Related papers: Transolver: A Fast Transformer Solver for PDEs on …

The use of deep learning methods for solving PDEs is a field in full expansion. In particular, Physical Informed Neural Networks, that implement a sampling of the physical domain and use a loss function that penalizes the violation of the…

This paper proposes a novel paradigm for machine learning that moves beyond traditional parameter optimization. Unlike conventional approaches that search for optimal parameters within a fixed geometric space, our core idea is to treat the…

We design a physics-aware auto-encoder to specifically reduce the dimensionality of solutions arising from convection-dominated nonlinear physical systems. Although existing nonlinear manifold learning methods seem to be compelling tools to…

Spatially localized deformation components are very useful for shape analysis and synthesis in 3D geometry processing. Several methods have recently been developed, with an aim to extract intuitive and interpretable deformation components.…

The paper introduces a very simple and fast computation method for high-dimensional integrals to solve high-dimensional Kolmogorov partial differential equations (PDEs). The new machine learning-based method is obtained by solving a…

The efficient solution of discretisations of coupled systems of partial differential equations (PDEs) is at the core of much of numerical simulation. Significant effort has been expended on scalable algorithms to precondition Krylov…

Local feature matching between images remains a challenging task, especially in the presence of significant appearance variations, e.g., extreme viewpoint changes. In this work, we propose DeepMatcher, a deep Transformer-based network built…

Neural networks have shown great potential in accelerating the solution of partial differential equations (PDEs). Recently, there has been a growing interest in introducing physics constraints into training neural PDE solvers to reduce the…

While convolutional neural networks have shown a tremendous impact on various computer vision tasks, they generally demonstrate limitations in explicitly modeling long-range dependencies due to the intrinsic locality of the convolution…

Polygonal meshes have become the standard for discretely approximating 3D shapes, thanks to their efficiency and high flexibility in capturing non-uniform shapes. This non-uniformity, however, leads to irregularity in the mesh structure,…

We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. We demonstrate in…

Fast and accurate solution of time-dependent partial differential equations (PDEs) is of key interest in many research fields including physics, engineering, and biology. Generally, implicit schemes are preferred over the explicit ones for…

The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…

Efficient and stable solution of partial differential equations (PDEs) is central to scientific and engineering applications, yet existing numerical solvers rely heavily on matrix based discretizations, while learning based methods require…

Traditional numerical schemes for simulating fluid flow and transport in porous media can be computationally expensive. Advances in machine learning for scientific computing have the potential to help speed up the simulation time in many…

Tabular data remains a challenging domain for generative models. In particular, the standard Variational Autoencoder (VAE) architecture, typically composed of multilayer perceptrons, struggles to model relationships between features,…

Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high…

Partial differential equations (PDEs) form the mathematical foundation for modeling physical systems in science and engineering, where numerical solutions demand rigorous accuracy-efficiency tradeoffs. Mesh movement techniques address this…

Fast and accurate solutions of time-dependent partial differential equations (PDEs) are of pivotal interest to many research fields, including physics, engineering, and biology. Generally, implicit/semi-implicit schemes are preferred over…

Deep learning-based garment draping has emerged as a promising alternative to traditional Physics-Based Simulation (PBS), yet robust collision handling remains a critical bottleneck. Most existing methods enforce physical validity through…