Recent advances of data-driven machine learning have revolutionized fields like computer vision, reinforcement learning, and many scientific engineering domains. In real-world problems, systems that generate data are governed by physical laws. work shows it provides potential benefits for models incorporating the prior collected data, which makes intersection physics become a prevailing paradigm. By integrating mathematical seamlessly, can guide model towards solutions physically plausible,...

Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning practical applications like the irregular mesh, multiple input functions, and complexity of PDEs' solution. To address these challenges, we propose a general neural operator transformer (GNOT), scalable effective transformer-based framework operators. By designing novel heterogeneous normalized attention layer, our model highly...

With the rapid development of UAV technology, intelligent control systems have become an important factor in improving their stability, efficiency and adaptability. Traditional flight methods limitations when dealing with complex environments dynamic tasks, while models based on artificial intelligence can achieve more efficient autonomous by combining technologies such as deep learning, reinforcement learning fuzzy control. This paper first reviews current research status analyzes...

Pre-training has been investigated to improve the efficiency and performance of training neural operators in data-scarce settings. However, it is largely its infancy due inherent complexity diversity, such as long trajectories, multiple scales varying dimensions partial differential equations (PDEs) data. In this paper, we present a new auto-regressive denoising pre-training strategy, which allows for more stable efficient on PDE data generalizes various downstream tasks. Moreover, by...

While significant progress has been made on Physics-Informed Neural Networks (PINNs), a comprehensive comparison of these methods across wide range Partial Differential Equations (PDEs) is still lacking. This study introduces PINNacle, benchmarking tool designed to fill this gap. PINNacle provides diverse dataset, comprising over 20 distinct PDEs from various domains, including heat conduction, fluid dynamics, biology, and electromagnetics. These encapsulate key challenges inherent...

Physics-informed neural networks (PINNs) have shown promise in solving various partial differential equations (PDEs). However, training pathologies negatively affected the convergence and prediction accuracy of PINNs, which further limits their practical applications. In this paper, we propose to use condition number as a metric diagnose mitigate PINNs. Inspired by classical numerical analysis, where measures sensitivity stability, highlight its pivotal role dynamics We prove theorems reveal...

For partial differential equations on domains of arbitrary shapes, existing works neural operators attempt to learn a mapping from geometries solutions. It often requires large dataset geometry-solution pairs in order obtain sufficiently accurate operator. However, for many industrial applications, e.g., engineering design optimization, it can be prohibitive satisfy the requirement since even single simulation may take hours or days computation. To address this issue, we propose reference...

We present a unified hard-constraint framework for solving geometrically complex PDEs with neural networks, where the most commonly used Dirichlet, Neumann, and Robin boundary conditions (BCs) are considered. Specifically, we first introduce "extra fields" from mixed finite element method to reformulate so as equivalently transform three types of BCs into linear equations. Based on reformulation, derive general solutions analytically, which employed construct an ansatz that automatically...

Reinforcement learning is able to obtain generalized low-level robot policies on diverse robotics datasets in embodied scenarios, and Transformer has been widely used model time-varying features. However, it still suffers from the issues of low data efficiency high inference latency. In this paper, we propose investigate task a new perspective frequency domain. We first observe that energy density domain robot's trajectory mainly concentrated low-frequency part. Then, present Fourier...

Learning a precise robotic grasping policy is crucial for embodied agents operating in complex real-world manipulation tasks. Despite significant advancements, most models still struggle with accurate spatial positioning of objects to be grasped. We first show that this generalization challenge stems primarily from the extensive data requirements adequate understanding. However, collecting such real robots prohibitively expensive, and relying on simulation often leads visual gaps upon...

In the field of clinical dental medicine, Cone Beam Computed Tomography (CBCT) is a useful tool for measurement various dimensions related to oral cavity, including height and thickness. This provides invaluable guidance reference risk assessment in orthodontic treatment, selection treatment plans implant treatment. However, segmentation teeth region from CBCT images daunting task due complex root morphology indistinct boundaries between alveolar bone. Manual annotation area...

Physics-informed Neural Networks (PINNs) have recently achieved remarkable progress in solving Partial Differential Equations (PDEs) various fields by minimizing a weighted sum of PDE loss and boundary loss. However, there are several critical challenges the training PINNs, including lack theoretical frameworks imbalance between In this paper, we present an analysis second-order non-homogeneous PDEs, which classified into three categories applicable to common problems. We also characterize...

Abstract The diagnosis of epilepsy often depends heavily on Magnetic Resonance Imaging (MRI). Unfortunately, the utilization MRI is constrained, due to its expensive price and lengthy operating times. More significantly, certain people with claustrophobia or cardiac pacemakers are not candidates for owing risk harm. Computed tomography (CT) images, in comparison, considerably faster, cheaper, free from same restrictions. As opposed conventional medical imaging synthetic techniques, which...

Abstract To improve the accuracy of tool wear detection, this paper proposes a detection method based on genetic neural network. Firstly, vibration signals during processing are collected, and these preprocessed to eliminate background noise. Then, in addition time-frequency analysis, Ensemble Empirical Mode Decomposition which is more suitable for non-stationary random also applied extract sensitive features from signals. reduce computational complexity network, some minor components can be...

A long-standing goal of reinforcement learning is to acquire agents that can learn on training tasks and generalize well unseen may share a similar dynamic but with different reward functions. The ability across important as it determines an agent's adaptability real-world scenarios where mechanisms might vary. In this work, we first show general world model utilize structures in these help train more generalizable agents. Extending models into the task generalization setting, introduce...

The neural operator has emerged as a powerful tool in learning mappings between function spaces PDEs. However, when faced with real-world physical data, which are often highly non-uniformly distributed, it is challenging to use mesh-based techniques such the FFT. To address this, we introduce Non-Uniform Neural Operator (NUNO), comprehensive framework designed for efficient non-uniform data. Leveraging K-D tree-based domain decomposition, transform data into uniform grids while effectively...

The low-frequency signal of the reflected seismic data contains a wealth information related to fluid mobility attribute, from which reservoir can be extracted so that identified using data. Therefore, in order improve resolution and efficiency, sparsity-based adaptive S-transform is introduced into computation mobility. method has exploited window parameters optimization based on sparsity adaptively control shape against different frequency components, calculating time-frequency...