonlinear analogues to the Finite Element Tearing and Interconnecting (FETI) solver. By increasing the importance of local nonlinear operations, this new technique reduces communications between processors throughout the parallel solving process. Moreover, the tangent systems produced at each step still have the exact shape of classically preconditioned linear FETI problems, which makes the tractability of the implementation barely modified. The efficiency of this new preconditioner is illustrated on two academic test cases, namely a water diffusion problem and a nonlinear thermal behavior.