Related papers: Data Generation-based Operator Learning for Solvin…

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…

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…

Operator learning aims to discover properties of an underlying dynamical system or partial differential equation (PDE) from data. Here, we present a step-by-step guide to operator learning. We explain the types of problems and PDEs amenable…

Partial differential equations (PDEs) underpin models across science and engineering, yet analytical solutions are atypical and classical mesh-based solvers can be costly in high dimensions. This dissertation presents a unified comparison…

Physics-Informed Neural Networks (PINNs) have emerged as powerful tools for solving partial differential equations (PDEs). However, training PINNs from scratch is often computationally intensive and time-consuming. To address this problem,…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical laws into neural network training. However, traditional PINN models are typically designed…

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…

We show that the physics-informed neural networks (PINNs), in combination with some recently developed discontinuity capturing neural networks, can be applied to solve optimal control problems subject to partial differential equations…

Physics-informed neural networks (PINNs) are an emerging technique to solve partial differential equations (PDEs). In this work, we propose a simple but effective PINN approach for the phase-field model of ferroelectric microstructure…

We introduce a generalizable approach that combines perturbation method and one-shot transfer learning to solve nonlinear ODEs with a single polynomial term, using Physics-Informed Neural Networks (PINNs). Our method transforms non-linear…

The evolution of dynamical systems is generically governed by nonlinear partial differential equations (PDEs), whose solution, in a simulation framework, requires vast amounts of computational resources. In this work, we present a novel…

We present a data-driven control framework for partial differential equations (PDEs). Our approach integrates Time-Integrated Deep Operator Networks (TI-DeepONets) as differentiable PDE surrogate models within the Differentiable Predictive…

Optimal control problems with nonsmooth objectives and nonlinear partial differential equation (PDE) constraints are challenging, mainly because of the underlying nonsmooth and nonconvex structures and the demanding computational cost for…

Stiff differential equations are prevalent in various scientific domains, posing significant challenges due to the disparate time scales of their components. As computational power grows, physics-informed neural networks (PINNs) have led to…

Physics-Informed Neural Network (PINN) has proven itself a powerful tool to obtain the numerical solutions of nonlinear partial differential equations (PDEs) leveraging the expressivity of deep neural networks and the computing power of…

"AI for Science" aims to solve fundamental scientific problems using AI techniques. As most physical phenomena can be described as Partial Differential Equations (PDEs) , approximating their solutions using neural networks has evolved as a…

Machine learning methods have been lately used to solve partial differential equations (PDEs) and dynamical systems. These approaches have been developed into a novel research field known as scientific machine learning in which techniques…

Soft- and hard-constrained Physics Informed Neural Networks (PINNs) have achieved great success in solving partial differential equations (PDEs). However, these methods still face great challenges when solving the Navier-Stokes equations…

Design and optimal control problems are among the fundamental, ubiquitous tasks we face in science and engineering. In both cases, we aim to represent and optimize an unknown (black-box) function that associates a performance/outcome to a…

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…