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We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function during the optimization…

Machine Learning · Computer Science 2023-04-05 Hubert Baty , Leo Baty

Training in unsupervised time series anomaly detection is constantly plagued by the discrimination between harmful `anomaly contaminations' and beneficial `hard normal samples'. These two samples exhibit analogous loss behavior that…

Machine Learning · Computer Science 2026-03-17 Ruyi Zhang , Hongzuo Xu , Songlei Jian , Yusong Tan , Haifang Zhou , Rulin Xu

Deep learning (DL) relies heavily on data, and the quality of data influences its performance significantly. However, obtaining high-quality, well-annotated datasets can be challenging or even impossible in many real-world applications,…

Machine Learning · Computer Science 2026-01-12 Jinshuai Bai , Laith Alzubaidi , Qingxia Wang , Ellen Kuhl , Mohammed Bennamoun , Yuantong Gu

Data augmentation (DA) is commonly used during model training, as it significantly improves test error and model robustness. DA artificially expands the training set by applying random noise, rotations, crops, or even adversarial…

Machine Learning · Computer Science 2019-05-09 Shashank Rajput , Zhili Feng , Zachary Charles , Po-Ling Loh , Dimitris Papailiopoulos

Neural operators have recently grown in popularity as Partial Differential Equation (PDE) surrogate models. Learning solution functionals, rather than functions, has proven to be a powerful approach to calculate fast, accurate solutions to…

Machine Learning · Computer Science 2024-09-25 Cooper Lorsung , Amir Barati Farimani

Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting…

Computational Physics · Physics 2021-01-06 Kiwon Um , Robert Brand , Yun , Fei , Philipp Holl , Nils Thuerey

We present an end-to-end framework to learn partial differential equations that brings together initial data production, selection of boundary conditions, and the use of physics-informed neural operators to solve partial differential…

Computational Physics · Physics 2023-08-21 Shawn G. Rosofsky , Hani Al Majed , E. A. Huerta

The black-box nature of Convolutional Neural Networks (CNNs) and their reliance on large datasets limit their use in complex domains with limited labeled data. Physics-Guided Neural Networks (PGNNs) have emerged to address these limitations…

Computer Vision and Pattern Recognition · Computer Science 2024-09-04 Kishor Datta Gupta , Marufa Kamal , Rakib Hossain Rifat , Mohd Ariful Haque , Roy George

Physics-guided Neural Networks (PGNNs) represent an emerging class of neural networks that are trained using physics-guided (PG) loss functions (capturing violations in network outputs with known physics), along with the supervision…

The physics solvers employed for neural network training are primarily iterative, and hence, differentiating through them introduces a severe computational burden as iterations grow large. Inspired by works in bilevel optimization, we show…

Machine Learning · Computer Science 2025-11-14 Kanishk Bhatia , Felix Koehler , Nils Thuerey

To improve predictive models for STEM applications, supplemental physics-based features computed from input parameters are introduced into single and multiple layers of a deep neural network (DNN). While many studies focus on informing DNNs…

Emerging Technologies · Computer Science 2024-09-02 Nicholus R. Clinkinbeard , Nicole N. Hashemi

With several advantages and as an alternative to predict physics field, machine learning methods can be classified into two distinct types: data-driven relying on training data and physics-driven using physics law. Choosing heat conduction…

Computational Physics · Physics 2020-05-19 Hao Ma , Xiangyu Hu , Yuxuan Zhang , Nils Thuerey , Oskar J. Haidn

Time-dependent partial differential equations are a significant class of equations that describe the evolution of various physical phenomena over time. One of the open problems in scientific computing is predicting the behaviour of the…

Numerical Analysis · Mathematics 2025-06-30 Zhenyi Zhu , Yuchen Huang , Liu Liu

Deep Learning (DL) methods have emerged as one of the most powerful tools for functional approximation and prediction. While the representation properties of DL have been well studied, uncertainty quantification remains challenging and…

Machine Learning · Statistics 2022-10-25 Yuexi Wang , Nicholas G. Polson , Vadim O. Sokolov

Exploring adversarial attack vectors and studying their effects on machine learning algorithms has been of interest to researchers. Deep neural networks working with time series data have received lesser interest compared to their image…

Machine Learning · Computer Science 2020-09-29 Anindya Sarkar , Anirudh Sunder Raj , Raghu Sesha Iyengar

Data augmentation is a popular technique largely used to enhance the training of convolutional neural networks. Although many of its benefits are well known by deep learning researchers and practitioners, its implicit regularization…

Computer Vision and Pattern Recognition · Computer Science 2019-06-27 Alex Hernández-García , Peter König

Sequential recommender systems have recently achieved significant performance improvements with the exploitation of deep learning (DL) based methods. However, although various DL-based methods have been introduced, most of them only focus…

Information Retrieval · Computer Science 2022-03-29 Joo-yeong Song , Bongwon Suh

Deep Neural Networks are well known for efficiently fitting training data, yet experiencing poor generalization capabilities whenever some kind of bias dominates over the actual task labels, resulting in models learning "shortcuts". In…

Machine Learning · Computer Science 2024-08-12 Pietro Morerio , Ruggero Ragonesi , Vittorio Murino

In this work we propose an extension of physics informed supervised learning strategies to parametric partial differential equations. Indeed, even if the latter are indisputably useful in many applications, they can be computationally…

Machine Learning · Computer Science 2024-01-22 Nicola Demo , Maria Strazzullo , Gianluigi Rozza

Deep neural networks (DNNs) often rely on massive labelled data for training, which is inaccessible in many applications. Data augmentation (DA) tackles data scarcity by creating new labelled data from available ones. Different DA methods…

Neural and Evolutionary Computing · Computer Science 2022-05-31 Binyan Hu , Yu Sun , A. K. Qin
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