Partial differential equations (PDEs) form the mathematical foundation for modeling physical systems in science and engineering, where numerical solutions demand rigorous accuracy-efficiency tradeoffs. Mesh movement techniques address this challenge by dynamically relocating mesh nodes to rapidly-varying regions, enhancing both simulation accuracy and computational efficiency. However, traditional approaches suffer from high computational complexity and geometric inflexibility, limiting their applicability, and existing supervised learning-based approaches face challenges in zero-shot generalization across diverse PDEs and mesh topologies. In this paper, we present an Unsupervised and Generalizable Mesh Movement Network (UGM2N). We first introduce unsupervised mesh adaptation through localized geometric feature learning, eliminating the dependency on pre-adapted meshes. We then develop a physics-constrained loss function, M-Uniform loss, that enforces mesh equidistribution at the nodal level. Experimental results demonstrate that the proposed network exhibits equation-agnostic generalization and geometric independence in efficient mesh adaptation. It demonstrates consistent superiority over existing methods, including robust performance across diverse PDEs and mesh geometries, scalability to multi-scale resolutions and guaranteed error reduction without mesh tangling.

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.

Scientific simulations and experimental measurements produce vast amounts of spatio-temporal data, yet extracting meaningful insights remains challenging due to high dimensionality, complex structures, and missing information. Traditional analysis methods often struggle with these issues, motivating the need for more robust, data-driven approaches. This dissertation explores deep learning methodologies to improve the analysis and visualization of spatio-temporal scientific ensembles, focusing on dimensionality reduction, flow estimation, and temporal interpolation. First, we address high-dimensional data representation through autoencoder-based dimensionality reduction for scientific ensembles. We evaluate the stability of projection metrics under partial labeling and introduce a Pareto-efficient selection strategy to identify optimal autoencoder variants, ensuring expressive and reliable low-dimensional embeddings. Next, we present FLINT, a deep learning model for high-quality flow estimation and temporal interpolation in both flow-supervised and flow-unsupervised settings. FLINT reconstructs missing velocity fields and generates high-fidelity temporal interpolants for scalar fields across 2D+time and 3D+time ensembles without domain-specific assumptions or extensive finetuning. To further improve adaptability and generalization, we introduce HyperFLINT, a hypernetwork-based approach that conditions on simulation parameters to estimate flow fields and interpolate scalar data. This parameter-aware adaptation yields more accurate reconstructions across diverse scientific domains, even with sparse or incomplete data. Overall, this dissertation advances deep learning techniques for scientific visualization, providing scalable, adaptable, and high-quality solutions for interpreting complex spatio-temporal ensembles.

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.