Inexact descent methods for elastic parameter optimization

Yan, Guowei; Li, Wei; Yang, Ruigang; Wang, Huamin

doi:10.1145/3272127.3275021

Cited by 7 publications

(8 citation statements)

References 48 publications

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“…While various solvers can be applied, given the quadratic property, we prefer to employ a Newton-type method for its associated quadratic convergence rate. Since the subproblems must be updated for the constraint Hessian and Lagrange multipliers in each Newton iteration, it is not necessary to exactly solve each subproblem; performing more Newton steps with less accurate descent directions is typically more efficient than spending more time finding better descent directions [Yan et al 2018]. As such, we use the Inexact Projected Newton (IPN) method [Nocedal and Wright 2006], taking the box constraints into account.…”

Section: Inexact Projected Newton Methodmentioning

confidence: 99%

FrictionalMonolith

Takahashi

Batty

2021

ACM Trans. Graph.

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We propose FrictionalMonolith , a monolithic pressure-friction-contact solver for more accurately, robustly, and efficiently simulating two-way interactions of rigid bodies with continuum granular materials or inviscid liquids. By carefully formulating the components of such systems within a single unified minimization problem, our solver can simultaneously handle unilateral incompressibility and implicit integration of friction for the interior of the continuum, frictional contact resolution among the rigid bodies, and mutual force exchanges between the continuum and rigid bodies. Our monolithic approach eliminates various problematic artifacts in existing weakly coupled approaches, including loss of volume in the continuum material, artificial drift and slip of the continuum at solid boundaries, interpenetrations of rigid bodies, and simulation instabilities. To efficiently handle this challenging monolithic minimization problem, we present a customized solver for the resulting quadratically constrained quadratic program that combines elements of staggered projections, augmented Lagrangian methods, inexact projected Newton, and active-set methods. We demonstrate the critical importance of a unified treatment and the effectiveness of our proposed solver in a range of practical scenarios.

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Section: Inexact Projected Newton Methodmentioning

confidence: 99%

FrictionalMonolith

Takahashi

Batty

2021

ACM Trans. Graph.

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“…Another approach that has recently seen increasing attention is sensitivity analysis, which eliminates state variables and constraints such as to obtain an unconstrained minimization problem with design parameters as only variables. Sensitivity analysis is a powerful method that has been used for inverse design of mechanisms Megaro et al 2017], clothing [Wang 2018], material optimization [Yan et al 2018; as well as for optimization-based forward design [Pérez et al 2017;Umetani et al 2011].…”

Section: Related Workmentioning

confidence: 99%

“…However, we believe that our selection of examples is representative for a large range of stiff inverse problems encountered in practice. For the case of non-stiff problems, on the other hand, inexact descent methods can be an attractive alternative [Yan et al 2018].…”

Section: Limitations and Future Workmentioning

confidence: 99%

SGN: Sparse Gauss-Newton for Accelerated Sensitivity Analysis

2021

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We present a sparse Gauss-Newton solver for accelerated sensitivity analysis with applications to a wide range of equilibrium-constrained optimization problems. Dense Gauss-Newton solvers have shown promising convergence rates for inverse problems, but the cost of assembling and factorizing the associated matrices has so far been a major stumbling block. In this work, we show how the dense Gauss-Newton Hessian can be transformed into an equivalent sparse matrix that can be assembled and factorized much more efficiently. This leads to drastically reduced computation times for many inverse problems, which we demonstrate on a diverse set of examples. We furthermore show links between sensitivity analysis and nonlinear programming approaches based on Lagrange multipliers and prove equivalence under specific assumptions that apply for our problem setting.

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“…For efficiency, some methods rely on the reduction of the solution space [14,15,19], while some others apply Sherman-Morrison-Woodbury formulas for fast inverse computation [23]. Recently, Yan et al [24] improved the efficiency by alternating between two phases, forward simulation and parameter updating in an inexact descent manner. Because the error coming from the asymmetric mesh is usually distributed in a non-smooth way, the adjustment of the material to compensate such error is often non-smoothly distributed.…”

Section: Materials Optimizationmentioning

confidence: 99%

Symmetry Based Material Optimization

et al. 2021

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Many man-made or natural objects are composed of symmetric parts and possess symmetric physical behavior. Although its shape can exactly follow a symmetry in the designing or modeling stage, its discretized mesh in the analysis stage may be asymmetric because generating a mesh exactly following the symmetry is usually costly. As a consequence, the expected symmetric physical behavior may not be faithfully reproduced due to the asymmetry of the mesh. To solve this problem, we propose to optimize the material parameters of the mesh for static and kinematic symmetry behavior. Specifically, under the situation of static equilibrium, Young’s modulus is properly scaled so that a symmetric force field leads to symmetric displacement. For kinematics, the mass is optimized to reproduce symmetric acceleration under a symmetric force field. To efficiently measure the deviation from symmetry, we formulate a linear operator whose kernel contains all the symmetric vector fields, which helps to characterize the asymmetry error via a simple ℓ2 norm. To make the resulting material suitable for the general situation, the symmetric training force fields are derived from modal analysis in the above kernel space. Results show that our optimized material significantly reduces the asymmetric error on an asymmetric mesh in both static and dynamic simulations.

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Inexact descent methods for elastic parameter optimization

Cited by 7 publications

References 48 publications

FrictionalMonolith

FrictionalMonolith

SGN: Sparse Gauss-Newton for Accelerated Sensitivity Analysis

Symmetry Based Material Optimization

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