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We introduce Structure Informed Neural Networks (SINNs), a novel method for solving boundary observation problems involving PDEs. The SINN methodology is a data-driven framework for creating approximate solutions to internal variables on…

Fluid Dynamics · Physics 2023-10-31 Jakub Horsky , Andrew Wynn

Biologically-informed neural networks (BINNs), an extension of physics-informed neural networks [1], are introduced and used to discover the underlying dynamics of biological systems from sparse experimental data. In the present work, BINNs…

Quantitative Methods · Quantitative Biology 2021-01-27 John H. Lagergren , John T. Nardini , Ruth E. Baker , Matthew J. Simpson , Kevin B. Flores

Though neural networks trained on large datasets have been successfully used to describe and predict many physical phenomena, there is a sense among scientists that, unlike traditional scientific models comprising simple mathematical…

Machine Learning · Computer Science 2026-04-23 Conor Rowan , Alireza Doostan

There is a growing consensus that solutions to complex science and engineering problems require novel methodologies that are able to integrate traditional physics-based modeling approaches with state-of-the-art machine learning (ML)…

Computational Physics · Physics 2022-03-15 Jared Willard , Xiaowei Jia , Shaoming Xu , Michael Steinbach , Vipin Kumar

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

In this paper, we review the new method Physics-Informed Neural Networks (PINNs) that has become the main pillar in scientific machine learning, we present recent practical extensions, and provide a specific example in data-driven discovery…

Machine Learning · Computer Science 2024-09-02 Maziar Raissi , Paris Perdikaris , Nazanin Ahmadi , George Em Karniadakis

Numerical modeling errors are unavoidable in finite element analysis. The presence of model errors inherently reflects both model accuracy and uncertainty. To date there have been few methods for explicitly quantifying errors at points of…

Machine Learning · Computer Science 2024-11-19 Bozhou Zhuang , Sashank Rana , Brandon Jones , Danny Smyl

Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems for partial differential equations. This article aims to…

Numerical Analysis · Mathematics 2024-11-20 Tim De Ryck , Siddhartha Mishra

Discovering the unknown governing equations of grid-connected inverters from external measurements holds significant attraction for analyzing modern inverter-intensive power systems. However, existing methods struggle to balance the…

Systems and Control · Electrical Eng. & Systems 2026-02-19 Jialin Zheng , Ruhaan Batta , Zhong Liu , Xiaonan Lu

Despite their ubiquity, the rich physics present in a plasma sheath has inhibited the development of a generally applicable description of this critical region. The present study utilizes a physics-informed neural network (PINN) to evaluate…

Plasma Physics · Physics 2026-04-27 Ethan Webb , Yuzhi Li , Christopher McDevitt

Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g.,…

Machine Learning · Computer Science 2024-10-22 Hamid El Bahja , Jan Christian Hauffen , Peter Jung , Bubacarr Bah , Issa Karambal

Ground-motion model (GMM) is the basis of many earthquake engineering studies. In this study, a novel physics-informed symbolic learner (PISL) method based on the Nest Generation Attenuation-West2 database is proposed to automatically…

Machine Learning · Computer Science 2023-03-27 Su Chen , Xianwei Liu , Lei Fu , Suyang Wang , Bin Zhang , Xiaojun Li

Methods: This work introduces a method supporting the collaborative definition of machine learning tasks by leveraging model-based engineering in the formalization of the systems modeling language SysML. The method supports the…

Software Engineering · Computer Science 2023-07-11 Simon Raedler , Juergen Mangler , Stefanie Rinderle-Ma

We develop Structured-Knowledge-Informed Neural Networks (SKINNs), a unified estimation framework that embeds theoretical, simulated, previously learned, or cross-domain insights as differentiable constraints within flexible neural function…

Machine Learning · Statistics 2026-04-02 Yi Cao , Zexun Chen , Lin William Cong , Heqing Shi

Physics-informed neural networks (PINNs) offer a powerful framework for seismic wavefield modeling, yet they typically require time-consuming retraining when applied to different velocity models. Moreover, their training can suffer from…

Geophysics · Physics 2025-06-03 Shijun Cheng , Tariq Alkhalifah

Spiking Neural Networks (SNNs) as Machine Learning (ML) models have recently received a lot of attention as a potentially more energy-efficient alternative to conventional Artificial Neural Networks. The non-differentiability and sparsity…

Machine Learning · Computer Science 2025-12-05 Maximilian Gollwitzer , Felix Dietrich

Simulation-Grounded Neural Networks (SGNNs) are predictive models trained entirely on synthetic data from mechanistic simulations. They have achieved state-of-the-art performance in domains where real-world labels are limited or unobserved,…

Machine Learning · Computer Science 2025-10-03 Carson Dudley , Marisa Eisenberg

Machine learning techniques have emerged as powerful tools to tackle various challenges. The integration of machine learning methods with Physics has led to innovative approaches in understanding, controlling, and simulating physical…

Physics Education · Physics 2025-05-20 G. Café de Miranda , Gubio G. de Lima , Tiago de S. Farias

For economic and efficiency reasons, blended acquisition of seismic data is becoming more and more commonplace. Seismic deblending methods are always computationally demanding and normally consist of multiple processing steps. Besides, the…

In scientific machine learning (SciML), a key challenge is learning unknown, evolving physical processes and making predictions across spatio-temporal scales. For example, in real-world manufacturing problems like additive manufacturing,…

Machine Learning · Computer Science 2025-06-16 Vispi Karkaria , Doksoo Lee , Yi-Ping Chen , Yue Yu , Wei Chen
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