We sincerely thank the reviewer for the thorough and constructive feedback on our manuscript.

[L2] Focused on Forward Swimming

We would like to clarify that our framework indeed supports more tasks than just forward swimming:

• Navigation Task: Our supplementary material and video already present this task on both our 3D jellyfish and 2D fish morphologies. This task demonstrates the agent's adaptability by requiring it to dynamically adjust its swimming gait to pursue a series of on-the-fly generated targets, showcasing its ability to handle diverse goals within a single episode.
• We have also conducted two new experiments on energy-efficient swimming and flow resistance, which we will detail in our subsequent responses.

In summary, our framework is not limited to forward swimming. These experiments demonstrate its capability to train policies that exhibit adaptability and can achieve diverse goals.

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[W1/Q1/L1] Multiple Learned Gaits on Single Morphology

We thank the reviewer for this excellent point on behavioral diversity. We believe our navigation task already demonstrates the adaptive capability in question. In this task, the learned policy on the 2d fish morphology exhibits context-driven gait switching: it naturally adopts a turning gait that exhibits asymmetric deformation to turn towards a target, then seamlessly transitions to a darting gait that exploits symmetric deformation for forward propulsion (Figure 5 in supplementary material and fish2d.mp4 in the media attached).

This adaptive behavior emerges from a single, simple reward function, which shows a promising sign that our framework's capacity to learn multiple strategies and seamless switching without explicit programming for each.

Furthermore, to clarify the "single task objective" point, our new energy-efficient swimming experiment demonstrates the objective's flexibility. By introducing an energy penalty into the reward, we elicit distinct gaits from the same morphology: one optimized for maximum speed and another for energy efficiency. This shows our framework can produce a spectrum of behaviors by simply adjusting the task objective.

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[Q2] Smooth Transitions between Different Gaits

As we explained in our response to [W1/Q1/L1] above, our navigation task demonstrates that a single policy can indeed produce smooth, context-driven gait transitions.

When the target deviates from the agent's path, the policy generates an asymmetric gait: it produces a stronger body bend towards the target and a weaker counter-stroke, creating the necessary yaw torque to change direction. Once aligned, the policy seamlessly transitions back to a symmetric, rhythmic gait to maximize forward propulsion.

Our reduced-mode control representation is particularly well-suited for this. It parameterizes the holistic deformation of the body, allowing the policy to learn to smoothly modulate just a few control parameters to create either the large-scale asymmetric bends needed for turning or the balanced oscillations for efficient forward swimming. This demonstrates that our representation is sufficiently expressive to support this form of adaptive control.

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[W4/Q5] Simplified Task Setup / Additional Tasks

We thank the reviewer for the suggestions, which highlight the importance of demonstrating our framework's versatility on more complex tasks. To this end, our experiments now cover three such tasks:

• Navigation: Our navigation task, already present in the supplement, directly addresses the turning task requested in this question. The agent learns to dynamically adjust its gait to follow the target, demonstrating adaptive turning.
• Energy-Efficient Locomotion: We have conducted new experiments where an energy penalty is added to the reward. The agent successfully learns a distinct, smoother gait that minimizes the energy cost, showcasing its ability to optimize for efficiency.
• Flow Resistance: We have added a new task where the agent must maintain its position against a persistent fluid flow, following DiffAqua [1]. This demonstrates the policy's ability to generate continuous corrective forces to maintain stability.

For a detailed analysis of the energy-efficient locomotion task, we respectfully refer the reviewer to our response to Reviewer Z1aA [Q2], where this is addressed in full.

Flow Resistance

We trained a 2D fish policy to maintain its position against a persistent head-on fluid flow. The policy was rewarded for minimizing its distance from the starting point. The learned policy demonstrated good stability.

This shows the agent learned to generate persistent, continuous counter-thrust to actively resist the environmental disturbance.

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[W2/Q3] Biological Framing

Thank you for this valuable feedback. Our biological connection is indeed qualitative: the learned behaviors match canonical swimming modes, such as the undulation in our eel/clownfish models and the pulsation in our jellyfish model (Fig. 4). Crucially, these distinct modes emerged autonomously from our framework without explicit priors. We agree our use of "rediscovering evolved behaviors" was imprecise and, per your suggestion, will revise our text to focus on the emergent similarity of the behaviors rather than “discovery”.

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[W3] Limited Novelty in Methodology

While we employed quite a few established techniques, we believe the merits of our framework also include their novel adaptation and non-trivial integration of a system that balances the competing demands of physical fidelity and computational speed required for soft robot learning.

Our methodological novelty lies in combining LBS with complementary dynamics. While LBS is a standard kinematic tool, we explore its application in a physics-based context where it defines a low-dimensional control space, and complementary dynamics ensure the resulting holistic deformations are physically plausible.

Furthermore, the design decisions for assembling a complete system that supports RL for complex swimming behaviors are highly non-trivial. The community has explored several technical combinations, including CFD with A2C [2], differentiable MPM for solids and fluids [3], or simplified fluid models [4]. However, these approaches often present trade-offs that limit their use for the free-form soft swimmer control we demonstrate: full CFD is often too slow for RL, differentiable simulators can struggle with the long-horizon stability required to learn robust controllers, and simplified models lack the physical realism to capture complex hydrodynamics.

Therefore, we believe that identifying and successfully integrating our specific combination of techniques is an original and significant result. It provides the community with a practical and effective platform that balances physical fidelity, computational efficiency, and generality, opening up new possibilities for research in this domain.

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[Q4] Co-design Potential

We thank the reviewer for this question. We believe our representation is compatible with both co-design paradigms.

Integration into a Differentiable Pipeline

The LBS computation is differentiable. By treating the control points as optimizable variables, our LBS-based kinematic mapping becomes a fully differentiable module. Furthermore, the complementary dynamics solver is also differentiable through standard adjoint methods. Therefore, our entire physics-based control module can be integrated into a gradient-based pipeline.

Integration into a Gradient-free Pipeline

On the other hand, the representation is highly suitable for gradient-free methods like evolutionary algorithms. Its compact and low-dimensional design introduces minimal computational overhead. This efficiency is a significant benefit for population-based approaches, which require a large number of simulation rollouts to effectively search the design space.

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[L3/L4] Limitations on Co-design and Sim-to-Real Transfer

Thank you for these valuable comments. We agree that joint co-optimization and sim-to-real transfer are both important and challenging avenues for future research. To provide the more balanced view you suggested, we will expand our conclusion to discuss these topics, framing them as key limitations and exciting directions for our work.

We are truly grateful for your insightful comments and constructive feedback. We hope that the additional details and experimental results we provided have effectively addressed your concerns. Please feel free to let us know if there are any remaining concerns. We look forward to hearing your thoughts on our rebuttal.

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References:

[1]. Ma, P., Du, T., Zhang, J. Z., ... & Matusik, W. (2021). Diffaqua: A differentiable computational design pipeline for soft underwater swimmers with shape interpolation. ACM Transactions on Graphics (TOG), 40(4), 1-14.

[2]. Zhang, T., Tian, R., Yang, H., ... & Xie, G. (2022). From simulation to reality: A learning framework for fish-like robots to perform control tasks. IEEE Transactions on Robotics, 38(6), 3861-3878.

[3]. Wang, T. H., Ma, P., Spielberg, A. E., ... & Gan, C. (2023). SoftZoo: A Soft Robot Co-design Benchmark For Locomotion In Diverse Environments. In The Eleventh International Conference on Learning Representations.

[4]. Min, S., Won, J., Lee, S., Park, J., & Lee, J. (2019). Softcon: Simulation and control of soft-bodied animals with biomimetic actuators. ACM Transactions on Graphics (TOG), 38(6), 1-12.

We thank the Reviewer for the positive evaluation and for providing detailed, constructive feedback on our work. We are encouraged by the reviewer's assessment and have found the suggestions regarding generalization, robustness, computational cost, and reward design to be very helpful for improving our manuscript.

[W1] Interpretation on Why the Controllers Work

On a physical level, the controllers work by discovering and executing time-varying body deformations that generate effective fluid-structure interactions for propulsion. Our analysis shows that the reinforcement learning agent, through trial and error, learns to create kinematic patterns that correspond to well-understood principles of thrust generation in fluids:

• For our undulatory swimmers (eel and fish models), the learned policies generate traveling waves along the body that shed vortices in a manner consistent with a reverse von Kármán vortex street. This specific wake signature is a known indicator of net thrust production [1].
• For our jellyfish model, the controller learns to produce rhythmic bell contractions that create and shed a starting vortex ring with each pulse. This generates an impulsive jet of fluid, propelling the body forward, which is the canonical mechanism [2] for pulsatile swimmers.

Therefore, the interpretation is that our framework enables the agent to learn the fundamental physics of fluid-based locomotion from scratch, successfully identifying gaits that manipulate pressure fields and vortex dynamics to its advantage.

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[W1] Discussion on Sim-to-Real Transfer

We thank the reviewer for this question. Sim-to-real transfer for soft robots in fluid is a big challenge for the field, requiring a multi-disciplinary effort that extends beyond the scope of a single work like ours. Bridging the sim-to-real gap is a well-known challenge for the field, involving significant hurdles in system identification, manufacturing inconsistencies, and sensor/actuator dynamics. Our work focuses on the critical prerequisite of establishing a robust simulation framework to discover optimal policies under idealized conditions, providing a vital baseline for future work dedicated to this challenge.

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[W2] Lack of Joint Optimization

Thank you for your comment. Co-designing soft robots is an important emerging topic, yet it faces challenges in scaling to high-fidelity 3D simulations and in developing unified design representations. While existing works have made valuable progress, they often operate within certain constraints, such as simplified 2D design space (e.g., EvoGym [3]) or challenges in efficiently discovering controllers for complex 3D environments (e.g., SoftZoo [4]). Although our work focuses on controller optimization only, the framework we have developed shows a promising sign of tackling both of these challenges, providing a unified control representation within a high-fidelity 3D environment. We will tone down the co-design claim in our manuscript and revise its text accordingly to better clarify the position of our work.

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[W3, Q1] General Controllers across Unseen Shapes

We thank the reviewer for raising this important point. While significant progress has been made in learning a Universal Controller for different rigid robot shapes in terrestrial locomotion tasks (e.g., MetaMorph [5]), transferring this capability to soft-bodied agents in fluid environments introduces substantial new difficulties due to the infinite-dimensional nature of soft-body deformations and complex fluid interactions.

Tackling this infinite-dimensional challenge requires a compact, low-dimensional representation that can jointly encode a soft agent's morphology and its actuation across diverse robot shapes. We believe this is the key to solving the generalization problem. Our work offers a promising approach for the actuation component of this representation. The proposed automated, universal method for defining control points can be applied to general soft-body mesh. This could be combined with established techniques for morphology representation (e.g., graph neural networks or point clouds) to form a complete, universal input for a generalized control policy.

Therefore, while our current work focuses on per-shape training, we see it as providing a promising component needed to develop universal controllers across various shapes in the future.

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[W4] Performance under Disturbance

Thank you for suggesting this study. To address this, we have conducted new experiments to evaluate the robustness of our learned controllers.

We tested robustness in a variant of the 2D trajectory tracking task (see Section 4.3 in supplementary materials for details): a straight-line moving target point guided the fish to a fixed goal while random lateral flow disturbances (width ≈ 0.3 body lengths) were applied. We define the following success rate to measure the swimmer's performance under disturbance and higher success rate indicates the policy is more capable of resisting disturbance: a trial is considered successful if the agent manages to reach the target point (defined as being within a distance of 0.2 units) within the episode's time limit after being disturbed. We conducted 50 independent trials with randomized disturbance positions to ensure a robust evaluation. Across 7 disturbance velocities reported in the table below, success rates remained high at 96% for disturbance velocity as large as 0.067 (c.f. the fish's swimming speed ≈ 0.05) and 68% at 0.1. These results indicate our trained controller's robustness under moderate disturbance.

The current validation was performed on a 2D navigation policy trained in a quiescent fluid environment (see Section 4.3 in supplementary material). We expect that incorporating disturbances directly into the training curriculum, for instance through domain randomization, would likely lead to even greater policy robustness.

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[W5 Q2] Computational Cost and Training Speed

Our simulator achieves frame rates of approximately 70 FPS for 2D morphologies and 30 FPS for 3D morphologies. Given our specified time step and episode duration (detailed in Supplementary Section 3), a single episode completes in approximately 85 seconds for 2D cases and 100 seconds for 3D cases. For comparison, at an equivalent fluid resolution, the DiffMPM-based simulator used in SoftZoo[4], one of the SOTA works on soft swimmers, requires approximately 350 seconds to complete a forward simulation of the same duration for its 3D scenes. As for the training time, a complete training run for one agent, consisting of 75000 environment steps (equivalent to 3 million simulation steps), typically takes 3-4 hours with parallel environments on 8 GPUs.

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[Q3] Reward Function and Weights

Each reward functions has a clear physical motivation:

• The smoothness penalty is the difference of action vectors between adjacent frames, encouraging more continuous actions, a common technique in robotics to reduce jittery motions.
• The action penalty is the norm of the action vector that prevents excessive deformation.

We will add more details on them to our supplementary material.

To determine proper reward weights, we began by tuning the primary task reward to achieve basic locomotion, then incrementally adjusted the regularization weights to refine the emergent gaits—for instance, increasing the smoothness penalty to mitigate jittery movements. This process led us to a set of baseline weights (w_s = -0.02, w_a = -0.01) that produced stable and effective gaits, which we then used consistently across all experiments for fair comparison.

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[Q3] Poor Tuned Reward Weights

Yes, a poorly tuned reward can limit the emergent strategy. Extreme reward weights lead to degenerated, albeit explainable solutions. An excessively high action penalty, for example, teaches the agent to remain nearly stationary, a trivial locomotion strategy that correctly minimizes the action penalty. Such cases are usually straightforward to identify and fix during initial tuning and confirm that the reward terms function as intended.

We are truly grateful for your insightful comments and constructive feedback. We hope that the additional details and experimental results we provided have effectively addressed your concerns. Please feel free to let us know if there are any remaining concerns. We look forward to hearing your thoughts on our rebuttal.

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References:

[1]. Triantafyllou, M. S., Triantafyllou, G. S., & Yue, D. K. (2000). Hydrodynamics of fishlike swimming. Annual review of fluid mechanics, 32(1), 33-53.

[2]. Lin, Z., Hess, A., Yu, Z., Cai, S., & Gao, T. (2019). A fluid–structure interaction study of soft robotic swimmer using a fictitious domain/active-strain method. Journal of Computational Physics, 376, 1138-1155.

[3]. Bhatia, J., Jackson, H., Tian, Y., Xu, J., & Matusik, W. (2021). Evolution gym: A large-scale benchmark for evolving soft robots. Advances in Neural Information Processing Systems, 34, 2201-2214.

[4]. Wang, T. H., Ma, P., Spielberg, A. E., Xian, Z., Zhang, H., Tenenbaum, J. B., ... & Gan, C. (2023). SoftZoo: A Soft Robot Co-design Benchmark For Locomotion In Diverse Environments. In The Eleventh International Conference on Learning Representations.

[5]. Gupta, A., Fan, L., Ganguli, S., & Fei-Fei, L. (2022). MetaMorph: Learning Universal Controllers with Transformers. International Conference on Learning Representations.

Hello,

The last step in the reviewing process is to process the updates from the authors that are key in clearing up final issues to ensure papers get a fair treatment. Please respond to the reviewers ASAP to address any final threads.

• AC

We sincerely thank the reviewer for the insightful and constructive feedback on our manuscript. We found the comments regarding energy efficiency, quantitative biological comparison, the scope of co-design, and sim-to-real transfer to be particularly valuable. These suggestions have helped us to significantly strengthen the evaluation and framing of our work.

[W1] The framework does not seem to optimize or evaluate energy usage. While action magnitudes are regularized, there is no explicit metric to assess or minimize energy consumption. [Q2] Does your method account for or optimize the energetic efficiency of swimming? If not, could your framework be extended to incorporate energy-based objectives ?

We thank the reviewer for raising this point. Energy efficiency is a key performance metric for swimming, and we prepared a new experiment to optimize the energetic efficiency of soft swimmers in our framework. We follow established methodologies from the biomechanics literature [1] and adopt a physically-grounded measure of energy consumption. Our framework is designed such that this energy cost (see table below) can be directly and efficiently calculated at each simulation step. This allows us to incorporate it as a penalty term within the reward function, enabling the training of policies that explicitly optimize for energy efficiency.

To demonstrate that our framework is capable of learning energy-efficient gaits, we have trained policies with different penalty coefficients (w_e) for this energy cost on the 3D clownfish model, which we selected as a representative case study. We believe the findings from this model are indicative of the framework's general capabilities across all our tested morphologies. The results from this experiment are summarized below:

To analyze gait efficiency, we adopted the widely-accepted Cost of Transport (CoT) metric, which normalizes energy consumption by distance traveled (lower is better). Our results demonstrate a clear trade-off between distance and efficiency. As the penalty increases ($0\to 0.005\to 0.02$), the trained policy demonstrates better energetic efficiency of swimming, while an excessive penalty (0.05) correctly produces a near-stationary policy. This validates that our framework robustly optimizes for energy-based objectives in a logical manner, and we believe these results fully address the reviewer's concerns.

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[W2] Claims about the similarity between learned behaviors and evolved biological swimming strategies are based on qualitative visual resemblance only. No quantitative biomechanical comparisons or gait analyses are provided. [Q1] You state that your method discovers swimming strategies “similar to those found in nature.” How do you measure this similarity? Have you considered comparing swimming trajectories or gait metrics with biological data?

Thank you for your question.

Our comparison to biological swimming is indeed primarily qualitative. A direct quantitative analysis presents non-trivial challenges, particularly in acquiring precise biological kinematic data and in bridging the significant sim-to-real gap in matching animal physiology.

We would like to add that our qualitative similarity extends beyond visual resemblance to a more scientific, taxonomy correspondence. Previous biomechanical research has identified several canonical swimming modes in aquatic animals, including undulation (eel), pulsation (jellyfish) and oscillation (paramecium) propulsion [2]. We have confirmed that our fluid-solid simulation can reproduce these three mechanisms.

Our unified framework, without any expert knowledge as input, spontaneously exhibits multiple biological swimming modes across diverse swimmer morphologies during training. The emergence of such diverse behaviors has a biological root and is a non-trivial result, which we largely attribute to the physical fidelity of our simulation. In contrast, prior works in soft swimmer learning have often focused on or exhibited undulation swimming mode only (e.g., DiffAqua [3], which focuses on anguilliform motion). This demonstrates a significant degree of generality in our approach.

We will carefully revise our wording in the manuscript to emphasize that our findings have a qualitative connection to these canonical biological swimming modes, and clarify our similarities with them to better position our work.

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[W3] Despite referencing "co-design," the work only addresses control learning on fixed shapes, and does not co-optimize morphology and control jointly.

Thank you for your comment. Co-designing soft robots is an important emerging topic, yet it faces challenges in scaling to high-fidelity 3D simulations and in developing unified design representations. While existing works have made valuable progress, they often operate within certain constraints, such as simplified 2D design space (e.g., EvoGym [4]) or challenges in efficiently discovering controllers for complex 3D environments (e.g., SoftZoo [5]). Although our work focuses on controller optimization only, the framework we have developed shows a promising sign of tackling both of these challenges, providing a unified control representation within a high-fidelity 3D environment. We will tone down the co-design claim in our manuscript and revise its text accordingly to better clarify the position of our work.

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[Q3] Have you considered deploying these controllers on physical soft robots? What challenges do you anticipate in transferring them from simulation to the real world?

We thank the reviewer for this question. Sim-to-real transfer for soft robots in fluid is a big challenge for the field, requiring a multi-disciplinary effort that extends beyond the scope of a single work like ours. The path to physical deployment of soft robotic swimmers involves at least three significant hurdles, which are shared challenges across the soft robotics community. First, modeling requires non-trivial and probably labor-intensive system identification of physical parameters like fluid viscosity, material stiffness and damping, to narrow the sim-to-real gap. Next, manufacturing introduces issues of consistency and fabrication imperfections, meaning any physical prototype will have variations not present in the idealized digital model. Finally, deployment must contend with real-world complexities such as sensor noise, state estimation errors, and actuation latency. Addressing these challenges constitutes a significant research topic in its own right. Our current work focuses on a critical prerequisite: establishing a robust framework to discover what an optimal policy looks like under idealized conditions. We believe this provides a vital baseline and a clear target for future research dedicated to addressing the well-established challenges of sim-to-real transfer.

We are truly grateful for your insightful comments and constructive feedback. We hope that the additional details and experimental results we provided have effectively addressed your concerns. Please feel free to let us know if there are any remaining concerns. We look forward to hearing your thoughts on our rebuttal.

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References:

[1]. Verma, S., Novati, G., & Koumoutsakos, P. (2018). Efficient collective swimming by harnessing vortices through deep reinforcement learning. Proceedings of the National Academy of Sciences, 115(23), 5849-5854.

[2]. Zhang, D., Zhang, J. D., & Huang, W. X. (2022). Physical models and vortex dynamics of swimming and flying: A review. Acta Mechanica, 233(4), 1249-1288.

[3]. Ma, P., Du, T., Zhang, J. Z., Wu, K., Spielberg, A., Katzschmann, R. K., & Matusik, W. (2021). Diffaqua: A differentiable computational design pipeline for soft underwater swimmers with shape interpolation. ACM Transactions on Graphics (TOG), 40(4), 1-14.

[4]. Bhatia, J., Jackson, H., Tian, Y., Xu, J., & Matusik, W. (2021). Evolution gym: A large-scale benchmark for evolving soft robots. Advances in Neural Information Processing Systems, 34, 2201-2214.

[5]. Wang, T. H., Ma, P., Spielberg, A. E., Xian, Z., Zhang, H., Tenenbaum, J. B., ... & Gan, C. SoftZoo: A Soft Robot Co-design Benchmark For Locomotion In Diverse Environments. In The Eleventh International Conference on Learning Representations.

We sincerely thank you for your recognition of our learning framework and visualizations, as well as your constructive feedback regarding the evaluation metrics and training stability analysis. We address each of the weaknesses and questions raised below.

[W1] The core contributions primarily lie in the modeling of the soft-body and its interaction with fluid dynamics, while the learning approach itself follows established reinforcement learning method. As such, the work may be better suited to other venues.

We thank the reviewer for recognizing our contributions in modeling the soft-body and its interaction with fluid dynamics.

Our work directly addresses the emerging topic of soft robot control in complex physical environments, a subject of growing interest within the learning community (e.g., recent works at NeurIPS [1,2] and ICLR [3]).

While our work builds upon established RL algorithms, we believe our contributions are of direct service to the learning community in the following ways:

• A unified and effective design for low-dimensional control of general soft objects. This enables the learning community to scale up prior research from simple morphologies to a much broader and more expressive class of soft robots.
• A high-fidelity solid-fluid simulator. This provides the community with a challenging new benchmark for developing and testing RL algorithms on more physically realistic swimming behaviors.
• Empirical validation of RL's feasibility for diverse soft swimmers. This result, demonstrating that RL can learn effective gaits for non-traditional soft objects, is a novel and non-trivial finding in itself, opening up new research questions for the community.

In summary, we believe our work is a strong fit for the NeurIPS community, and we hope these contributions will foster further research into this challenging and important domain.

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[W2] The evaluation largely relies on task-specific rewards that may include regularization or smoothing terms, which can obscure direct assessment of locomotion quality. Inclusion of more interpretable and standardized metrics—such as forward swimming speed, displacement over time, or time-to-target—would provide clearer insight into the quantitative effectiveness of the learned policies.

Thank you for the question. We would like to clarify that the normalized reward reported in the tables in our manuscript has excluded all regularization terms, purely reflecting the forward swimming distance achieved within the time limit. For example, the data in Table 1(Section 6.2, Quantitative Results), when divided by 5 (action signal frequency in our experiment), gives the actual movement distance (in meters). Regarding the forward swimming speed metric, as the forward swimming task fixes the time horizon, the speed is in direct proportion to the reported swimming distance (i.e., dividing it by the fixed time horizon). From table1, It can be observed that our optimized swimming strategies have an average speed ranging from 0.1 to 0.3 m/s (the body length of the swimmers is around 1 meter).

For the turning task in our supplementary material, as well as for the two new tasks we added in the rebuttal (energy-efficient swimming and station-keeping), we will add the standardized performance metrics you suggested to the revised manuscript.

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[W3] Given the stochastic nature of reinforcement learning, it is important to report training consistency and stability. However, the manuscript does not specify how many training trials were repeated or whether the final performance is robust across seeds. Including training curves and variance across runs would strengthen the empirical evaluation. [Q2] How many training runs were conducted, and how consistent is the performance across different seeds and across the training.

We fully agree that training stability should be validated given RL's stochasticity. To address this, we conducted additional experiments on the 2D fish morphology. We trained forward swimming policies across 6 random seeds with identical hyperparameters.

We analyzed the intermediate rewards collected at 5%, 15%, 25%, 50% and 100% of training episodes. The results are reported below in the table.

From this data, we draw three key conclusions:

• Consistent Final Performance: The low standard deviation in the final (100%) reward demonstrates that all runs reliably converge to policies of similar high quality (as a reference, the final average speed is about 0.09 m/s, while the standard deviation is only 0.01m/s).
• Stable Learning Trajectory: The consistently low standard deviation at every milestone (25%, 50%, 75%) confirms the learning process itself is stable and reproducible.
• Effective Progress: The monotonic increase in the mean reward across all milestones shows this stable process is also effective at making consistent progress.

Collectively, these quantitative results demonstrate that our training framework is robust, and its performance is consistent and reproducible across different random seeds. We would be happy to provide more evaluations if requested.

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[Q1] What is the simulation frame rate (FPS) achieved for the soft-body fluid-structure simulation?

Thank you for your question regarding the computational cost.

Our system achieves approximately 30 FPS for the 3D scenes presented in the paper, using a single GPU. To provide a concrete example, the clownfish in the forward swimming task (see Fig. 2), which uses a 128x128x512 fluid grid, a fish model comprising 3,543 finite elements, and a time step of 0.005s, runs at an average of 29.9 FPS.

Further details on the simulation parameters can be found in Section 3 of the supplementary material.

We are truly grateful for your insightful comments and constructive feedback. We hope that the additional details and experimental results we provided have effectively addressed your concerns. Please feel free to let us know if there are any remaining concerns. We look forward to hearing your thoughts on our rebuttal.

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References:

[1] Bhatia, J., Jackson, H., Tian, Y., Xu, J., & Matusik, W. (2021). Evolution gym: A large-scale benchmark for evolving soft robots. Advances in Neural Information Processing Systems, 34, 2201-2214.

[2] Wang, T. H. J., Zheng, J., Ma, P., Du, Y., Kim, B., Spielberg, A., ... & Rus, D. (2023). Diffusebot: Breeding soft robots with physics-augmented generative diffusion models. Advances in Neural Information Processing Systems, 36, 44398-44423.

[3] Wang, T. H., Ma, P., Spielberg, A. E., Xian, Z., Zhang, H., Tenenbaum, J. B., ... & Gan, C. SoftZoo: A Soft Robot Co-design Benchmark For Locomotion In Diverse Environments. In The Eleventh International Conference on Learning Representations.

Hello,

The last step in the reviewing process is to process the updates from the authors that are key in clearing up final issues to ensure papers get a fair treatment. Please respond to the reviewers ASAP to address any final threads.

• AC