Accurately modeling complex dynamic spatio-temporal systems requires capturing flow-mediated interdependencies and context-sensitive interaction dynamics. Existing methods, predominantly graph-based or attention-driven, rely on similarity-driven connectivity assumptions, neglecting asymmetric flow exchanges that govern system evolution. We propose Spatio-Temporal Flow, a physics-inspired paradigm that explicitly models dynamic node couplings through quantifiable flow transfers governed by conservation principles. Building on this, we design FlowNet, a novel architecture leveraging flow tokens as information carriers to simulate source-to-destination transfers via Flow Allocation Modules, ensuring state redistribution aligns with conservation laws. FlowNet dynamically adjusts the interaction radius through an Adaptive Spatial Masking module, suppressing irrelevant noise while enabling context-aware propagation. A cascaded architecture enhances scalability and nonlinear representation capacity. Experiments demonstrate that FlowNet significantly outperforms existing state-of-the-art approaches on seven metrics in the modeling of three real-world systems, validating its efficiency and physical interpretability. We establish a principled methodology for modeling complex systems through spatio-temporal flow interactions.

We thank all reviewers for their efforts and positive comments. To Review #1: Thank you for the comments and we will follow the suggestions to do more experiments and analyses. To Review #2: Thank you very much for confirming our contributions. Q1) [Strong priors]: "geometry-consistency" is not a manually designed prior for specific scenes. Our contribution is more deeply leveraging SfM theory in unsupervised depth learning.

Power flow estimation plays a vital role in ensuring the stability and reliability of electrical power systems, particularly in the context of growing network complexities and renewable energy integration. However, existing studies often fail to adequately address the unique characteristics of power systems, such as the sparsity of network connections and the critical importance of the unique Slack node, which poses significant challenges in achieving high-accuracy estimations. In this paper, we present SenseFlow, a novel physics-informed and self-ensembling iterative framework that integrates two main designs, the Physics-Informed Power Flow Network (FlowNet) and Self-Ensembling Iterative Estimation (SeIter), to carefully address the unique properties of the power system and thereby enhance the power flow estimation. Specifically, SenseFlow enforces the FlowNet to gradually predict high-precision voltage magnitudes and phase angles through the iterative SeIter process. On the one hand, FlowNet employs the Virtual Node Attention and Slack-Gated Feed-Forward modules to facilitate efficient global-local communication in the face of network sparsity and amplify the influence of the Slack node on angle predictions, respectively. On the other hand, SeIter maintains an exponential moving average of FlowNet's parameters to create a robust ensemble model that refines power state predictions throughout the iterative fitting process. Experimental results demonstrate that SenseFlow outperforms existing methods, providing a promising solution for high-accuracy power flow estimation across diverse grid configurations.

We present a hybrid machine learning and flow analysis feature detection method, RipViz, to extract rip currents from stationary videos. Rip currents are dangerous strong currents that can drag beachgoers out to sea. Most people are either unaware of them or do not know what they look like. In some instances, even trained personnel such as lifeguards have difficulty identifying them. RipViz produces a simple, easy to understand visualization of rip location overlaid on the source video. With RipViz, we first obtain an unsteady 2D vector field from the stationary video using optical flow. Movement at each pixel is analyzed over time. At each seed point, sequences of short pathlines, rather a single long pathline, are traced across the frames of the video to better capture the quasi-periodic flow behavior of wave activity. Because of the motion on the beach, the surf zone, and the surrounding areas, these pathlines may still appear very cluttered and incomprehensible. Furthermore, lay audiences are not familiar with pathlines and may not know how to interpret them. To address this, we treat rip currents as a flow anomaly in an otherwise normal flow. To learn about the normal flow behavior, we train an LSTM autoencoder with pathline sequences from normal ocean, foreground, and background movements. During test time, we use the trained LSTM autoencoder to detect anomalous pathlines (i.e., those in the rip zone). The origination points of such anomalous pathlines, over the course of the video, are then presented as points within the rip zone. RipViz is fully automated and does not require user input. Feedback from domain expert suggests that RipViz has the potential for wider use.

Convolutional Neural Networks (CNNs) constitute a class of Deep Learning models which have been used in the recent past to resolve many problems in computer vision, in particular optical flow estimation. Measuring displacement and strain fields can be regarded as a particular case of this problem. However, it seems that CNNs have never been used so far to perform such measurements. This work is aimed at implementing a CNN able to retrieve displacement and strain fields from pairs of reference and deformed images of a flat speckled surface, as Digital Image Correlation (DIC) does. This paper explains how a CNN called StrainNet can be developed to reach this goal, and how specific ground truth datasets are elaborated to train this CNN. The main result is that StrainNet successfully performs such measurements, and that it achieves competing results in terms of metrological performance and computing time. The conclusion is that CNNs like StrainNet offer a viable alternative to DIC, especially for real-time applications.

Generating a long, coherent text such as a paragraph requires a high-level control of different levels of relations between sentences (e.g., tense, coreference). We call such a logical connection between sentences as a (paragraph) flow. In order to produce a coherent flow of text, we explore two forms of intersentential relations in a paragraph: one is a human-created linguistical relation that forms a structure (e.g., discourse tree) and the other is a relation from latent representation learned from the sentences themselves. Our two proposed models incorporate each form of relations into document-level language models: the former is a supervised model that jointly learns a language model as well as discourse relation prediction, and the latter is an unsupervised model that is hierarchically conditioned by a recurrent neural network (RNN) over the latent information. Our proposed models with both forms of relations outperform the baselines in partially conditioned paragraph generation task. Our codes and data are publicly available.

Even though probabilistic treatments of neural networks have a long history, they have not found widespread use in practice. Sampling approaches are often too slow already for simple networks. The size of the inputs and the depth of typical CNN architectures in computer vision only compound this problem. Uncertainty in neural networks has thus been largely ignored in practice, despite the fact that it may provide important information about the reliability of predictions and the inner workings of the network. In this paper, we introduce two lightweight approaches to making supervised learning with probabilistic deep networks practical: First, we suggest probabilistic output layers for classification and regression that require only minimal changes to existing networks. Second, we employ assumed density filtering and show that activation uncertainties can be propagated in a practical fashion through the entire network, again with minor changes. Both probabilistic networks retain the predictive power of the deterministic counterpart, but yield uncertainties that correlate well with the empirical error induced by their predictions. Moreover, the robustness to adversarial examples is significantly increased.

In the era of end-to-end deep learning, many advances in computer vision are driven by large amounts of labeled data. In the optical flow setting, however, obtaining dense per-pixel ground truth for real scenes is difficult and thus such data is rare. Therefore, recent end-to-end convolutional networks for optical flow rely on synthetic datasets for supervision, but the domain mismatch between training and test scenarios continues to be a challenge. Inspired by classical energy-based optical flow methods, we design an unsupervised loss based on occlusion-aware bidirectional flow estimation and the robust census transform to circumvent the need for ground truth flow. On the KITTI benchmarks, our unsupervised approach outperforms previous unsupervised deep networks by a large margin, and is even more accurate than similar supervised methods trained on synthetic datasets alone. By optionally fine-tuning on the KITTI training data, our method achieves competitive optical flow accuracy on the KITTI 2012 and 2015 benchmarks, thus in addition enabling generic pre-training of supervised networks for datasets with limited amounts of ground truth.

Recent work has shown that optical flow estimation can be formulated as a supervised learning problem. Moreover, convolutional networks have been successfully applied to this task. However, supervised flow learning is obfuscated by the shortage of labeled training data. As a consequence, existing methods have to turn to large synthetic datasets for easily computer generated ground truth. In this work, we explore if a deep network for flow estimation can be trained without supervision. Using image warping by the estimated flow, we devise a simple yet effective unsupervised method for learning optical flow, by directly minimizing photometric consistency. We demonstrate that a flow network can be trained from end-to-end using our unsupervised scheme. In some cases, our results come tantalizingly close to the performance of methods trained with full supervision.