Fish use their lateral lines to sense flows and pressure gradients, enabling them to detect nearby objects and organisms. Towards replicating this capability, we demonstrated successful leader-follower formation swimming using flow pressure sensing in our undulatory robotic fish ($\mu$Bot/MUBot). The follower $\mu$Bot is equipped at its head with bilateral pressure sensors to detect signals excited by both its own and the leader's movements. First, using experiments with static formations between an undulating leader and a stationary follower, we determined the formation that resulted in strong pressure variations measured by the follower. This formation was then selected as the desired formation in free swimming for obtaining an expert policy. Next, a long short-term memory neural network was used as the control policy that maps the pressure signals along with the robot motor commands and the Euler angles (measured by the onboard IMU) to the steering command. The policy was trained to imitate the expert policy using behavior cloning and Dataset Aggregation (DAgger). The results show that with merely two bilateral pressure sensors and less than one hour of training data, the follower effectively tracked the leader within distances of up to 200 mm (= 1 body length) while swimming at speeds of 155 mm/s (= 0.8 body lengths/s). This work highlights the potential of fish-inspired robots to effectively navigate fluid environments and achieve formation swimming through the use of flow pressure feedback.

Using machine learning (ML) to construct interatomic interactions and thus potential energy surface (PES) has become a common strategy for materials design and simulations. However, those current models of machine learning interatomic potential (MLIP) provide no relevant physical constrains, and thus may owe intrinsic out-of-domain difficulty which underlies the challenges of model generalizability and physical scalability. Here, by incorporating physics-informed Universal-Scaling law and nonlinearity-embedded interaction function, we develop a Super-linear MLIP with both Ultra-Small parameterization and greatly expanded expressive capability, named SUS2-MLIP. Due to the global scaling rooting in universal equation of state (UEOS), SUS2-MLIP not only has significantly-reduced parameters by decoupling the element space from coordinate space, but also naturally outcomes the out-of-domain difficulty and endows the potentials with inherent generalizability and scalability even with relatively small training dataset. The nonlinearity-enbeding transformation for interaction function expands the expressive capability and make the potentials super-linear. The SUS2-MLIP outperforms the state-of-the-art MLIP models with its exceptional computational efficiency especially for multiple-element materials and physical scalability in property prediction. This work not only presents a highly-efficient universal MLIP model but also sheds light on incorporating physical constraints into artificial-intelligence-aided materials simulation.

This paper proposes a Curriculum-Transfer-Learning based physics-informed neural network (CTL-PINN) for long-term simulation of physical and mechanical behaviors. The main innovation of CTL-PINN lies in decomposing long-term problems into a sequence of short-term subproblems. Initially, the standard PINN is employed to solve the first sub-problem. As the simulation progresses, subsequent time-domain problems are addressed using a curriculum learning approach that integrates information from previous steps. Furthermore, transfer learning techniques are incorporated, allowing the model to effectively utilize prior training data and solve sequential time domain transfer problems. CTL-PINN combines the strengths of curriculum learning and transfer learning, overcoming the limitations of standard PINNs, such as local optimization issues, and addressing the inaccuracies over extended time domains encountered in CL-PINN and the low computational efficiency of TL-PINN. The efficacy and robustness of CTL-PINN are demonstrated through applications to nonlinear wave propagation, Kirchhoff plate dynamic response, and the hydrodynamic model of the Three Gorges Reservoir Area, showcasing its superior capability in addressing long-term computational challenges.

Sampling from unnormalized densities is a fundamental task across various domains. Flow-based samplers generate samples by learning a velocity field that satisfies the continuity equation, but this requires estimating the intractable time derivative of the partition function. While importance sampling provides an approximation, it suffers from high variance. To mitigate this, we introduce a velocity-driven Sequential Monte Carlo method combined with control variates to reduce variance. Additionally, we incorporate a shortcut model to improve efficiency by minimizing the number of sampling steps. Empirical results on both synthetic datasets and $n$-body system targets validate the effectiveness of our approach.

Imagination in world models is crucial for enabling agents to learn long-horizon policy in a sample-efficient manner. Existing recurrent state-space model (RSSM)-based world models depend on single-step statistical inference to capture the environment dynamics, and, hence, they are unable to perform long-term imagination tasks due to the accumulation of prediction errors. Inspired by the dual-process theory of human cognition, we propose a novel dual-mind world model (DMWM) framework that integrates logical reasoning to enable imagination with logical consistency. DMWM is composed of two components: an RSSM-based System 1 (RSSM-S1) component that handles state transitions in an intuitive manner and a logic-integrated neural network-based System 2 (LINN-S2) component that guides the imagination process through hierarchical deep logical reasoning. The inter-system feedback mechanism is designed to ensure that the imagination process follows the logical rules of the real environment. The proposed framework is evaluated on benchmark tasks that require long-term planning from the DMControl suite. Extensive experimental results demonstrate that the proposed framework yields significant improvements in terms of logical coherence, trial efficiency, data efficiency and long-term imagination over the state-of-the-art world models.

Multi-robot systems are essential for environmental monitoring, particularly for tracking spatial phenomena like pollution, soil minerals, and water salinity, and more. This study addresses the challenge of deploying a multi-robot team for optimal coverage in environments where the density distribution, describing areas of interest, is unknown and changes over time. We propose a fully distributed control strategy that uses Gaussian Processes (GPs) to model the spatial field and balance the trade-off between learning the field and optimally covering it. Unlike existing approaches, we address a more realistic scenario by handling time-varying spatial fields, where the exploration-exploitation trade-off is dynamically adjusted over time. Each robot operates locally, using only its own collected data and the information shared by the neighboring robots. To address the computational limits of GPs, the algorithm efficiently manages the volume of data by selecting only the most relevant samples for the process estimation. The performance of the proposed algorithm is evaluated through several simulations and experiments, incorporating real-world data phenomena to validate its effectiveness.

We consider the problem of approximating a $d \times d$ covariance matrix $M$ with a rank-$k$ matrix under $(\varepsilon,\delta)$-differential privacy. We present and analyze a complex variant of the Gaussian mechanism and obtain upper bounds on the Frobenius norm of the difference between the matrix output by this mechanism and the best rank-$k$ approximation to $M$. Our analysis provides improvements over previous bounds, particularly when the spectrum of $M$ satisfies natural structural assumptions. The novel insight is to view the addition of Gaussian noise to a matrix as a continuous-time matrix Brownian motion. This viewpoint allows us to track the evolution of eigenvalues and eigenvectors of the matrix, which are governed by stochastic differential equations discovered by Dyson. These equations enable us to upper bound the Frobenius distance between the best rank-$k$ approximation of $M$ and that of a Gaussian perturbation of $M$ as an integral that involves inverse eigenvalue gaps of the stochastically evolving matrix, as opposed to a sum of perturbation bounds obtained via Davis-Kahan-type theorems. Subsequently, again using the Dyson Brownian motion viewpoint, we show that the eigenvalues of the matrix $M$ perturbed by Gaussian noise have large gaps with high probability. These results also contribute to the analysis of low-rank approximations under average-case perturbations, and to an understanding of eigenvalue gaps for random matrices, both of which may be of independent interest.

The focus of our work is improving the interpretability of anomalies in climate models and advancing our understanding of Arctic melt dynamics. The Arctic and Antarctic ice sheets are experiencing rapid surface melting and increased freshwater runoff, contributing significantly to global sea level rise. Understanding the mechanisms driving snowmelt in these regions is crucial. ERA5, a widely used reanalysis dataset in polar climate studies, offers extensive climate variables and global data assimilation. However, its snowmelt model employs an energy imbalance approach that may oversimplify the complexity of surface melt. In contrast, the Glacier Energy and Mass Balance (GEMB) model incorporates additional physical processes, such as snow accumulation, firn densification, and meltwater percolation/refreezing, providing a more detailed representation of surface melt dynamics. In this research, we focus on analyzing surface snowmelt dynamics of the Greenland Ice Sheet using feature attribution for anomalous melt events in ERA5 and GEMB models. We present a novel unsupervised attribution method leveraging counterfactual explanation method to analyze detected anomalies in ERA5 and GEMB. Our anomaly detection results are validated using MEaSUREs ground-truth data, and the attributions are evaluated against established feature ranking methods, including XGBoost, Shapley values, and Random Forest. Our attribution framework identifies the physics behind each model and the climate features driving melt anomalies. These findings demonstrate the utility of our attribution method in enhancing the interpretability of anomalies in climate models and advancing our understanding of Arctic melt dynamics.

Global leaders and policymakers are unified in their unequivocal commitment to decarbonization efforts in support of Net-Zero agreements. District Heating Systems (DHS), while contributing to carbon emissions due to the continued reliance on fossil fuels for heat production, are embracing more sustainable practices albeit with some sense of vulnerability as it could constrain their ability to adapt to dynamic demand and production scenarios. As demographic demands grow and renewables become the central strategy in decarbonizing the heating sector, the need for accurate demand forecasting has intensified. Advances in digitization have paved the way for Machine Learning (ML) based solutions to become the industry standard for modeling complex time series patterns. In this paper, we focus on building a Deep Learning (DL) model that uses deconstructed components of independent and dependent variables that affect heat demand as features to perform multi-step ahead forecasting of head demand. The model represents the input features in a time-frequency space and uses an attention mechanism to generate accurate forecasts. The proposed method is evaluated on a real-world dataset and the forecasting performance is assessed against LSTM and CNN-based forecasting models. Across different supply zones, the attention-based models outperforms the baselines quantitatively and qualitatively, with an Mean Absolute Error (MAE) of 0.105 with a standard deviation of 0.06kW h and a Mean Absolute Percentage Error (MAPE) of 5.4% with a standard deviation of 2.8%, in comparison the second best model with a MAE of 0.10 with a standard deviation of 0.06kW h and a MAPE of 5.6% with a standard deviation of 3%.

Modeling and simulation of complex fluid flows with dynamics that span multiple spatio-temporal scales is a fundamental challenge in many scientific and engineering domains. Full-scale resolving simulations for systems such as highly turbulent flows are not feasible in the foreseeable future, and reduced-order models must capture dynamics that involve interactions across scales. In the present work, we propose a novel framework, Graph-based Learning of Effective Dynamics (Graph-LED), that leverages graph neural networks (GNNs), as well as an attention-based autoregressive model, to extract the effective dynamics from a small amount of simulation data. GNNs represent flow fields on unstructured meshes as graphs and effectively handle complex geometries and non-uniform grids. The proposed method combines a GNN based, dimensionality reduction for variable-size unstructured meshes with an autoregressive temporal attention model that can learn temporal dependencies automatically. We evaluated the proposed approach on a suite of fluid dynamics problems, including flow past a cylinder and flow over a backward-facing step over a range of Reynolds numbers. The results demonstrate robust and effective forecasting of spatio-temporal physics; in the case of the flow past a cylinder, both small-scale effects that occur close to the cylinder as well as its wake are accurately captured.