Related papers: Discover physical concepts and equations with mach…

The search for physics beyond the Standard Model is hindered by a combinatorial explosion of possible theories. We introduce \textsc{Albert}, a neuro-symbolic artificial intelligence framework to systematically navigate this vast theory…

We have developed a new data-driven paradigm for the rapid inference, modeling and simulation of the physics of transport phenomena by deep learning. Using conditional generative adversarial networks (cGAN), we train models for the direct…

Modern power systems require fast and accurate dynamic simulations for stability assessment, digital twins, and real-time control, but classical ODE solvers are often too slow for large-scale or online applications. We propose a…

In recent years, machine learning methods have been used to assist scientists in scientific research. Human scientific theories are based on a series of concepts. How machine learns the concepts from experimental data will be an important…

Humans have a remarkable capacity to understand the physical dynamics of objects in their environment, flexibly capturing complex structures and interactions at multiple levels of detail. Inspired by this ability, we propose a hierarchical…

In this paper, numerical methods using Physics-Informed Neural Networks (PINNs) are presented with the aim to solve higher-order ordinary differential equations (ODEs). Indeed, this deep-learning technique is successfully applied for…

Data-driven algorithms, in particular neural networks, can emulate the effect of sub-grid scale processes in coarse-resolution climate models if trained on high-resolution climate simulations. However, they may violate key physical…

Machine learning methods have found novel application areas in various disciplines as they offer low-computational cost solutions to complex problems. Recently, metasurface design has joined among these applications, and neural networks…

The connection of Taylor maps and polynomial neural networks (PNN) to solve ordinary differential equations (ODEs) numerically is considered. Having the system of ODEs, it is possible to calculate weights of PNN that simulates the dynamics…

Physics-based simulations are often used to model and understand complex physical systems and processes in domains like fluid dynamics. Such simulations, although used frequently, have many limitations which could arise either due to the…

BridgeNet is a novel hybrid framework that integrates convolutional neural networks with physics-informed neural networks to efficiently solve non-linear, high-dimensional Fokker-Planck equations (FPEs). Traditional PINNs, which typically…

First formulated by Sir Isaac Newton in his work "Philosophiae Naturalis Principia Mathematica", the concept of the Three-Body Problem was put forth as a study of the motion of the three celestial bodies within the Earth-Sun-Moon system. In…

Spurred by tremendous success in pattern matching and prediction tasks, researchers increasingly resort to machine learning to aid original scientific discovery. Given large amounts of observational data about a system, can we uncover the…

Physics-informed neural networks (PINNs) represent a new paradigm for solving partial differential equations (PDEs) by integrating physical laws into the learning process of neural networks. However, ensuring that such frameworks fully…

Deep learning has been widely used within learning algorithms for robotics. One disadvantage of deep networks is that these networks are black-box representations. Therefore, the learned approximations ignore the existing knowledge of…

Providing fast and accurate solutions to partial differential equations is a problem of continuous interest to the fields of applied mathematics and physics. With the recent advances in machine learning, the adoption learning techniques in…

In this work, we propose an end-to-end graph network that learns forward and inverse models of particle-based physics using interpretable inductive biases. Physics-informed neural networks are often engineered to solve specific problems…

We revisit the classic signal-to-symbol barrier in light of the remarkable ability of deep neural networks to generate realistic synthetic data. DeepFakes and spoofing highlight the feebleness of the link between physical reality and its…

Maxwell's equations govern light propagation and its interaction with matter. Therefore, the solution of Maxwell's equations using computational electromagnetic simulations plays a critical role in understanding light-matter interaction and…

We introduce conditional PINNs (physics informed neural networks) for estimating the solution of classes of eigenvalue problems. The concept of PINNs is expanded to learn not only the solution of one particular differential equation but the…