Modeling the evolution of physical systems is critical to many applications in science and engineering. As the evolution of these systems is governed by partial differential equations (PDEs), there are a number of computational simulations which resolve these systems with high accuracy. However, as these simulations incur high computational costs, they are infeasible to be employed for large-scale analysis. A popular alternative to simulators are neural network surrogates which are trained in a data-driven manner and are much more computationally efficient. However, these surrogate models suffer from high rollout error when used autoregressively, especially when confronted with training data paucity. Existing work proposes to improve surrogate rollout error by either including physical loss terms directly in the optimization of the model or incorporating computational simulators as'differentiable layers' in the neural network. Both of these approaches have their challenges, with physical loss functions suffering from slow convergence for stiff PDEs and simulator layers requiring gradients which are not always available, especially in legacy simulators. We propose the Hybrid PDE Predictor with Reinforcement Learning (HyPER) model: a modelagnostic, RL based, cost-aware model which combines a neural surrogate, RL decision model, and a physics simulator (with or without gradients) to reduce surrogate rollout error significantly. In addition to reducing in-distribution rollout error by 47%-78%, HyPER learns an intelligent policy that is adaptable to changing physical conditions and resistant to noise corruption. Scientific simulations have been the workhorse enabling novel discoveries across many scientific disciplines. However, executing fine-grained simulations of a scientific process of interest is a costly undertaking requiring large computational resources and long execution times.

While magnetic micro-robots have demonstrated significant potential across various applications, including drug delivery and microsurgery, the open issue of precise navigation and control in complex fluid environments is crucial for in vivo implementation. This paper introduces a novel flow-aware navigation and control strategy for magnetic micro-robots that explicitly accounts for the impact of fluid flow on their movement. First, the proposed method employs a Physics-Informed U-Net (PI-UNet) to refine the numerically predicted fluid velocity using local observations. Then, the predicted velocity is incorporated in a flow-aware A* path planning algorithm, ensuring efficient navigation while mitigating flow-induced disturbances. Finally, a control scheme is developed to compensate for the predicted fluid velocity, thereby optimizing the micro-robot's performance. A series of simulation studies and real-world experiments are conducted to validate the efficacy of the proposed approach. This method enhances both planning accuracy and control precision, expanding the potential applications of magnetic micro-robots in fluid-affected environments typical of many medical scenarios.

The Physics-Constrained DeepONet (PC-DeepONet), an architecture that incorporates fundamental physics knowledge into the data-driven DeepONet model, is presented in this study. This methodology is exemplified through surrogate modeling of fluid dynamics over a curved backward-facing step, a benchmark problem in computational fluid dynamics. The model was trained on computational fluid dynamics data generated for a range of parameterized geometries. The PC-DeepONet was able to learn the mapping from the parameters describing the geometry to the velocity and pressure fields. While the DeepONet is solely data-driven, the PC-DeepONet imposes the divergence constraint from the continuity equation onto the network. The PC-DeepONet demonstrates higher accuracy than the data-driven baseline, especially when trained on sparse data. Both models attain convergence with a small dataset of 50 samples and require only 50 iterations for convergence, highlighting the efficiency of neural operators in learning the dynamics governed by partial differential equations.

Earthquake detection is essential for earthquake early warning (EEW) systems. Traditional methods struggle with low signal-to-noise ratios and single-station reliance, limiting their effectiveness. We propose a Spatio-Temporal Graph Convolutional Network (GCN) using Spectral Structure Learning Convolution (Spectral SLC) to model static and dynamic relationships across seismic stations. Our approach processes multi-station waveform data and generates station-specific detection probabilities. Experiments show superior performance over a conventional GCN baseline in terms of true positive rate (TPR) and false positive rate (FPR), highlighting its potential for robust multi-station earthquake detection. The code repository for this study is available at https://github.com/SuchanunP/eq_detector.

This research addresses the challenge of performing search missions in dynamic environments, particularly for drifting targets whose movement is dictated by a flow field. This is accomplished through a dynamical system that integrates two partial differential equations: one governing the dynamics and uncertainty of the probability distribution, and the other regulating the potential field for ergodic multi-agent search. The target probability field evolves in response to the target dynamics imposed by the environment and accomplished sensing efforts, while being explored by multiple robot agents guided by the potential field gradient. The proposed methodology was tested on two simulated search scenarios, one of which features a synthetically generated domain and showcases better performance when compared to the baseline method with static target probability over a range of agent to flow field velocity ratios. The second search scenario represents a realistic sea search and rescue mission where the search start is delayed, the search is performed in multiple robot flight missions, and the procedure for target drift uncertainty compensation is demonstrated. Furthermore, the proposed method provides an accurate survey completion metric, based on the known detection/sensing parameters, that correlates with the actual number of targets found independently.

Due to excellent mechanism characteristics of high rigidity, maneuverability and strength-to-weight ratio, 6 Degree-of-Freedom (DoF) Stewart structure is widely adopted to construct flight simulator platforms for replicating motion feelings during training pilots. Unlike conventional serial link manipulator based mechanisms, Upset Prevention and Recovery Training (UPRT) in complex flight status is often accompanied by large speed and violent rate of change in angular velocity of the simulator. However, Classical Washout Filter (CWF) based Motion Cueing Algorithm (MCA) shows limitations in providing rapid response to drive motors to satisfy high accuracy performance requirements. This paper aims at exploiting Model Predictive Control (MPC) based MCA which is proved to be efficient in Hexapod-based motion simulators through controlling over limited linear workspace. With respect to uncertainties and control solution errors from the extraction of Terminal Constraints (COTC), this paper proposes a Switchable Model Predictive Control (S-MPC) based MCA under model adaptive architecture to mitigate the solution uncertainties and inaccuracies. It is verified that high accurate tracking is achievable using the MPC-based MCA with COTC within the simulator operating envelope. The proposed method provides optimal tracking solutions by switching to MPC based MCA without COTC outside the operating envelope. By demonstrating the UPRT with horizontal stall conditions following Average Absolute Scale(AAS) evaluation criteria, the proposed S-MPC based MCA outperforms MPC based MCA and SWF based MCA by 42.34% and 65.30%, respectively.

Understanding the dynamic nature of biological systems is fundamental to deciphering cellular behavior, developmental processes, and disease progression. Single-cell RNA sequencing (scRNA-seq) has provided static snapshots of gene expression, offering valuable insights into cellular states at a single time point. Recent advancements in temporally resolved scRNA-seq, spatial transcriptomics (ST), and time-series spatial transcriptomics (temporal-ST) have further revolutionized our ability to study the spatiotemporal dynamics of individual cells. These technologies, when combined with computational frameworks such as Markov chains, stochastic differential equations (SDEs), and generative models like optimal transport and Schr\"odinger bridges, enable the reconstruction of dynamic cellular trajectories and cell fate decisions. This review discusses how these dynamical system approaches offer new opportunities to model and infer cellular dynamics from a systematic perspective.

Traditional three-dimensional magnetotelluric (MT) numerical forward modeling methods, such as the finite element method (FEM) and finite volume method (FVM), suffer from high computational costs and low efficiency due to limitations in mesh refinement and computational resources. We propose a novel neural network architecture named MTAGU-Net, which integrates an attention gating mechanism for 3D MT forward modeling. Specifically, a dual-path attention gating module is designed based on forward response data images and embedded in the skip connections between the encoder and decoder. This module enables the fusion of critical anomaly information from shallow feature maps during the decoding of deep feature maps, significantly enhancing the network's capability to extract features from anomalous regions. Furthermore, we introduce a synthetic model generation method utilizing 3D Gaussian random field (GRF), which accurately replicates the electrical structures of real-world geological scenarios with high fidelity. Numerical experiments demonstrate that MTAGU-Net outperforms conventional 3D U-Net in terms of convergence stability and prediction accuracy, with the structural similarity index (SSIM) of the forward response data consistently exceeding 0.98. Moreover, the network can accurately predict forward response data on previously unseen datasets models, demonstrating its strong generalization ability and validating the feasibility and effectiveness of this method in practical applications.

We present a large real-world dataset obtained from monitoring a smart company facility over the course of six years, from 2018 to 2023. The dataset includes energy consumption data from various facility areas and components, energy production data from a photovoltaic system and a combined heat and power plant, operational data from heating and cooling systems, and weather data from an on-site weather station. The measurement sensors installed throughout the facility are organized in a hierarchical metering structure with multiple sub-metering levels, which is reflected in the dataset. The dataset contains measurement data from 72 energy meters, 9 heat meters and a weather station. Both raw and processed data at different processing levels, including labeled issues, is available. In this paper, we describe the data acquisition and post-processing employed to create the dataset. The dataset enables the application of a wide range of methods in the domain of energy management, including optimization, modeling, and machine learning to optimize building operations and reduce costs and carbon emissions.

Minimizing response times to meet legal requirements and serve patients in a timely manner is crucial for Emergency Medical Service (EMS) systems. Achieving this goal necessitates optimizing operational decision-making to efficiently manage ambulances. Against this background, we study a centrally controlled EMS system for which we learn an online ambulance dispatching and redeployment policy that aims at minimizing the mean response time of ambulances within the system by dispatching an ambulance upon receiving an emergency call and redeploying it to a waiting location upon the completion of its service. We propose a novel combinatorial optimization-augmented machine learning pipeline that allows to learn efficient policies for ambulance dispatching and redeployment. In this context, we further show how to solve the underlying full-information problem to generate training data and propose an augmentation scheme that improves our pipeline's generalization performance by mitigating a possible distribution mismatch with respect to the considered state space. Compared to existing methods that rely on augmentation during training, our approach offers substantial runtime savings of up to 87.9% while yielding competitive performance. To evaluate the performance of our pipeline against current industry practices, we conduct a numerical case study on the example of San Francisco's 911 call data. Results show that the learned policies outperform the online benchmarks across various resource and demand scenarios, yielding a reduction in mean response time of up to 30%.