Related papers: Physically Informed Synchronic-adaptive Learning f…
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…
Partial differential equations (PDEs) are a model candidate for soft sensors in industrial processes with spatiotemporal dependence. Although physics-informed neural networks (PINNs) are a promising machine learning method for solving PDEs,…
Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…
Physics-informed deep learning has emerged as a promising framework for solving partial differential equations (PDEs). Nevertheless, training these models on complex problems remains challenging, often leading to limited accuracy and…
Physics-informed neural networks (PINNs) have shown to be an effective tool for solving forward and inverse problems of partial differential equations (PDEs). PINNs embed the PDEs into the loss of the neural network, and this PDE loss is…
With the increases in computational power and advances in machine learning, data-driven learning-based methods have gained significant attention in solving PDEs. Physics-informed neural networks (PINNs) have recently emerged and succeeded…
Physics-informed neural networks (PINNs) have garnered significant interest for their potential in solving partial differential equations (PDEs) that govern a wide range of physical phenomena. By incorporating physical laws into the…
In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…
This study presents a novel physics-informed neural network (PINN) framework for modeling poroelasticity in heterogeneous media with material interfaces. The approach introduces a composite neural network (CoNN) where separate neural…
The numerical approximation of partial differential equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and…
Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, solving high-fidelity PDEs remains…
Physics-informed neural networks (PINNs) have received significant attention as a unified framework for forward, inverse, and surrogate modeling of problems governed by partial differential equations (PDEs). Training PINNs for forward…
A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating the residual term from governing partial differential equations (PDEs), to ensure its output is consistent with fundamental physics laws.…
A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…
Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training…
This work is concerned with discovering the governing partial differential equation (PDE) of a physical system. Existing methods have demonstrated the PDE identification from finite observations but failed to maintain satisfying results…
Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. Accurately solving unbounded domain PDEs requires efficient…
Physics-Informed Neural Networks present a novel approach in SciML that integrates physical laws in the form of partial differential equations directly into the NN through soft constraints in the loss function. This work studies the…
Partial differential equations (PDEs) are widely used to describe relevant phenomena in dynamical systems. In real-world applications, we commonly need to combine formal PDE models with (potentially noisy) observations. This is especially…
Physics-Informed Neural Networks (PINNs) have become a kind of attractive machine learning method for obtaining solutions of partial differential equations (PDEs). Training PINNs can be seen as a semi-supervised learning task, in which only…