Related papers: Adaptive Coordinate Transforms for Neural Operator…

Point cloud processing has become a cornerstone technology in many 3D vision tasks. However, arbitrary rotations introduce variations in point cloud orientations, posing a long-standing challenge for effective representation learning. The…

While Transformers have demonstrated remarkable potential in modeling Partial Differential Equations (PDEs), modeling large-scale unstructured meshes with complex geometries remains a significant challenge. Existing efficient architectures…

Machine learning has become increasingly popular for efficiently modelling the dynamics of complex physical systems, demonstrating a capability to learn effective models for dynamics which ignore redundant degrees of freedom. Learned…

The point cloud learning community witnesses a modeling shift from CNNs to Transformers, where pure Transformer architectures have achieved top accuracy on the major learning benchmarks. However, existing point Transformers are…

Partial differential equations (PDEs) govern diverse physical phenomena, yet high-fidelity numerical solutions are computationally expensive and Machine Learning approaches lack generalization. While Scientific Foundation Models (SFMs) aim…

The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations. Despite the existence of many operator learning algorithms to…

Recently, the fundamental problem of unsupervised domain adaptation (UDA) on 3D point clouds has been motivated by a wide variety of applications in robotics, virtual reality, and scene understanding, to name a few. The point cloud data…

Existing neural operator architectures face challenges when solving multiphysics problems with coupled partial differential equations (PDEs) due to complex geometries, interactions between physical variables, and the limited amounts of…

Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input…

In this article we extend the adaptive cross approximation (ACA) method known for the efficient approximation of discretisations of integral operators to a block-adaptive version. While ACA is usually employed to assemble hierarchical…

Adversarial training has been proven to be an effective technique for improving the adversarial robustness of models. However, there seems to be an inherent trade-off between optimizing the model for accuracy and robustness. To this end, we…

Machine learning approaches for solving partial differential equations require learning mappings between function spaces. While convolutional or graph neural networks are constrained to discretized functions, neural operators present a…

Precise arbitrary trajectory tracking for quadrotors is challenging due to unknown nonlinear dynamics, trajectory infeasibility, and actuation limits. To tackle these challenges, we present Deep Adaptive Trajectory Tracking (DATT), a…

Physics-Informed Neural Networks (PINNs), which incorporate PDEs as soft constraints, train with a composite loss function that contains multiple training point types: different types of collocation points chosen during training to enforce…

Learning PDE dynamics with neural solvers can significantly improve wall-clock efficiency and accuracy compared with classical numerical solvers. In recent years, foundation models for PDEs have largely adopted multi-scale windowed…

Vision Transformers (ViTs) partition input images into uniformly sized patches regardless of their content, resulting in long input sequence lengths for high-resolution images. We present Adaptive Patch Transformers (APT), which addresses…

In this paper, we propose a new adaptive technique, named adaptive trajectories sampling (ATS), which is used to select training points for the numerical solution of partial differential equations (PDEs) with deep learning methods. The key…

A computed approximation of the solution operator to a system of partial differential equations (PDEs) is needed in various areas of science and engineering. Neural operators have been shown to be quite effective at predicting these…

Transformer with self-attention has led to the revolutionizing of natural language processing field, and recently inspires the emergence of Transformer-style architecture design with competitive results in numerous computer vision tasks.…

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…