Related papers: Generalization Limits of In-Context Operator Netwo…

Some autoregressive models exhibit in-context learning capabilities: being able to learn as an input sequence is processed, without undergoing any parameter changes, and without being explicitly trained to do so. The origins of this…

The presence of occlusions has provided substantial challenges to typically-powerful object recognition algorithms. Additional sources of information can be extremely valuable to reduce errors caused by occlusions. Scene context is known to…

Large Language Models (LLMs) have demonstrated the ability to solve complex tasks through In-Context Learning (ICL), where models learn from a few input-output pairs without explicit fine-tuning. In this paper, we explore the capacity of…

Physics-informed neural networks (PINNs) have become a popular choice for solving high-dimensional partial differential equations (PDEs) due to their excellent approximation power and generalization ability. Recently, Extended PINNs…

Many problems in computer vision require dealing with sparse, unordered data in the form of point clouds. Permutation-equivariant networks have become a popular solution-they operate on individual data points with simple perceptrons and…

We propose PO-CKAN, a physics-informed deep operator framework based on Chunkwise Rational Kolmogorov--Arnold Networks (KANs), for approximating the solution operators of partial differential equations. This framework leverages a Deep…

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…

Operator learning enables fast surrogate modeling of high-dimensional dynamical systems, but existing approaches face two fundamental limitations: quadratic inference complexity and unreliable uncertainty quantification in safety-critical…

A novel multi-scale operator for unorganized 3D point clouds is introduced. The Difference of Normals (DoN) provides a computationally efficient, multi-scale approach to processing large unorganized 3D point clouds. The application of DoN…

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…

As the field of representation learning grows, there has been a proliferation of different loss functions to solve different classes of problems. We introduce a single information-theoretic equation that generalizes a large collection of…

We propose Graph-Coupled Oscillator Networks (GraphCON), a novel framework for deep learning on graphs. It is based on discretizations of a second-order system of ordinary differential equations (ODEs), which model a network of nonlinear…

This article explores operator learning models that can deduce solutions to partial differential equations (PDEs) on arbitrary domains without requiring retraining. We introduce two innovative models rooted in boundary integral equations…

Partial differential equations (PDEs) serve as the cornerstone of mathematical physics. In recent years, Physics-Informed Neural Networks (PINNs) have significantly reduced the dependence on large datasets by embedding physical laws…

Neural operator learning models have emerged as very effective surrogates in data-driven methods for partial differential equations (PDEs) across different applications from computational science and engineering. Such operator learning…

Performing data augmentation for learning deep neural networks is well known to be important for training visual recognition systems. By artificially increasing the number of training examples, it helps reducing overfitting and improves…

This paper introduces Strict Partial Order Networks (SPON), a novel neural network architecture designed to enforce asymmetry and transitive properties as soft constraints. We apply it to induce hypernymy relations by training with is-a…

Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…

The recently-introduced class of ordinary differential equation networks (ODE-Nets) establishes a fruitful connection between deep learning and dynamical systems. In this work, we reconsider formulations of the weights as…

Deep operator networks (DeepONets, DONs) offer a distinct advantage over traditional neural networks in their ability to be trained on multi-resolution data. This property becomes especially relevant in real-world scenarios where…