We thank all reviewers for their constructive comments and address the raised issues below. As described in Secion 3.2 of the manuscript, we introduce the The source code, as mentioned on L141, will be made available to the public. R1: Why the adaptive flow filtering is a better way of reducing artifacts? Our method could be seen as a learnable median filter in spirit. Although the quantitative improvement from the adaptive flow filtering (ada.) is small, this component is important in generating results with higher visual quality SepConv has originally been trained on high-quality videos with large motion.

We describe SynthPix, a synthetic image generator for Particle Image Velocimetry (PIV) with a focus on performance and parallelism on accelerators, implemented in JAX. SynthPix supports the same configuration parameters as existing tools but achieves a throughput several orders of magnitude higher in image-pair generation per second. SynthPix was developed to enable the training of data-hungry reinforcement learning methods for flow estimation and for reducing the iteration times during the development of fast flow estimation methods used in recent active fluids control studies with real-time PIV feedback. We believe SynthPix to be useful for the fluid dynamics community, and in this paper we describe the main ideas behind this software package.

For centuries, khalasi (Gujarati for sailor) have skillfully harnessed ocean currents to navigate vast waters with minimal effort. Emulating this intuition in autonomous systems remains a significant challenge, particularly for Autonomous Surface Vehicles tasked with long duration missions under strict energy budgets. In this work, we present a learning-based approach for energy-efficient surface vehicle navigation in vortical flow fields, where partial observability often undermines traditional path-planning methods. We present an end to end reinforcement learning framework based on Soft Actor Critic that learns flow-aware navigation policies using only local velocity measurements. Through extensive evaluation across diverse and dynamically rich scenarios, our method demonstrates substantial energy savings and robust generalization to previously unseen flow conditions, offering a promising path toward long term autonomy in ocean environments. The navigation paths generated by our proposed approach show an improvement in energy conservation 30 to 50 percent compared to the existing state of the art techniques.

This work proposes a method of estimating and using the higher-order information, i.e. acceleration, for optical flow estimation such that the interpolated frames can capture motions more naturally. The idea is interesting and straightforward and I am surprised that no one has done this before. The work is very well presented with sufficient experiments. The SM is well prepared. The flow reversal layer is somehow novel, but it is not very clear what exactly learned by the reversal layer.

Figure 1: (a) Field of view of the blowfly Calliphora vicina mapped onto a panoramic view of an indoor scene. Blue and red borders outline the visual field of the left and right eyes; tinted area denotes area of binocular overlap.

Despite extensive theoretical work on biologically plausible learning rules, clear evidence about whether and how such rules are implemented in the brain has been difficult to obtain.

First, we thank the reviewers for their detailed, constructive, and positive feedback on the paper. Below we address specific feedback from the reviewers. We leave more detailed investigation of this approach to future studies. We thank the reviewer for pointing out the work of V on Funck et al., we will cite We are not claiming that detail is preserved from the input point cloud to the output geometry. We will rephrase L50 to be more accurate.

In this work, we propose a novel flow field-based motion planning method that drives a robot from any initial state to a desired reference trajectory such that it converges to the trajectory's end point. Despite demonstrated efficacy in using Koopman operator theory for modeling dynamical systems, Koopman does not inherently enforce convergence to desired trajectories nor to specified goals - a requirement when learning from demonstrations (LfD). We present KoopMotion which represents motion flow fields as dynamical systems, parameterized by Koopman Operators to mimic desired trajectories, and leverages the divergence properties of the learnt flow fields to obtain smooth motion fields that converge to a desired reference trajectory when a robot is placed away from the desired trajectory, and tracks the trajectory until the end point. To demonstrate the effectiveness of our approach, we show evaluations of KoopMotion on the LASA human handwriting dataset and a 3D manipulator end-effector trajectory dataset, including spectral analysis. We also perform experiments on a physical robot, verifying KoopMotion on a miniature autonomous surface vehicle operating in a non-static fluid flow environment. Our approach is highly sample efficient in both space and time, requiring only 3\% of the LASA dataset to generate dense motion plans. Additionally, KoopMotion provides a significant improvement over baselines when comparing metrics that measure spatial and temporal dynamics modeling efficacy. Code at: \href{https://alicekl.github.io/koop-motion/}{\color{blue}{https://alicekl.github.io/koop-motion}}.