Related papers: Lie Point Symmetry Data Augmentation for Neural PD…
Data Augmentation (DA) is a technique to increase the quantity and diversity of the training data, and by that alleviate overfitting and improve generalisation. However, standard DA produces synthetic data for augmentation with limited…
In this paper, we explore and compare multiple solutions to the problem of data augmentation in image classification. Previous work has demonstrated the effectiveness of data augmentation through simple techniques, such as cropping,…
The curse of dimensionality is commonly encountered in numerical partial differential equations (PDE), especially when uncertainties have to be modeled into the equations as random coefficients. However, very often the variability of…
Lithography modeling is a crucial problem in chip design to ensure a chip design mask is manufacturable. It requires rigorous simulations of optical and chemical models that are computationally expensive. Recent developments in machine…
In this work, we propose data-integrated neural networks (DataInNet) for solving partial differential equations (PDEs), offering a novel approach to leveraging data (e.g., source terms, initial conditions, and boundary conditions). The core…
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 has achieved remarkable results in many computer vision tasks. Deep neural networks typically rely on large amounts of training data to avoid overfitting. However, labeled data for real-world applications may be limited. By…
In order to reduce overfitting, neural networks are typically trained with data augmentation, the practice of artificially generating additional training data via label-preserving transformations of existing training examples. While these…
In this paper we show how to augment classical methods for inverse problems with artificial neural networks. The neural network acts as a prior for the coefficient to be estimated from noisy data. Neural networks are global, smooth function…
Data augmentation is a popular technique which helps improve generalization capabilities of deep neural networks. It plays a pivotal role in remote-sensing scenarios in which the amount of high-quality ground truth data is limited, and…
We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral…
A hybrid computational approach that integrates the finite element method (FEM) with least squares support vector regression (LSSVR) is introduced to solve partial differential equations. The method combines FEM's ability to provide the…
High-dimensional partial differential equations (PDEs) pose significant challenges for numerical computation due to the curse of dimensionality, which limits the applicability of traditional mesh-based methods. Since 2017, the Deep BSDE…
Machine learned partial differential equation (PDE) solvers trade the reliability of standard numerical methods for potential gains in accuracy and/or speed. The only way for a solver to guarantee that it outputs the exact solution is to…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
Neural operators effectively solve PDE problems from data without knowing the explicit equations, which learn the map from the input sequences of observed samples to the predicted values. Most existing works build the model in the original…
Deep learning (DL) has become one of the mainstream and effective methods for point cloud analysis tasks such as detection, segmentation and classification. To reduce overfitting during training DL models and improve model performance…
Neural operators have emerged as data-driven surrogates for solving partial differential equations (PDEs), and their success hinges on efficiently modeling the long-range, global coupling among spatial points induced by the underlying…
Verification of Neural Networks (NNs) that approximate the solution of Partial Differential Equations (PDEs) is a major milestone towards enhancing their trustworthiness and accelerating their deployment, especially for safety-critical…
In the rapidly evolving field of large language models (LLMs), data augmentation (DA) has emerged as a pivotal technique for enhancing model performance by diversifying training examples without the need for additional data collection. This…