Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 8: Strong Accept: Technically strong paper, with novel ideas, excellent impact on at least one area, or high-to-excellent impact on multiple areas, with excellent evaluation, resources, and reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper proposes to learn a PlasticityNet to facilitate implicit Euler method for simulating plastic deformation. 

- Given a deformation gradient, the PlasticityNet behaves like an energy function, which gradients represents the force/stress of the plastic materials. Such formulation allows the user to write the forward step as an optimization problem and enables the implicit Euler method.
- The plasticityNet only needs to be locally accurate around input deformation gradients for plastic deformation. Based on this property, the authors propose a fix-point iteration method with a regularization term that better exploits the locality to stablize the training.
- The authors conducted experiments on a wide range of materials and achieve good performance.
strengths_and_weaknesses: Strength:

- Simulating plastic material has a wide range of applications, from animation to robotics. This paper attacks the fundamental problem of plastic material simulation. It introduces a learning-based method to enable implicit Euler, which will have an impact on the field of learning-based simulation and facilitate research on other domains.
- The proposed techniques are very novel to me. Learning a Pseudo-energy function for implicit Euler is a good idea and may have potential to generalize on other fields. Besides, the idea of parameterizing the function with F_0 for local approximation and the special form that embeds physical prior both are also very interesting.
- The paper is well-written and the presentation is very clear and easy to follow.

Weakness:

- What I find missing is the discussion about the time complexity. Will the network and the fixed-point iteration introduce an additional computation burden, canceling out the benefits of the implicit Euler?
- The paper could be strengthened for readers from the learning community by adding an ablation study or baseline comparisons. For example, what would happen if we directly learn a global function without inputting F_0, or if we do not introduce the “linear correction” but learn the potential energy directly? It would be interesting to have those experiments to help understand the philosophy behind the particular design. Such ablation studies are necessary to support the method. I would also be interested if the learned network can generalize to different scenes.
questions: Regarding the stability regularization, it seems that due to the locality of the PlasticityNet, we need to solve a constrained optimization problem within the pre-defined trust regions. Isn’t it better to add the hard constrain directly? 
limitations: yes
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: The authors propose a neural network-based approach, which enables the simulation of a wide range of arbitrary elasticity-plasticity combinations using time step-independent, unconditionally stable optimization-based time integrators.

strengths_and_weaknesses: This paper proposes a general framework to enable the simulation of objects with a wide range of materials. The framework is novel and reliable. The paper is well-written, and the experimental setting is clear. I think this is a good paper.
questions: 1. In Fig.9, why the errors of sand and snow are reduced along with simulation, but the error of metal increases.
2. How about the generalization ability to a different initial shape with the same material and a different initial shape with different material? For example, give a model trained on the sand with the initial shape of a cube (term it as 'sand cube'),  and then test it on the 'sand sphere'. Further, test the model on the 'snow sphere'.

limitations: Yes, limitations and societal impact were appropriately addressed.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: This paper presents a neural network model to learn a plastic material’s energy function in elastoplastic simulation. The paper argues that constructing such an energy model enables optimization-based solvers for the time integration problem, which is more advantageous than solving the force equilibrium directly. Additionally, the paper introduces a few useful extensions on top of the network model: hardening effects, stability regularizer, and volume-preserving return mapping. The paper presents various 2D and 3D examples (sand, snow, and metal) to demonstrate the value of the proposed network.
strengths_and_weaknesses: Strength: this paper discussed a serious physics simulation problem. The mathematical and physical background is fairly solid. Implementing MPM, FEM, and IPC are nontrivial, for which the authors deserve some credits if they coded everything from scratch. The 2D and 3D demos are also visually pleasing.

Weaknesses: I feel the paper still lacks a deeper insight behind the introduction of the network model. I also think the evaluation section misses some critical points.

Overall, I think this paper is very interesting and promising, but I am afraid it is not there yet. My initial score is rejection, but I am happy to re-evaluate the paper if the authors can address my questions.

questions: 1. For solving the time integration, this paper seems to favor energy minimization (Eqn. 3) instead of solving the governing equation (Eqn. 1). However, I am under the impression that both approaches have been equally popular in deformable-body simulation, and the argument in lines 116-118 doesn’t fully convince me because we could also solve Eqn. 1 using Newton’s method plus line search/other safeguards. Maybe I am unaware of some critical reference papers here. Could you please comment more on this?

2. On a related note, I am not sure I get what lines 138-140 intend to say. To me, directly feeding Z(F) to the elastic potential (followed by solving the nonlinear root-finding or energy minimization problem) seems to be a legit solution. Could you clarify this?

3. I really appreciate the magic equation 8. Could you tell me more about how you derived it?

4. Eqn 11: why is shear modulus used as the weight of the regularizer? Is there physical intuition behind this choice?

5. One general concern that I always have with such network methods is that they don’t seem to guarantee physical plausibility. For example, a reasonable energy potential is expected to be bounded below, which is easy to guarantee for an analytical energy potential function but could be difficult to enforce for a network model (The discussion on Hessians in the limitation section might be somewhat relevant to this point). Could you give me a strong motivation for why we should appreciate these network models?

6. I am confused by the experiments that compare ground-truth simulation generated using explicit time integration with your approach that solves implicit time integration. Why not use implicit time integration in both settings?

7. I also didn’t find statistics about the wall clock time cost. I get that having the network to model the energy potential unlocks a larger time step than explicit methods, but doesn’t each implicit time step cost more wall-clock time? Therefore, what is the final time cost for generating each row in Fig. 5?

8. For Fig 7 row 2 and row 3: not sure I understand why adjusting both time step size and Young’s modulus between these two rows.

9. I also didn’t find a discussion about the generalization of the trained network model. Actually, I am not sure how generalization/training data/test data should be defined for this model. I am raising this concern because network models typically over-parametrize physics models (physics laws often only have a few parameters while networks can easily have thousands or more).

limitations: The limitation section looks good to me.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: The authors proposed a learning-based model to simulate plasticity effects. The method is based on optimization based time integration and trains a network to predict the energy given the deformation gradients and the hardening states. Results show that the predicted energy can successfully guide the simulation to behave similarly as ground truth ones.

strengths_and_weaknesses: Strengths:
 - The network only tries to learn the energy mapping for a certain point, which provides the ability to scale the method to arbitrary scenes.
 - Using neural network to predict the energy can enable larger step time, which in turn speed up the simulation.

Weaknesses:
 - Missing references:
   - Hu, Y., Anderson, L., Li, T. M., Sun, Q., Carr, N., Ragan-Kelley, J., & Durand, F. (2019, September). DiffTaichi: Differentiable Programming for Physical Simulation. In International Conference on Learning Representations.
   - Qiao, Y., Liang, J., Koltun, V., & Lin, M. (2021). Differentiable simulation of soft multi-body systems. Advances in Neural Information Processing Systems, 34, 17123-17135.
   These two papers combines machine learning with simulation via differentiating the simulation as a whole which can enable efficient inverse problem solving as well. I suggest the authors discuss this direction and if possible, compare with DiffTaichi since it also uses MPM.
 - It is not clear how much performance gain there is after using the learned model. The step time is indeed 100x larger (from 1e-5 to 1e-3, as mentioned in the text), but to achieve convergence, the authors adopted a fixed point iteration which is not required in traditional simulations. *A few number* of iterations as mentioned by the authors are not accurate enough to evaluate the strengths of this approach. I would like to see performance tables or figures that shows significant improvement with the proposed approach so that it can be strongly supported.
 - It seems the network has to be trained all over again if the material parameters are different, which limits the generalization ability of this approach. While it is a common open problem for all learning-based simulations, I suggest the authors discuss and provide insights towards solving it in the limitation and future work section.
 - It is not clear how the 100x step time is achieved. Why 100x but not 1000x? Is there any theorectical hypothesis on how much at most a learning based model can improve? Does the error goes up with the step time, and how is the trend like? 
questions: See above.
limitations: No. See above.
review_title: null

Meta-review: metareview: After rebuttal, all reviewers vote to accept this submission due to its technical novelty, presentation, and wide potential applications.  The AC agrees.   Congratulations.
confidence: Certain
Decision: Accept