Related papers: Neural Geometry for PDEs: Regularity, Stability, a…

Implicit neural representations (INRs) have been successfully used to compress a variety of 3D surface representations such as Signed Distance Functions (SDFs), voxel grids, and also other forms of structured data such as images, videos,…

Whilst the Universal Approximation Theorem guarantees the existence of approximations to Sobolev functions -- the natural function spaces for PDEs -- by Neural Networks (NNs) of sufficient size, low-regularity solutions may lead to poor…

Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…

While much attention of neural network methods is devoted to high-dimensional PDE problems, in this work we consider methods designed to work for elliptic problems on domains $\Omega \subset \mathbb{R} ^d, $ $d=1,2,3$ in association with…

Implicit neural representations (INRs), which leverage neural networks to represent signals by mapping coordinates to their corresponding attributes, have garnered significant attention. They are extensively utilized for image…

Implicit Neural Representations (INRs) parameterize continuous signals via multilayer perceptrons (MLPs), enabling compact, resolution-independent modeling for tasks like image, audio, and 3D reconstruction. However, fitting high-resolution…

Neural networks have emerged as a powerful tool for modeling physical systems, offering the ability to learn complex representations from limited data while integrating foundational scientific knowledge. In particular, neuro-symbolic…

Impressive progress in 3D shape extraction led to representations that can capture object geometries with high fidelity. In parallel, primitive-based methods seek to represent objects as semantically consistent part arrangements. However,…

Implicit Neural Representations (INRs) have emerged as a transformative paradigm in signal processing and computer vision, excelling in tasks from image reconstruction to 3D shape modeling. Yet their effectiveness is fundamentally limited…

We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…

We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…

Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…

We present a unified convergence theory for gradient-based training of neural network methods for partial differential equations (PDEs), covering both physics-informed neural networks (PINNs) and the Deep Ritz method. For linear PDEs, we…

Physics-informed neural networks (PINNs), owing to their mesh-free nature, offer a powerful approach for solving high-dimensional partial differential equations (PDEs) in complex geometries, including irregular domains. This capability…

Artificial neural networks (ANNs) are powerful tools capable of approximating any arbitrary mathematical function, but their interpretability remains limited, rendering them as black box models. To address this issue, numerous methods have…

Graph Neural Networks (GNN) can capture the geometric properties of neural representations in EEG data. Here we utilise those to study how reinforcement-based motor learning affects neural activity patterns during motor planning, leveraging…

Neural implicit surfaces are a promising tool for geometry processing that represent a solid object as the zero level set of a neural network. Usually trained to approximate a signed distance function of the considered object, these methods…

Reward maximization, safe exploration, and intrinsic motivation are often studied as separate objectives in reinforcement learning (RL). We present a unified geometric framework, that views these goals as instances of a single optimization…

This work addresses the accurate and efficient simulation of physical phenomena governed by parametric Partial Differential Equations (PDEs) characterized by varying boundary conditions, where parametric instances modify not only the…

Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be…