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The rise of deep learning challenges the longstanding scientific ideal of insight - the human capacity to understand phenomena by uncovering underlying mechanisms. In many modern applications, accurate predictions no longer require…

Computational Physics · Physics 2025-06-05 Jean-Michel Tucny , Mihir Durve , Sauro Succi

This paper reviews recent studies in understanding neural-network representations and learning neural networks with interpretable/disentangled middle-layer representations. Although deep neural networks have exhibited superior performance…

Computer Vision and Pattern Recognition · Computer Science 2018-02-08 Quanshi Zhang , Song-Chun Zhu

Mechanistic Interpretability (MI) promises a path toward fully understanding how neural networks make their predictions. Prior work demonstrates that even when trained to perform simple arithmetic, models can implement a variety of…

Machine Learning · Computer Science 2024-05-28 Ouail Kitouni , Niklas Nolte , Víctor Samuel Pérez-Díaz , Sokratis Trifinopoulos , Mike Williams

To tackle increasingly complex tasks, it has become an essential ability of neural networks to learn abstract representations. These task-specific representations and, particularly, the invariances they capture turn neural networks into…

Computer Vision and Pattern Recognition · Computer Science 2020-08-06 Robin Rombach , Patrick Esser , Björn Ommer

While most modern machine learning methods offer speed and accuracy, few promise interpretability or explainability -- two key features necessary for highly sensitive industries, like medicine, finance, and engineering. Using eight datasets…

Machine Learning · Computer Science 2025-04-08 Nataly R. Panczyk , Omer F. Erdem , Majdi I. Radaideh

Physics-Informed Neural Networks (PINNs) present a transformative approach for smart grid modeling by integrating physical laws directly into learning frameworks, addressing critical challenges of data scarcity and physical consistency in…

Machine Learning · Computer Science 2025-09-01 Julen Cestero , Carmine Delle Femine , Kenji S. Muro , Marco Quartulli , Marcello Restelli

Physics-informed neural networks (PINNs) have emerged as a versatile and widely applicable concept across various science and engineering domains over the past decade. This article offers a comprehensive overview of the fundamentals of…

Computational Engineering, Finance, and Science · Computer Science 2024-10-02 Sai Ganga , Ziya Uddin

The rapid evolution of machine learning (ML) has led to the widespread adoption of complex "black box" models, such as deep neural networks and ensemble methods. These models exhibit exceptional predictive performance, making them…

Machine Learning · Computer Science 2025-03-28 Moncef Garouani , Josiane Mothe , Ayah Barhrhouj , Julien Aligon

Physics-informed neural networks (PINNs) have earned high expectations in solving partial differential equations (PDEs), but their optimization usually faces thorny challenges due to the unique derivative-dependent loss function. By…

Machine Learning · Computer Science 2025-05-20 Haixu Wu , Yuezhou Ma , Hang Zhou , Huikun Weng , Jianmin Wang , Mingsheng Long

We propose Gradient Informed Neural Networks (GradINNs), a methodology inspired by Physics Informed Neural Networks (PINNs) that can be used to efficiently approximate a wide range of physical systems for which the underlying governing…

Machine Learning · Computer Science 2024-09-04 Filippo Aglietti , Francesco Della Santa , Andrea Piano , Virginia Aglietti

Deep neural networks have been well-known for their superb handling of various machine learning and artificial intelligence tasks. However, due to their over-parameterized black-box nature, it is often difficult to understand the prediction…

Machine Learning · Computer Science 2022-07-18 Xuhong Li , Haoyi Xiong , Xingjian Li , Xuanyu Wu , Xiao Zhang , Ji Liu , Jiang Bian , Dejing Dou

The importance of explainability in AI has become a pressing concern, for which several explainable AI (XAI) approaches have been recently proposed. However, most of the available XAI techniques are post-hoc methods, which however may be…

Machine Learning · Computer Science 2022-04-15 Leonardo Lucio Custode , Giovanni Iacca

Physics-informed neural networks (PINNs) have been popularized as a deep learning framework that can seamlessly synthesize observational data and partial differential equation (PDE) constraints. Their practical effectiveness however can be…

Machine Learning · Computer Science 2023-08-17 Sifan Wang , Shyam Sankaran , Hanwen Wang , Paris Perdikaris

Deep learning as represented by the artificial deep neural networks (DNNs) has achieved great success in many important areas that deal with text, images, videos, graphs, and so on. However, the black-box nature of DNNs has become one of…

Machine Learning · Computer Science 2021-09-29 Fenglei Fan , Jinjun Xiong , Mengzhou Li , Ge Wang

Neural networks have greatly boosted performance in computer vision by learning powerful representations of input data. The drawback of end-to-end training for maximal overall performance are black-box models whose hidden representations…

Computer Vision and Pattern Recognition · Computer Science 2020-04-29 Patrick Esser , Robin Rombach , Björn Ommer

Differential equations are indispensable to engineering and hence to innovation. In recent years, physics-informed neural networks (PINN) have emerged as a novel method for solving differential equations. PINN method has the advantage of…

Computational Engineering, Finance, and Science · Computer Science 2022-01-07 Mayank Raj , Pramod Kumbhar , Ratna Kumar Annabattula

We propose a self-supervised physics-informed neural network (PINN) framework that adaptively balances physics-based and data-driven supervision for scientific machine learning under data scarcity. Unlike prior PINNs that rely on fixed or…

Machine Learning · Computer Science 2026-05-08 Reza Pirayeshshirazinezhad

Deep neural networks (DNNs) are known as black-box models. In other words, it is difficult to interpret the internal state of the model. Improving the interpretability of DNNs is one of the hot research topics. However, at present, the…

Machine Learning · Computer Science 2019-09-17 Masanari Kimura , Masayuki Tanaka

The lack of interpretability has hindered the large-scale adoption of AI technologies. However, the fundamental idea of interpretability, as well as how to put it into practice, remains unclear. We provide notions of interpretability based…

Machine Learning · Computer Science 2021-11-18 Hangcheng Dong , Bingguo Liu , Fengdong Chen , Dong Ye , Guodong Liu

Interpretability has emerged as a crucial aspect of building trust in machine learning systems, aimed at providing insights into the working of complex neural networks that are otherwise opaque to a user. There are a plethora of existing…

Machine Learning · Statistics 2021-01-19 Rushil Anirudh , Jayaraman J. Thiagarajan , Rahul Sridhar , Peer-Timo Bremer