Related papers: Physics-Informed Deep B-Spline Networks
Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been…
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…
Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial differential equation (PDE)-constrained optimization problems with initial conditions and boundary conditions as soft constraints. These soft…
Machine learning methods for solving nonlinear partial differential equations (PDEs) are hot topical issues, and different algorithms proposed in the literature show efficient numerical approximation in high dimension. In this paper, we…
Physics-informed deep learning often faces optimization challenges due to the complexity of solving partial differential equations (PDEs), which involve exploring large solution spaces, require numerous iterations, and can lead to unstable…
In this paper, we propose a novel Physics-Informed Neural Network (PINN) framework based on the Cord\`{e}s condition for solving both linear and fully nonlinear partial differential equations (PDEs) in non-divergence form, together with…
Many scientific and industrial applications require solving Partial Differential Equations (PDEs) to describe the physical phenomena of interest. Some examples can be found in the fields of aerodynamics, astrodynamics, combustion and many…
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…
Identifying parameters in partial differential equations (PDEs) represents a very broad class of applied inverse problems. In recent years, several unsupervised learning approaches using (deep) neural networks have been developed to solve…
We present a deep learning emulator for stochastic and chaotic spatio-temporal systems, explicitly conditioned on the parameter values of the underlying partial differential equations (PDEs). Our approach involves pre-training the model on…
In the realm of computational fluid dynamics, traditional numerical methods, which heavily rely on discretization, typically necessitate the formulation of partial differential equations (PDEs) in conservative form to accurately capture…
Recently, physics informed neural networks (PINNs) have been explored extensively for solving various forward and inverse problems and facilitating querying applications in fluid mechanics applications. However, work on PINNs for unsteady…
While complex simulations of physical systems have been widely used in engineering and scientific computing, lowering their often prohibitive computational requirements has only recently been tackled by deep learning approaches. In this…
This paper proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler-Bernoulli and Timoshenko theory, where the double beams are…
Partial differential equations (PDEs) govern nearly every physical process in science and engineering, yet solving them at scale remains prohibitively expensive. Generative AI has transformed language, vision, and protein science, but…
The convergence of statistical learning and molecular physics is transforming our approach to modeling biomolecular systems. Physics-informed machine learning (PIML) offers a systematic framework that integrates data-driven inference with…
In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (e.g., aircraft shape optimization over many design…
We present a unified hard-constraint framework for solving geometrically complex PDEs with neural networks, where the most commonly used Dirichlet, Neumann, and Robin boundary conditions (BCs) are considered. Specifically, we first…
Our recent intensive study has found that physics-informed neural networks (PINN) tend to be local approximators after training. This observation leads to this novel physics-informed radial basis network (PIRBN), which can maintain the…
Understanding real-world dynamical phenomena remains a challenging task. Across various scientific disciplines, machine learning has advanced as the go-to technology to analyze nonlinear dynamical systems, identify patterns in big data, and…