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Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…

Numerical Analysis · Mathematics 2020-06-16 Chengping Rao , Hao Sun , Yang Liu

In this paper, an innovative Physical Model-driven Neural Network (PMNN) method is proposed to solve time-fractional differential equations. It establishes a temporal iteration scheme based on physical model-driven neural networks which…

Machine Learning · Computer Science 2023-10-10 Zhiying Ma , Jie Hou , Wenhao Zhu , Yaxin Peng , Ying Li

Physics-constrained neural networks are commonly employed to enhance prediction robustness compared to purely data-driven models, achieved through the inclusion of physical constraint losses during the model training process. However, one…

Machine Learning · Computer Science 2024-02-06 Hao Zhou , Sibo Cheng , Rossella Arcucci

Physics-informed neural networks (PINNs) constitute a flexible approach to both finding solutions and identifying parameters of partial differential equations. Most works on the topic assume noiseless data, or data contaminated with weak…

Machine Learning · Statistics 2024-06-21 Philipp Pilar , Niklas Wahlström

Parkinson's disease (PD) is a neurological disorder requiring early and accurate diagnosis for effective management. Machine learning (ML) has emerged as a powerful tool to enhance PD classification and diagnostic accuracy, particularly by…

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

Machine Learning · Computer Science 2022-01-31 Pu Ren , Chengping Rao , Yang Liu , Jianxun Wang , Hao Sun

In practical scenarios involving the measurement of surface electromyography (sEMG) in muscles, particularly those areas near the heart, one of the primary sources of contamination is the presence of electrocardiogram (ECG) signals. To…

Signal Processing · Electrical Eng. & Systems 2024-06-14 Cho-Yuan Lee , Kuan-Chen Wang , Kai-Chun Liu , Yu-Te Wang , Xugang Lu , Ping-Cheng Yeh , Yu Tsao

Accurate computational modeling of damage and fracture remains a central challenge in solid mechanics. The finite element method (FEM) is widely used for numerical modeling of fracture problems; however, classical damage models without…

Soft Condensed Matter · Physics 2025-11-07 Aditya Konale , Vikas Srivastava

The potential of learned models for fundamental scientific research and discovery is drawing increasing attention worldwide. Physics-informed neural networks (PINNs), where the loss function directly embeds governing equations of scientific…

Neural and Evolutionary Computing · Computer Science 2023-12-07 Nicholas Sung Wei Yong , Jian Cheng Wong , Pao-Hsiung Chiu , Abhishek Gupta , Chinchun Ooi , Yew-Soon Ong

When investigating epidemic dynamics through differential models, the parameters needed to understand the phenomenon and to simulate forecast scenarios require a delicate calibration phase, often made even more challenging by the scarcity…

Numerical Analysis · Mathematics 2023-09-11 Giulia Bertaglia , Chuan Lu , Lorenzo Pareschi , Xueyu Zhu

Physics-informed machine learning (PIML) has emerged as a promising new approach for simulating complex physical and biological systems that are governed by complex multiscale processes for which some data are also available. In some…

Machine Learning · Computer Science 2022-05-18 Khemraj Shukla , Mengjia Xu , Nathaniel Trask , George Em Karniadakis

Magnetoencephalography (MEG) and Electroencephalography (EEG) source estimates have thus far mostly been derived sample by sample, i.e., independent of each other in time. However, neuronal assemblies are heavily interconnected,…

Quantitative Methods · Quantitative Biology 2019-09-09 Christoph Dinh , John GW Samuelsson , Alexander Hunold , Matti S Hämäläinen , Sheraz Khan

Wearable health devices have a strong demand in real-time biomedical signal processing. However traditional methods often require data transmission to centralized processing unit with substantial computational resources after collecting it…

Signal Processing · Electrical Eng. & Systems 2025-11-07 Yuqi Ding , Elisa Donati , Haobo Li , Hadi Heidari

Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…

Numerical Analysis · Mathematics 2025-07-10 Dimitrios Gazoulis , Ioannis Gkanis , Charalambos G. Makridakis

Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…

Neural and Evolutionary Computing · Computer Science 2019-12-03 E. Kharazmi , Z. Zhang , G. E. Karniadakis

Physics-Informed Neural Networks (PINNs) have aroused great attention for its ability to address forward and inverse problems of partial differential equations. However, approximating discontinuous functions by neural networks poses a…

Computational Engineering, Finance, and Science · Computer Science 2024-09-10 Luyang Zhao , Qian Shao

Subject motion in whole-body dynamic PET introduces inter-frame mismatch and seriously impacts parametric imaging. Traditional non-rigid registration methods are generally computationally intense and time-consuming. Deep learning approaches…

Image and Video Processing · Electrical Eng. & Systems 2022-06-29 Xueqi Guo , Bo Zhou , David Pigg , Bruce Spottiswoode , Michael E. Casey , Chi Liu , Nicha C. Dvornek

Real-time, physically-consistent predictions on low-power edge devices is critical for the next generation embodied AI systems, yet it remains a major challenge. Physics-Informed Neural Networks (PINNs) combine data-driven learning with…

Machine Learning · Computer Science 2025-12-01 Chi Zhang , Lin Wang

Soft robots can revolutionize several applications with high demands on dexterity and safety. When operating these systems, real-time estimation and control require fast and accurate models. However, prediction with first-principles (FP)…

There has been an increasing interest in integrating physics knowledge and machine learning for modeling dynamical systems. However, very limited studies have been conducted on seismic wave modeling tasks. A critical challenge is that these…

Geophysics · Physics 2022-11-03 Pu Ren , Chengping Rao , Su Chen , Jian-Xun Wang , Hao Sun , Yang Liu