Related papers: PID-GAN: A GAN Framework based on a Physics-inform…

This short note describes the concept of guided training of deep neural networks (DNNs) to learn physically reasonable solutions. DNNs are being widely used to predict phenomena in physics and mechanics. One of the issues of DNNs is that…

System Identification (SysID) is crucial for modeling and understanding dynamical systems using experimental data. While traditional SysID methods emphasize linear models, their inability to fully capture nonlinear dynamics has driven the…

Subsurface seismic velocity structure is essential for earthquake source studies, including hypocenter determination. Conventional hypocenter determination methods ignore the inherent uncertainty in seismic velocity structure models, and…

Uncertainty quantification (UQ) in machine learning is currently drawing increasing research interest, driven by the rapid deployment of deep neural networks across different fields, such as computer vision, natural language processing, and…

We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to learning and discovery in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN,…

We developed a new class of physics-informed generative adversarial networks (PI-GANs) to solve in a unified manner forward, inverse and mixed stochastic problems based on a limited number of scattered measurements. Unlike standard GANs…

Physics-informed machine learning (PIML) integrates mechanistic knowledge, typically in the form of partial differential equations (PDE), into data-driven models. Despite strong empirical performance, its statistical generalisation…

Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…

We present a new category of physics-informed neural networks called physics informed variational embedding generative adversarial network (PI-VEGAN), that effectively tackles the forward, inverse, and mixed problems of stochastic…

Motivation: Despite its great success in various physical modeling, differential geometry (DG) has rarely been devised as a versatile tool for analyzing large, diverse and complex molecular and biomolecular datasets due to the limited…

Quantifying and propagating modeling uncertainties is crucial for reliability analysis, robust optimization, and other model-based algorithmic processes in engineering design and control. Now, physics-informed machine learning (PIML)…

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…

Emerging deep-learning (DL)-based techniques have significant potential to revolutionize biomedical imaging. However, one outstanding challenge is the lack of reliability assessment in the DL predictions, whose errors are commonly revealed…

Uncertainty quantification (UQ) is crucial for deploying machine learning models in high-stakes applications, where overconfident predictions can lead to serious consequences. An effective UQ method must balance computational efficiency…

Generative adversarial network (GAN) has been shown to be useful in various applications, such as image recognition, text processing and scientific computing, due its strong ability to learn complex data distributions. In this study, a…

Big-data-based artificial intelligence (AI) supports profound evolution in almost all of science and technology. However, modeling and forecasting multi-physical systems remain a challenge due to unavoidable data scarcity and noise.…

Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, solving high-fidelity PDEs remains…

In recent years, Scientific Machine Learning (SciML) methods for solving partial differential equations (PDEs) have gained increasing popularity. Within such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep learning…

Equations, particularly differential equations, are fundamental for understanding natural phenomena and predicting complex dynamics across various scientific and engineering disciplines. However, the governing equations for many complex…

Physics-informed neural networks have proven to be a powerful tool for solving differential equations, leveraging the principles of physics to inform the learning process. However, traditional deep neural networks often face challenges in…