NeuralClothSim: Neural Deformation Fields Meet the Thin Shell Theory

Summary

The paper uses Physics-Informed Neural Networks (PINNs) to solve cloth quasistatics. The cloth is represented by a neural implicit function, which provides infinite resolution. The cloth elasticity is modeled using Kirchhoff-Love thin shell theory. The equilibrated displacement field is obtained by minimizing the potential energy of the system. Boundary conditions are strictly enforced through reparameterization tricks.

Strengths

PINNs can offer infinite resolution, ensuring that the cloth does not suffer from numerical locking issues that arise from spatial discretization in mesh-based simulation methods.

Weaknesses

The paper is targeted at computer graphics applications. But it only solves quasistatics and doesn’t consider collisions, making it actually a less suitable candidate for computer graphics applications where realistic dynamics and collision resolution are vital. The paper proposes a visualization of the trajectory from the rest shape to equilibrium, but it appears very damped. The proposed method seems to run much slower than the classical simulators.

Questions

The framework presented in the paper shares many components with the work, [Physics-Informed Deep Learning for Computational Elastodynamics without Labeled Data](https://arxiv.org/abs/2006.08472). However, this mentioned paper is not cited. The primary difference lies in the type of elasticity: the mentioned paper addresses volumetric elasticity, while this paper focuses on thin shell elasticity. Both papers use the same trick to strictly enforce boundary conditions. Additionally, the mentioned paper solves dynamics by incorporating a temporal term in the governing PDE, where the displacement field is a neural implicit function that depends on $(\boldsymbol{x}, t)$, which is more expressive than this paper. The approach of using potential minimization to solve quasistatic elasticity is also explored in [NTopo](https://proceedings.neurips.cc/paper/2021/hash/55d99a37b2e1badba7c8df4ccd506a88-Abstract.html). These facts significantly weaken the technical contributions of the paper. Please consider differentiating between background knowledge and your contributions. I think the solver framework is not novel, while the continuous shell representation and the introduction of shell elasticity to the PINN community are new. The inconsistency in classical simulators can be alleviated by increasing the resolution. A well-defined FEM-based cloth solver should exhibit convergence under refinement. I am interested in whether increasing the resolution of a FEM solver, so that the computation time is roughly the same as the proposed method, will make the inconsistency negligible. In Fig.6, why does the proposed method have the concept of discretization? That is, what do discretizations I, II, and III mean for the proposed method?

Rating

5

Confidence

5

Soundness

3

Presentation

3

Contribution

2

Limitations

Limitations are well discussed.

Summary

The paper proposes a cloth simulation model based on the Kirchoff-Love thin shell theory, using a neural network (SIREN activations) to parameterize a deformation field (NDF) from a base parameterization. The model can handle periodic and Dirichlet boundary conditions, and uses the network to calculate the necessary higher-order derivatives. This continuous NDF allows the model to be discretized at any resolution via sampling more coarsely or finely, and also allows for material conditioning. It is tested against the Belytschko obstacle course to show validity, and in a few simple scenarios against DiffCloth and DiffArcSim, two mesh-based differentiable simulators, and shows comparable performance with superior memory performance.

Strengths

1. The use of an NDF allows for simulation without knowledge of the necessary resolution beforehand. * It also lessens the memory footprint. 2. The method leverages a principled and sophisticated thin shell theory and thus is able to reproduce several anisotropic and buckling effects that are challenging for simpler traditional mesh-based models. 3. The work may spur further work in neural cloth simulation by educating readers about the potential advantages of a continuous NDF representation, and a working implementation of it. 4. There are many details and additional validations in the supplementary material. It is a pretty thorough presentation of the work at hand.

Weaknesses

1. No collision detection or friction, which are approximated by DiffCloth and DiffArcSim, as acknowledged by the authors. 2. The training time is quite high, and I believe it's slower than simulation time for state-of-the-art FEM systems (see App. A).

Questions

1. Can the framework handle multiple panels joined at seams? If so, did you try any such models? 2. For the initial fitting to an input mesh, do you have any examples of this? If so, it should be put in the main text, as this represents a nice demonstration of applicability beyond simpler test scenarios. 3. Can the method be used for inverse design scenarios with respect to material parameters, or with determination of external forces to achieve a trajectory? These were applications considered in comparison methods, and I'd be curious to know if this was attempted at all.

Rating

6

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

The authors have acknowledged the limitations of the method throughout their text.

Summary

The paper proposes to model the cloth as a fixed parameter domain embedded via a function encoded as a neural network. The network weights are then optimized to minimize a Kirchoff-Love free energy, thus implementing a quasistatic cloth deformation model without a mesh discretization.

Strengths

The method is technically sound, and the appendices document extensively the choices made. The results are compelling, and they show the benefits of mesh-independence.

Weaknesses

### Discretization-independence The neural cloth simulation is not "sensitive to the finite element discretisations" (49-50). But this is because discretization is used only in a post-simulation evaluation step. Perhaps a fairer analogue of discretization independence would be whether the results are sensitive to the initialization of the neural network weights. ### Generality The paper proposes representations for rectangular cloth patches with point constraints as well as cylindrical sleeves. Can this framework be extended to garments of arbitrary rest shape and topology? Is it possible to support non-boundary point constraints or shape constraints? The NDF editing application allows editing the scene parameters after simulation, but it seems like it might be hard to adapt this method to real-time editing of point constraints, which would be desirable for artists. ### Minor details The paper needs general copy editing, but here are some specific points: - "therefore, inherently assume" => "inherently assuming" (26) - "a detailed" => "detailed" (227) - "stretching, and" => "stretching and" (232)

Questions

- The second spatial derivatives of $\mathcal{F}_{\Theta}$ are required to exist (164), but what about mixed second partials in $\Theta$ and $\mathbf{\xi}$? Presumably this is not a major problem. - The paper proposes representations for rectangular cloth patches with point constraints as well as cylindrical sleeves. Can this framework be extended to garments of arbitrary rest shape and topology? - How simple would it be to extend the trajectory model to accurately model dynamics? - How do you sample the surface

Rating

7

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

The authors freely point out that they "do not claim qualitative superiority over classical cloth simulation methods" (64).

Thank you

Thank you for the clarifying responses. I will be keeping my score as is, entering the discussion phase. Reviewer