81 research outputs found
LiCROM: Linear-Subspace Continuous Reduced Order Modeling with Neural Fields
Linear reduced-order modeling (ROM) simplifies complex simulations by
approximating the behavior of a system using a simplified kinematic
representation. Typically, ROM is trained on input simulations created with a
specific spatial discretization, and then serves to accelerate simulations with
the same discretization. This discretization-dependence is restrictive.
Becoming independent of a specific discretization would provide flexibility
to mix and match mesh resolutions, connectivity, and type (tetrahedral,
hexahedral) in training data; to accelerate simulations with novel
discretizations unseen during training; and to accelerate adaptive simulations
that temporally or parametrically change the discretization.
We present a flexible, discretization-independent approach to reduced-order
modeling. Like traditional ROM, we represent the configuration as a linear
combination of displacement fields. Unlike traditional ROM, our displacement
fields are continuous maps from every point on the reference domain to a
corresponding displacement vector; these maps are represented as implicit
neural fields.
With linear continuous ROM (LiCROM), our training set can include multiple
geometries undergoing multiple loading conditions, independent of their
discretization. This opens the door to novel applications of reduced order
modeling. We can now accelerate simulations that modify the geometry at
runtime, for instance via cutting, hole punching, and even swapping the entire
mesh. We can also accelerate simulations of geometries unseen during training.
We demonstrate one-shot generalization, training on a single geometry and
subsequently simulating various unseen geometries
Dimensional hyper-reduction of nonlinear finite element models via empirical cubature
We present a general framework for the dimensional reduction, in terms of number of degrees of freedom as well as number of integration points (“hyper-reduction”), of nonlinear parameterized finite element (FE) models. The reduction process is divided into two sequential stages. The first stage consists in a common Galerkin projection onto a reduced-order space, as well as in the condensation of boundary conditions and external forces. For the second stage (reduction in number of integration points), we present a novel cubature scheme that efficiently determines optimal points and associated positive weights so that the error in integrating reduced internal forces is minimized. The distinguishing features of the proposed method are: (1) The minimization problem is posed in terms of orthogonal basis vector (obtained via a partitioned Singular Value Decomposition) rather that in terms of snapshots of the integrand. (2) The volume of the domain is exactly integrated. (3) The selection algorithm need not solve in all iterations a nonnegative least-squares problem to force the positiveness of the weights. Furthermore, we show that the proposed method converges to the absolute minimum (zero integration error) when the number of selected points is equal to the number of internal force modes included in the objective function. We illustrate this model reduction methodology by two nonlinear, structural examples (quasi-static bending and resonant vibration of elastoplastic composite plates). In both examples, the number of integration points is reduced three order of magnitudes (with respect to FE analyses) without significantly sacrificing accuracy.Peer ReviewedPostprint (published version
Space-time editing of elastic motion through material optimization and reduction
We present a novel method for elastic animation editing with space-time constraints. In a sharp departure from previous approaches, we not only optimize control forces added to a linearized dynamic model, but also optimize material properties to better match user constraints and provide plausible and consistent motion. Our approach achieves efficiency and scalability by performing all computations in a reduced rotation-strain (RS) space constructed with both cubature and geometric reduction, leading to two orders of magnitude improvement over the original RS method. We demonstrate the utility and versatility of our method in various applications, including motion editing, pose interpolation, and estimation of material parameters from existing animation sequences
Efficient Deformations Using Custom Coordinate Systems
Physics-based deformable object simulations have been playing an increasingly important role in 3D computer graphics. They have been adopted for humanoid character animations as well as special effects such as fire and explosion. However, simulations of large, complex systems can consume large amounts of computation and mostly remain offline, which prohibits their use for interactive applications.We present several highly efficient schemes for deformable object simulation using custom spatial coordinate systems. Our choices span the spectrum of subspace to full space and both Lagrangian and Eulerian viewpoints.Subspace methods achieve massive speedups over their “full space” counterparts by drastically reducing the degrees of freedom involved in the simulation. A long standing difficulty in subspace simulation is incorporating various non-linearities. They introduce expensive computational bottlenecks and quite often cause novel deformations that are outside the span of the subspace.We address these issues in articulated deformable body simulations from a Lagrangian viewpoint. We remove the computational bottleneck of articulated self-contact handling by deploying a pose-space cubature scheme, a generalization of the standard “cubature” approximation. To handle novel deformations caused by arbitrary external collisions, we introduce a generic approach called subspace condensation, which activates full space simulation on the fly when an out-of-basis event is encountered. Our proposed frameworkefficiently incorporates various non-linearities and allows subspace methods to be used in cases where they previously would not have been considered.Deformable solids can interact not only with each other, but also with fluids. Wedesign a new full space method that achieves a two-way coupling between deformable solids and an incompressible fluid where the underlying geometric representation is entirely Eulerian. No-slip boundary conditions are automatically satisfied by imposing a global divergence-free condition. We are able to simulate multiple solids undergoing complex, frictional contact while simultaneously interacting with a fluid. The complexity of the scenarios we are able to simulate surpasses those that we have seen from any previous method
Finite Strain Homogenization Using a Reduced Basis and Efficient Sampling
The computational homogenization of hyperelastic solids in the geometrically
nonlinear context has yet to be treated with sufficient efficiency in order to
allow for real-world applications in true multiscale settings. This problem is
addressed by a problem-specific surrogate model founded on a reduced basis
approximation of the deformation gradient on the microscale. The setup phase is
based upon a snapshot POD on deformation gradient fluctuations, in contrast to
the widespread displacement-based approach. In order to reduce the
computational offline costs, the space of relevant macroscopic stretch tensors
is sampled efficiently by employing the Hencky strain. Numerical results show
speed-up factors in the order of 5-100 and significantly improved robustness
while retaining good accuracy. An open-source demonstrator tool with 50 lines
of code emphasizes the simplicity and efficiency of the method.Comment: 28 page
Study of the optimal location of wing sensors using model-order reduction
The overall goal of this work is to numerically determine the optimal location of sensors for predicting the vibration behavior of a wing. The methodology to achieve this goal will be to construct, using as starting point finite element simulations, a reduced-order model able to capture the essential vibrational characteristic of the wing
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