SpringTime: Learning Simulatable Models of Cloth with Spatially-varying Constitutive Properties

TL;DR

This approach demonstrates the ability to accurately model spatially varying material properties from a variety of data sources, and immunity to membrane locking which plagues FEM-based simulations, and compares to graph-based networks and neural ODE-based architectures.

Abstract

Materials used in real clothing exhibit remarkable complexity and spatial variation due to common processes such as stitching, hemming, dyeing, printing, padding, and bonding. Simulating these materials, for instance using finite element methods, is often computationally demanding and slow. Worse, such methods can suffer from numerical artifacts called ``membrane locking'' that makes cloth appear artificially stiff. Here we propose a general framework, called SpringTime, for learning a simple yet efficient surrogate model that captures the effects of these complex materials using only motion observations. The cloth is discretized into a mass-spring network with unknown material parameters that are learned directly from the motion data, using a novel force-and-impulse loss function. Our approach demonstrates the ability to accurately model spatially varying material properties from a variety of data sources, and immunity to membrane locking which plagues FEM-based simulations. Compared to graph-based networks and neural ODE-based architectures, our method achieves significantly faster training times, higher reconstruction accuracy, and improved generalization to novel dynamic scenarios. Codebase for the paper can be found at https://github.com/ericchen321/springtime.

Figures (12)

• Figure 1: The folding experiment. A square piece of cloth is pinned at diagonally opposite corners, in two ways. (a) Illustration with 2x2 mesh, with pinned corners (red) and the fold line (dashed blue). In the "aligned" case, the fold is aligned with mesh edges; membrane locking occurs when it is "misaligned." (b) Aligned (blue) vs misaligned (red) low-resolution ($16 \times 16$) mesh at an equilibrium configuration. The misaligned case appears stiffer due to locking. (c) Aligned (blue) vs misaligned (red) high-resolution ($61 \times 61$) mesh at an equilibrium configuration. The differences due to locking are reduced. (d) SpringTime (blue mass-spring sheet) vs low-resolution mesh landmarks used for training (blue dots) vs high-resolution mesh (red) in misaligned rest configuration. Even though SpringTime was trained on the low-resolution mesh, its behavior is closer the high resolution mesh, with less locking. (e) SpringTime trained on mesh with bending stiffness (blue) vs high-resolution mesh without bending stiffness (red), in the aligned configuration. This shows that SpringTime can learn real bending stiffness while resisting locking. White dots are mesh vertices; all meshes have the same mass and physical dimensions, and only differ in bending stiffness or resolution.
• Figure 2: Results from different surrogate models (blue) after $8$ seconds of simulation, compared with the ground truth (red). (Left) Our surrogate model; (middle), (right) are popular alternatives. Notice that SpringTime yields comparable steady-state reconstruction error as MeshGraphNet (MGN, middle), while Neural ODE (right) completely fails to reconstruct long rollouts.
• Figure 3: Method overview. (a) The material modeling pipeline. We sample system state $(\mathbf{y}_0, \dot{\mathbf{y}_0})$ from the source cloth at the first time step of a rollout, resample following the scheme in Sec. \ref{['sec:spatial_disc']} to get target particle positions, feed it to the neural constitutive model $h_{\theta}$ to predict neural particle force $\mathbf{f}_t$, then integrate. To further evolve the surrogate we use previously predicted states. (b)-(e) illustrates the architecture of our SpringTime which models a simple rectangular cloth, with rest configuration shown in (b) and a deformed configuration in (c). (d): Each neural spring (circle) takes the relative position and velocity of particles at its two ends, and predicts the spring's internal force. Then each particle accumulates forces applied by its surrounding springs. (e) Neural spring. At every time step, the module computes elastic and damping force and sums them up. Parts with learnable parameters are in dark red.
• Figure 4: Spatial discretization of the surrogate system (left) and the source system (right). Bending springs and diagonal springs from top-left to bottom-right can be optionally excluded on construction. For simplicity, we only show two bending springs; the full surrogate contains bending springs connected at $\text{stride}=1$. The dotted lines show how we compute the target position of each surrogate particle from the positions of nearby source landmarks via barycentric interpolation. Note that in training only landmarks from the source are needed, and topolgical information are not necessary.
• Figure 5: Generating $N=3$ rollouts of equal lengths but with different initial conditions (top) and boundary conditions. Equilibrium states reached by the last step (bottom). Stiffer regions are colored darker.