High-order differentiable autoencoder for nonlinear model reduction

Abstract

With a GPU-based implementation, we are able to wield deep autoencoders (e.g., 10+ layers) with a relatively high-dimension latent space in real-time. Along this pipeline, we also design a sampling network and a weighting network to enable weight-varying Cubature integration in order to incorporate nonlinearity in the model reduction. We believe this work will inspire and benefit future research efforts in nonlinearly reduced physical simulation problems.CCS Concepts: • Computing methodologies → Physical simulation; Dimensionality reduction and manifold learning.

Fine-grained differentiable physics: a yarn-level model for fabrics

“…In addition, our model can be embedded as a layer into a neural network, which helps learning control policies for cloth manipulation. Further, our model potentially enables a synergy between empirical physics modeling and deep learning, where our model can serve as a deterministic physics layer and other layers can incorporate non-linearity such as high-frequency dynamics in the system (Shen et al, 2021). Finally, our modeling of general forces such as friction and shear contributes to differentiable physical modeling in a wider range, given the universal presence of such forces in the real world.…”

HoD-Net: High-Order Differentiable Deep Neural Networks and Applications

“…Classic reduced simulations use linear maps like PCA (Treuille, Lewis, and Popović 2006) and modal analysis (Hurty 1960). Recently, DL has also been exploited to establish the nonlinear map between generalized and fullspace coordinates, often in the structure of encoder-decoder (Fulton et al 2019;Shen et al 2021).…”

“…In Newtonian dynamics, any map of model's trajectory takes at least second-order differentiation to extract necessary inertia information (i.e., the acceleration-triggered dynamics). Unlike (Shen et al 2021), our model reduction is fully network based (i.e., without using PCA). Under FEM discretization, the motion of a deformable solid can be described with the Euler-Lagrange equation: M ü + f int (u) = f ext .…”

Neural Jacobian Fields: Learning Intrinsic Mappings of Arbitrary Meshes

“…Many methods focus on a single mesh, or a set of variations of the same mesh [Bogo et al 2014;Osman et al 2020;Varol et al 2017;Zuffi et al 2017], and define an arbitrary fixed correspondence of vertices and/or faces to the entries of a predicted tensor, thereby enabling machine learning algorithms to associate predicted quantities to geometric elements. This enables treating the input and output as general tensors of a homogeneous dataset and applying off-the-shelf tools for data analysis, such as Principal Component Analysis [Anguelov et al 2005], Gaussian Mixture Models [Bogo et al 2016], as well as neural networks, which assign per-vertex coordinates [Shen et al 2021] or offsets from a simpler (e.g., linear) model [Bailey et al 2020[Bailey et al , 2018Romero et al 2021;Yin et al 2021;Zheng et al 2021]. As they are not shape-aware in the sense discussed in Section 1, such methods often need to add additional regularizers such as ARAP [Sun et al 2021] or the Laplacian [Kanazawa et al 2018].…”

“…Deformation fields are commonly used to generalize across different triangulations and even geometric domains. Specifically, one can learn to predict an implicit vector field which maps every point in the volume to its new location [Groueix et al 2018a[Groueix et al , 2019Yang et al 2021]. This representation acts in a point-wise manner, and is not aware of the underlying surface, thus these maps tend to not preserve local surface details.…”