Related papers: Physics-Informed Neural Networks and Neural Operat…
Solving inverse problems in dynamical systems governed by high-dimensional coupled ordinary differential equations (ODEs) is a ubiquitous challenge in scientific machine learning. In many real-world applications, researchers seek to uncover…
Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…
Mathematical models in neural networks are powerful tools for solving complex differential equations and optimizing their parameters; that is, solving the forward and inverse problems, respectively. A forward problem predicts the output of…
Physics-Informed Neural Networks (PINNs) are a new family of numerical methods, based on deep learning, for modeling boundary value problems. They offer an advantage over traditional numerical methods for high-dimensional, parametric, and…
Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed…
The importance and cost of time-domain simulations when studying power systems have exponentially increased in the last decades. With the growing share of renewable energy sources, the slow and predictable responses from large turbines are…
Physics-informed neural networks (PINNs) have emerged as a promising deep learning method, capable of solving forward and inverse problems governed by differential equations. Despite their recent advance, it is widely acknowledged that…
This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…
Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…
Physics-informed neural networks (PINNs) are a versatile tool in the burgeoning field of scientific machine learning for solving partial differential equations (PDEs). However, determining suitable training strategies for them is not…
We present a unified theoretical framework for analyzing the stability and consistency of Physics-Informed Neural Networks (PINNs), grounded in operator coercivity, variational formulations, and non-asymptotic perturbation theory. PINNs…
Physics-informed neural networks (PINNs) have proven to be a promising method for the rapid solving of partial differential equations (PDEs) in both forward and inverse problems. However, due to the smoothness assumption of functions…
Engineering design problems often involve solving parametric Partial Differential Equations (PDEs) under variable PDE parameters and domain geometry. Recently, neural operators have shown promise in learning PDE operators and quickly…
Physics-informed neural networks (PINNs) have recently emerged as a prominent paradigm for solving partial differential equations (PDEs), yet their training strategies remain underexplored. While hard prioritization methods inspired by…
Solving partial differential equations (PDE) is an indispensable part of many branches of science as many processes can be modelled in terms of PDEs. However, recent numerical solvers require manual discretization of the underlying equation…
Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…
Learning the full family of solutions to parameterized partial differential equations (PDEs) is a central challenge to our ability to model the behavior of heterogeneous systems, with a variety of fundamental and application-oriented…
Modelling complex multiphysics systems governed by nonlinear and strongly coupled partial differential equations (PDEs) is a cornerstone in computational science and engineering. However, it remains a formidable challenge for traditional…
Inverse problems involving differential equations often require identifying unknown parameters or functions from data. Existing approaches, such as Physics-Informed Neural Networks (PINNs), Universal Differential Equations (UDEs) and…
Physics Informed Neural Networks (PINNs) have been emerging as a powerful computational tool for solving differential equations. However, the applicability of these models is still in its initial stages and requires more standardization to…