NeuralClothSim: Neural Deformation Fields Meet the Thin Shell Theory

TL;DR

This paper proposes NeuralClothSim, a new quasistatic cloth simulator using thin shells, in which surface deformation is encoded in neural network weights in the form of a neural field, based on a new continuous coordinate-based surface representation called neural deformation fields (NDFs).

Abstract

Despite existing 3D cloth simulators producing realistic results, they predominantly operate on discrete surface representations (e.g. points and meshes) with a fixed spatial resolution, which often leads to large memory consumption and resolution-dependent simulations. Moreover, back-propagating gradients through the existing solvers is difficult, and they cannot be easily integrated into modern neural architectures. In response, this paper re-thinks physically plausible cloth simulation: We propose NeuralClothSim, i.e., a new quasistatic cloth simulator using thin shells, in which surface deformation is encoded in neural network weights in the form of a neural field. Our memory-efficient solver operates on a new continuous coordinate-based surface representation called neural deformation fields (NDFs); it supervises NDF equilibria with the laws of the non-linear Kirchhoff-Love shell theory with a non-linear anisotropic material model. NDFs are adaptive: They 1) allocate their capacity to the deformation details and 2) allow surface state queries at arbitrary spatial resolutions without re-training. We show how to train NeuralClothSim while imposing hard boundary conditions and demonstrate multiple applications, such as material interpolation and simulation editing. The experimental results highlight the effectiveness of our continuous neural formulation. See our project page: https://4dqv.mpi-inf.mpg.de/NeuralClothSim/.

Figures (23)

• Figure 1: NeuralClothSim is the first neural cloth simulator representing surface deformation as a neural field. It is supervised for each target scenario with the laws of the Kirchhoff-Love thin shell theory with non-linear strain (left). Once trained, the simulation can be queried continuously and consistently enabling different spatial resolutions (center). NeuralClothSim can also incorporate learnt priors such as material properties that can be edited at test time (right).
• Figure 2: Kirchhoff-Love shell
• Figure 3: NeuralClothSim takes as input a thin shell in the reference state and its material properties, boundary motion and external forces. It then learns an NDF, i.e., a coordinate-based implicit 3D deformation field. At inference, NDF can be continuously queried for the deformed state of the surface at equilibrium using curvilinear coordinates from the parametric domain. We use the Kirchhoff-Love thin shell modelling to supervise the cloth quasistatics with the potential energy functional.
• Figure 4: Boundary conditions. In contrast to Dirichlet conditions that alter the network output (c), we impose periodic boundaries by remapping the network input to its sine and cosine values (d).
• Figure 5: Belytschko obstacle course for which we generate accurate displacements (rescaled for better visualisation).

Theorems & Definitions (6)

• Lemma B.1: Deformation gradient
• proof
• Theorem B.2: Membrane strain
• proof
• Theorem B.3: Bending strain
• proof