Related papers: Physics-Informed Neural Networks for Modeling Gala…

This paper proposes a tractable framework to determine key characteristics of non-linear dynamic systems by converting physics-informed neural networks to a mixed integer linear program. Our focus is on power system applications.…

Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…

Enhancing neural networks with knowledge of physical equations has become an efficient way of solving various physics problems, from fluid flow to electromagnetism. Graph neural networks show promise in accurately representing irregularly…

We present a Bayesian machine learning architecture that combines a physically motivated parametrization and an analytic error model for the likelihood with a deep generative model providing a powerful data-driven prior for complex signals.…

Inverse problems arise almost everywhere in science and engineering where we need to infer on a quantity from indirect observation. The cases of medical, biomedical, and industrial imaging systems are the typical examples. A very high…

Inverse problems arise across scientific and engineering domains, where the goal is to infer hidden parameters or physical fields from indirect and noisy observations. Classical approaches, such as variational regularization and Bayesian…

Physics Informed Neural Networks offer a mesh free framework for solving PDEs but are highly sensitive to loss weight selection. We propose two dimensional analysis based weighting schemes, one based on quantifiable terms, and another also…

Foundation models for partial differential equations (PDEs) have emerged as powerful surrogates pre-trained on diverse physical systems, but adapting them to new downstream tasks remains challenging due to limited task-specific data and…

The integration of physics-based knowledge with machine learning models is increasingly shaping the monitoring, diagnostics, and prognostics of electrical transformers. In this two-part series, the first paper introduced the foundations of…

Understanding the time evolution of physical systems is crucial to revealing fundamental characteristics that are hidden in frequency domain. In optical science, high-quality resonance cavities and enhanced interactions with matters are at…

We establish a unified theoretical framework addressing the stability, consistency, and convergence of neural networks under realistic training conditions, specifically, in the presence of non-IID data, geometric constraints, and embedded…

Substitution of well-grounded theoretical models by data-driven predictions is not as simple in engineering and sciences as it is in social and economic fields. Scientific problems suffer most times from paucity of data, while they may…

In this paper, physics-informed neural network models are developed to predict the concentrate gold grade in froth flotation cells. Accurate prediction of concentrate grades is important for the automatic control and optimization of mineral…

Physics-based models of dynamical systems are often used to study engineering and environmental systems. Despite their extensive use, these models have several well-known limitations due to simplified representations of the physical…

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…

The application of deep learning toward discovery of data-driven models requires careful application of inductive biases to obtain a description of physics which is both accurate and robust. We present here a framework for discovering…

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…

Modeling the dynamics of real-world physical systems is critical for spatiotemporal prediction tasks, but challenging when data is limited. The scarcity of real-world data and the difficulty in reproducing the data distribution hinder…

Data-driven learning approaches for physics simulation, sometimes referred to as world models, have emerged as promising alternatives to traditional physics simulators due to their differentiable nature. Prior work has demonstrated…

Unveiling the underlying governing equations of nonlinear dynamic systems remains a significant challenge. Insufficient prior knowledge hinders the determination of an accurate candidate library, while noisy observations lead to imprecise…