We present a differentiable framework that leverages the Discrete Empirical Interpolation Method (DEIM) for interpretable deep learning and dynamical system analysis. Although DEIM efficiently approximates nonlinear terms in projection-based reduced-order models (POD-ROM), its fixed interpolation points limit the adaptability to complex and time-varying dynamics. To address this limitation, we first develop a differentiable adaptive DEIM formulation for the one-dimensional viscous Burgers equation, which allows neural networks to dynamically select interpolation points in a computationally efficient and physically consistent manner. We then apply DEIM as an interpretable analysis tool for examining the learned dynamics of a pre-trained Neural Ordinary Differential Equation (NODE) on a two-dimensional vortex-merging problem. The DEIM trajectories reveal physically meaningful features in the learned dynamics of NODE and expose its limitations when extrapolating to unseen flow configurations. These findings demonstrate that DEIM can serve not only as a model reduction tool but also as a diagnostic framework for understanding and improving the generalization behavior of neural differential equation models.

Breakthroughs, discoveries, and DIY tips sent every weekday. A pink flamingo is typically associated with a laid back lifestyle, but the way that these leggy birds with big personalities feed is anything but chill. When they dip their curved necks into the water, the birds use their feet, heads, and beaks to create swirling water tornadoes to efficiently group their prey together and slurp up them up. The findings are detailed in a study published this week in the journal Proceedings of the National Academy of Sciences (PNAS). "Flamingos are actually predators, they are actively looking for animals that are moving in the water, and the problem they face is how to concentrate these animals, to pull them together and feed," Victor Ortega Jiménez, a study co-author and biologist specializing in biomechanics at the University of California, Berkeley, said in a statement.

Unmanned aerial vehicles (UAVs) are becoming more commonly used in populated areas, raising concerns about noise pollution generated from their propellers. This study investigates the acoustic performance of unconventional propeller designs, specifically toroidal and uneven-blade spaced propellers, for their potential in reducing psychoacoustic annoyance. Our experimental results show that these designs noticeably reduced acoustic characteristics associated with noise annoyance.

Navigating autonomously in marine environments including dynamic and static obstacles, and strong flow disturbances, such as in high-flow rivers, poses significant challenges for USVs. To address these challenges, we propose a novel methodology that leverages two types of attention: spatial attention, which learns to integrate diverse environmental factors and sensory information into navigation decisions, and temporal attention within a transformer framework to account for the dynamic, continuously changing nature of the environment. We devise MarineFormer, a Trans${\bf \text{former}}$-based navigation policy for dynamic ${\bf \text{Marine}}$ environments, trained end-to-end through reinforcement learning (RL). At its core, MarineFormer uses graph attention to capture spatial information and a transformer architecture to process temporal sequences in an environment that simulates a 2D turbulent marine condition involving multiple static and dynamic obstacles. We extensively evaluate the performance of the proposed method versus the state-of-the-art methods, as well as other classical planners. Our approach outperforms the state-of-the-art by nearly $20\%$ in episode completion success rate and additionally enhances the USV's path length efficiency.

In this paper, we construct a pretraining framework for fluid environment perception, which includes an information compression model and the corresponding pretraining method. We test this framework in a two-cylinder problem through numerical simulation. The results show that after unsupervised pretraining with this framework, the intelligent agent can acquire key features of surrounding fluid environment, thereby adapting more quickly and effectively to subsequent multi-scenario tasks. In our research, these tasks include perceiving the position of the upstream obstacle and actively avoiding shedding vortices in the flow field to achieve drag reduction. Better performance of the pretrained agent is discussed in the sensitivity analysis.

This work presents an approach for the automatic detection of locally turbulent vortices within turbulent 2D flows such as instabilites. First, given a time step of the flow, methods from Topological Data Analysis (TDA) are leveraged to extract the geometry of the vortices. Specifically, the enstrophy of the flow is simplified by topological persistence, and the vortices are extracted by collecting the basins of the simplified enstrophy's Morse complex. Next, the local kinetic energy power spectrum is computed for each vortex. We introduce a set of indicators based on the kinetic energy power spectrum to estimate the correlation between the vortex's behavior and that of an idealized turbulent vortex. Our preliminary experiments show the relevance of these indicators for distinguishing vortices which are turbulent from those which have not yet reached a turbulent state and thus known as laminar.

In a landscape where scientific discovery is increasingly driven by data, the integration of machine learning (ML) with traditional scientific methodologies has emerged as a transformative approach. This paper introduces a novel, data-driven framework that synergizes physics-based priors with advanced ML techniques to address the computational and practical limitations inherent in first-principle-based methods and brute-force machine learning methods. Our framework showcases four algorithms, each embedding a specific physics-based prior tailored to a particular class of nonlinear systems, including separable and nonseparable Hamiltonian systems, hyperbolic partial differential equations, and incompressible fluid dynamics. The intrinsic incorporation of physical laws preserves the system's intrinsic symmetries and conservation laws, ensuring solutions are physically plausible and computationally efficient. The integration of these priors also enhances the expressive power of neural networks, enabling them to capture complex patterns typical in physical phenomena that conventional methods often miss. As a result, our models outperform existing data-driven techniques in terms of prediction accuracy, robustness, and predictive capability, particularly in recognizing features absent from the training set, despite relying on small datasets, short training periods, and small sample sizes.

Abstract--Vortices are studied in various scientific disciplines, offering insights into fluid flow behavior. Visualizing the boundary of vortices is crucial for understanding flow phenomena and detecting flow irregularities. This paper addresses the challenge of accurately extracting vortex boundaries using deep learning techniques. While existing methods primarily train on velocity components, we propose a novel approach incorporating particle trajectories (streamlines or pathlines) into the learning process. By leveraging the regional/local characteristics of the flow field captured by streamlines or pathlines, our methodology aims to enhance the accuracy of vortex boundary extraction. In aerodynamics, researchers focus on studying vortices that form in the wake of an aircraft, aiming to mitigate the creation of vortices with long lifetimes; persistent vortices can potentially impede commercial aviation's operational capacity [1]-[3]. Oceanographers, on the other hand, study mesoscale eddies modeled as vortices, to understand the transportation of nutrients and heat in ocean currents [4]- [6].

Sound can propel a microscopic robot shaped like a piece of pasta through artificial blood vessels, which could eventually lead to a new way of delivering drugs inside the human body. You can feel the sound from a large speaker in your body because the mechanical vibrations of the sound waves penetrate organic tissue. Daniel Ahmed at the Swiss Federal Institute of Technology in Zürich and his colleagues want to use this phenomenon to move a tiny robot inside the human body. The robot looks like a 350-micrometre-long piece of corkscrew-shaped rotini pasta – a design that Ahmed says was inspired by the shape of certain bacteria. The robot does not have any motors or internal power source.

We apply Fourier neural operators (FNOs), a state-of-the-art operator learning technique, to forecast the temporal evolution of experimentally measured velocity fields. FNOs are a recently developed machine learning method capable of approximating solution operators to systems of partial differential equations through data alone. The learned FNO solution operator can be evaluated in milliseconds, potentially enabling faster-than-real-time modeling for predictive flow control in physical systems. Here we use FNOs to predict how physical fluid flows evolve in time, training with particle image velocimetry measurements depicting cylinder wakes in the subcritical vortex shedding regime. We train separate FNOs at Reynolds numbers ranging from Re = 240 to Re = 3060 and study how increasingly turbulent flow phenomena impact prediction accuracy. We focus here on a short prediction horizon of ten non-dimensionalized time-steps, as would be relevant for problems of predictive flow control. We find that FNOs are capable of accurately predicting the evolution of experimental velocity fields throughout the range of Reynolds numbers tested (L2 norm error < 0.1) despite being provided with limited and imperfect flow observations. Given these results, we conclude that this method holds significant potential for real-time predictive flow control of physical systems.