40 research outputs found
A survey on deep geometry learning: from a representation perspective
Researchers have achieved great success in dealing with 2D images using deep learning. In recent years, 3D computer vision and geometry deep learning have gained ever more attention. Many advanced techniques for 3D shapes have been proposed for different applications. Unlike 2D images, which can be uniformly represented by a regular grid of pixels, 3D shapes have various representations, such as depth images, multi-view images, voxels, point clouds, meshes, implicit surfaces, etc. The performance achieved in different applications largely depends on the representation used, and there is no unique representation that works well for all applications. Therefore, in this survey, we review recent developments in deep learning for 3D geometry from a representation perspective, summarizing the advantages and disadvantages of different representations for different applications. We also present existing datasets in these representations and further discuss future research directions
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
Modal-Graph 3D Shape Servoing of Deformable Objects with Raw Point Clouds
Deformable object manipulation (DOM) with point clouds has great potential as
non-rigid 3D shapes can be measured without detecting and tracking image
features. However, robotic shape control of deformable objects with point
clouds is challenging due to: the unknown point-wise correspondences and the
noisy partial observability of raw point clouds; the modeling difficulties of
the relationship between point clouds and robot motions. To tackle these
challenges, this paper introduces a novel modal-graph framework for the
model-free shape servoing of deformable objects with raw point clouds. Unlike
the existing works studying the object's geometry structure, our method builds
a low-frequency deformation structure for the DOM system, which is robust to
the measurement irregularities. The built modal representation and graph
structure enable us to directly extract low-dimensional deformation features
from raw point clouds. Such extraction requires no extra point processing of
registrations, refinements, and occlusion removal. Moreover, to shape the
object using the extracted features, we design an adaptive robust controller
which is proved to be input-to-state stable (ISS) without offline learning or
identifying both the physical and geometric object models. Extensive
simulations and experiments are conducted to validate the effectiveness of our
method for linear, planar, tubular, and solid objects under different settings
Spatially Adaptive Cloth Regression with Implicit Neural Representations
The accurate representation of fine-detailed cloth wrinkles poses significant
challenges in computer graphics. The inherently non-uniform structure of cloth
wrinkles mandates the employment of intricate discretization strategies, which
are frequently characterized by high computational demands and complex
methodologies. Addressing this, the research introduced in this paper
elucidates a novel anisotropic cloth regression technique that capitalizes on
the potential of implicit neural representations of surfaces. Our first core
contribution is an innovative mesh-free sampling approach, crafted to reduce
the reliance on traditional mesh structures, thereby offering greater
flexibility and accuracy in capturing fine cloth details. Our second
contribution is a novel adversarial training scheme, which is designed
meticulously to strike a harmonious balance between the sampling and simulation
objectives. The adversarial approach ensures that the wrinkles are represented
with high fidelity, while also maintaining computational efficiency. Our
results showcase through various cloth-object interaction scenarios that our
method, given the same memory constraints, consistently surpasses traditional
discrete representations, particularly when modelling highly-detailed localized
wrinkles.Comment: 16 pages, 13 figure
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Harnessing Simulated Data with Graphs
Physically accurate simulations allow for unlimited exploration of arbitrarily crafted environments. From a scientific perspective, digital representations of the real world are useful because they make it easy validate ideas. Virtual sandboxes allow observations to be collected at-will, without intricate setting up for measurements or needing to wait on the manufacturing, shipping, and assembly of physical resources. Simulation techniques can also be utilized over and over again to test the problem without expending costly materials or producing any waste.
Remarkably, this freedom to both experiment and generate data becomes even more powerful when considering the rising adoption of data-driven techniques across engineering disciplines. These are systems that aggregate over available samples to model behavior, and thus are better informed when exposed to more data. Naturally, the ability to synthesize limitless data promises to make approaches that benefit from datasets all the more robust and desirable.
However, the ability to readily and endlessly produce synthetic examples also introduces several new challenges. Data must be collected in an adaptive format that can capture the complete diversity of states achievable in arbitrary simulated configurations while too remaining amenable to downstream applications. The quantity and zoology of observations must also straddle a range which prevents overfitting but is descriptive enough to produce a robust approach. Pipelines that naively measure virtual scenarios can easily be overwhelmed by trying to sample an infinite set of available configurations. Variations observed across multiple dimensions can quickly lead to a daunting expansion of states, all of which must be processed and solved. These and several other concerns must first be addressed in order to safely leverage the potential of boundless simulated data.
In response to these challenges, this thesis proposes to wield graphs in order to instill structure over digitally captured data, and curb the growth of variables. The paradigm of pairing data with graphs introduced in this dissertation serves to enforce consistency, localize operators, and crucially factor out any combinatorial explosion of states. Results demonstrate the effectiveness of this methodology in three distinct areas, each individually offering unique challenges and practical constraints, and together showcasing the generality of the approach. Namely, studies observing state-of-the-art contributions in design for additive manufacturing, side-channel security threats, and large-scale physics based contact simulations are collectively achieved by harnessing simulated datasets with graph algorithms
Model reduction for the material point method via an implicit neural representation of the deformation map
This work proposes a model-reduction approach for the material point method
on nonlinear manifolds. Our technique approximates the by
approximating the deformation map using an implicit neural representation that
restricts deformation trajectories to reside on a low-dimensional manifold. By
explicitly approximating the deformation map, its spatiotemporal gradients --
in particular the deformation gradient and the velocity -- can be computed via
analytical differentiation. In contrast to typical model-reduction techniques
that construct a linear or nonlinear manifold to approximate the (finite number
of) degrees of freedom characterizing a given spatial discretization, the use
of an implicit neural representation enables the proposed method to approximate
the deformation map. This allows the kinematic
approximation to remain agnostic to the discretization. Consequently, the
technique supports dynamic discretizations -- including resolution changes --
during the course of the online reduced-order-model simulation.
To generate for the generalized coordinates, we propose a
family of projection techniques. At each time step, these techniques: (1)
Calculate full-space kinematics at quadrature points, (2) Calculate the
full-space dynamics for a subset of `sample' material points, and (3) Calculate
the reduced-space dynamics by projecting the updated full-space position and
velocity onto the low-dimensional manifold and tangent space, respectively. We
achieve significant computational speedup via hyper-reduction that ensures all
three steps execute on only a small subset of the problem's spatial domain.
Large-scale numerical examples with millions of material points illustrate the
method's ability to gain an order of magnitude computational-cost saving --
indeed -- with negligible errors