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Many physical and engineering systems require solving direct problems to predict behavior and inverse problems to determine unknown parameters from measurement. In this work, we study both aspects for systems governed by differential…

Numerical Analysis · Mathematics 2026-03-04 Noura Al Helwani , Sophie Moufawad , Georges Sakr

We develop improved physics-informed neural networks (PINNs) for high-order and high-dimensional power system models described by nonlinear ordinary differential equations. We propose some novel enhancements to improve PINN training and…

Machine Learning · Computer Science 2024-10-11 Vineet Jagadeesan Nair

Quantum Fisher Information (QFI) sets the ultimate precision limit for parameter estimation and is therefore a central quantity in quantum metrology. In time-dependent many-body systems, however, maximizing QFI is a highly non-trivial task…

Data-driven discovery of governing equations in computational science has emerged as a new paradigm for obtaining accurate physical models and as a possible alternative to theoretical derivations. The recently developed physics-informed…

Machine Learning · Computer Science 2023-10-18 Zongren Zou , Xuhui Meng , George Em Karniadakis

The recent explosion of machine learning (ML) and artificial intelligence (AI) shows great potential in the breakthrough of metal additive manufacturing (AM) process modeling. However, the success of conventional machine learning tools in…

Computational Engineering, Finance, and Science · Computer Science 2020-09-17 Qiming Zhu , Zeliang Liu , Jinhui Yan

Scientific machine learning (SciML) represents a significant advancement in integrating machine learning (ML) with scientific methodologies. At the forefront of this development are Physics-Informed Neural Networks (PINNs), which offer a…

Machine Learning · Computer Science 2024-11-19 Reyhaneh Taj

Tracer-kinetic models allow for the quantification of kinetic parameters such as blood flow from dynamic contrast-enhanced magnetic resonance (MR) images. Fitting the observed data with multi-compartment exchange models is desirable, as…

Image and Video Processing · Electrical Eng. & Systems 2022-04-08 Rudolf L. M. van Herten , Amedeo Chiribiri , Marcel Breeuwer , Mitko Veta , Cian M. Scannell

We enhance machine learning algorithms for learning model parameters in complex systems represented by ordinary differential equations (ODEs) with domain decomposition methods. The study evaluates the performance of two approaches, namely…

Numerical Analysis · Mathematics 2024-10-03 Tirtho S. Saha , Alexander Heinlein , Cordula Reisch

Real-time prediction of the dynamics of energetic electrons in Earth's radiation belts incorporating incomplete observation data is important to protect valuable artificial satellites and to understand their physical processes.…

Space Physics · Physics 2021-11-15 Enrico Camporeale , George J. Wilkie , Alexander Drozdov , Jacob Bortnik

System-level condition monitoring methods estimate the electrical parameters of multiple components in a converter to assess their health status. The estimation accuracy and variation can differ significantly across parameters. For…

Signal Processing · Electrical Eng. & Systems 2025-04-30 Shuyu Ou , Subham Sahoo , Ariya Sangwongwanich , Frede Blaabjerg , Mahyar Hassanifar , Martin Votava , Marius Langwasser , Marco Liserre

Epidemic propagation on networks represents an important departure from traditional massaction models. However, the high-dimensionality of the exact models poses a challenge to both mathematical analysis and parameter inference. By using…

Quantitative Methods · Quantitative Biology 2023-02-07 István Z. Kiss , Luc Berthouze , Wasiur R. KhudaBukhsh

In this study, the capabilities of the Physics-Informed Neural Network (PINN) method are investigated for three major tasks: modeling, simulation, and optimization in the context of the heat conduction problem. In the modeling phase, the…

Computational Physics · Physics 2025-10-31 Ehsan Ghaderi , Mohamad Ali Bijarchi , Siamak Kazemzadeh Hannani , Ali Nouri Boroujerdi

This article introduces Perception-Informed Neural Networks (PrINNs), a framework designed to incorporate perception-based information into neural networks, addressing both systems with known and unknown physics laws or differential…

Machine Learning · Computer Science 2025-05-27 Mehran Mazandarani , Marzieh Najariyan

Pharmacometric models are pivotal across drug discovery and development, playing a decisive role in determining the progression of candidate molecules. However, the derivation of mathematical equations governing the system is a…

Machine Learning · Computer Science 2024-05-02 Imran Nasim , Adam Nasim

Varying power-infeed from converter-based generation units introduces great uncertainty on system parameters such as inertia and damping. As a consequence, system operators face increasing challenges in performing dynamic security…

Systems and Control · Electrical Eng. & Systems 2021-04-16 Jochen Stiasny , George S. Misyris , Spyros Chatzivasileiadis

Demographic forecasting remains a fundamental challenge for policy planning in rapidly evolving nations such as India, where fertility transitions, policy interventions, and age structured dynamics interact in complex ways. In this study,…

Machine Learning · Computer Science 2025-12-02 Subarna Khanra , Vijay Kumar Kukreja , Indu Bala

Physics-informed neural networks (PINNs) impose known physical laws into the learning of deep neural networks, making sure they respect the physics of the process while decreasing the demand of labeled data. For systems represented by…

Physics-informed neural networks (PINNs) are a promising approach that combines the power of neural networks with the interpretability of physical modeling. PINNs have shown good practical performance in solving partial differential…

Statistics Theory · Mathematics 2026-01-26 Nathan Doumèche , Gérard Biau , Claire Boyer

Physics-informed neural networks (PINNs) is an emerging category of neural networks which can be trained to solve supervised learning tasks while taking into consideration given laws of physics described by general nonlinear partial…

Cryptography and Security · Computer Science 2026-04-07 Solon Falas , Charalambos Konstantinou , Maria K. Michael

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical laws into neural network training. However, traditional PINN models are typically designed…

Machine Learning · Computer Science 2025-05-05 Keon Vin Park
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