Related papers: Physics-Informed Deep Learning: A Promising Techni…

We present a deep learning framework for quantifying and propagating uncertainty in systems governed by non-linear differential equations using physics-informed neural networks. Specifically, we employ latent variable models to construct…

Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are sample efficient, and interpretable but often rely on rigid assumptions. Furthermore, direct numerical approximation…

This paper presents a simulation free framework for solving reliability analysis problems. The method proposed is rooted in a recently developed deep learning approach, referred to as the physics-informed neural network. The primary idea is…

This document is a hands-on, comprehensive guide to deep learning in the realm of physical simulations. Rather than just theory, we emphasize practical application: every concept is paired with interactive Jupyter notebooks to get you up…

The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge. Such constraints are often imposed as soft penalties…

In the context of aircraft system performance assessment, deep learning technologies allow to quickly infer models from experimental measurements, with less detailed system knowledge than usually required by physics-based modeling. However,…

We consider the use of Deep Learning methods for modeling complex phenomena like those occurring in natural physical processes. With the large amount of data gathered on these phenomena the data intensive paradigm could begin to challenge…

For many systems in science and engineering, the governing differential equation is either not known or known in an approximate sense. Analyses and design of such systems are governed by data collected from the field and/or laboratory…

Increasingly sophisticated mathematical modelling processes from Machine Learning are being used to analyse complex data. However, the performance and explainability of these models within practical critical systems requires a rigorous and…

Deep learning is a topic of considerable current interest. The availability of massive data collections and powerful software resources has led to an impressive amount of results in many application areas that reveal essential but hidden…

Combining physics with machine learning models has advanced the performance of machine learning models in many different applications. In this paper, we evaluate adding a weak physics constraint, i.e., a physics-based empirical…

Physics-informed neural networks have emerged as an alternative method for solving partial differential equations. However, for complex problems, the training of such networks can still require high-fidelity data which can be expensive to…

Recent advances of data-driven machine learning have revolutionized fields like computer vision, reinforcement learning, and many scientific and engineering domains. In many real-world and scientific problems, systems that generate data are…

We explore the possibility to use physics-informed neural networks to drastically accelerate the solution of ordinary differential-algebraic equations that govern the power system dynamics. When it comes to transient stability assessment,…

Whilst the partial differential equations that govern the dynamics of our world have been studied in great depth for centuries, solving them for complex, high-dimensional conditions and domains still presents an incredibly large…

Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take…

This tutorial paper focuses on safe physics-informed machine learning in the context of dynamics and control, providing a comprehensive overview of how to integrate physical models and safety guarantees. As machine learning techniques…

This paper presents a novel physics-informed diffusion model for generating synthetic net load data, addressing the challenges of data scarcity and privacy concerns. The proposed framework embeds physical models within denoising networks,…

Deep learning (DL) relies heavily on data, and the quality of data influences its performance significantly. However, obtaining high-quality, well-annotated datasets can be challenging or even impossible in many real-world applications,…

Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to address two…