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We present our progress on the application of physics informed deep learning to reservoir simulation problems. The model is a neural network that is jointly trained to respect governing physical laws and match boundary conditions. The…
We develop improved physics-informed neural networks (PINNs) for high-order and high-dimensional power system models described by nonlinear ordinary differential equations. We propose some novel enhancements to improve PINN training and…
We present a Physics-Informed Neural Network (PINN) to simulate the thermochemical evolution of a composite material on a tool undergoing cure in an autoclave. In particular, we solve the governing coupled system of differential equations…
We present an open-source Physics Informed Neural Network environment for simulations of transient phenomena on two-dimensional rectangular domains, with the following features: (1) it is compatible with Google Colab which allows automatic…
Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing…
Prior-data fitted networks (PFNs) are a promising alternative to time-consuming Gaussian process (GP) inference for creating fast surrogates of physical systems. PFN reduces the computational burden of GP-training by replacing Bayesian…
Physics-informed neural networks (PINNs) integrate fundamental physical principles with advanced data-driven techniques, driving significant advancements in scientific computing. However, PINNs face persistent challenges with stiffness in…
Physics-Informed Neural Networks (PINNs) have advanced the data-driven solution of differential equations (DEs) in dynamic physical systems, yet challenges remain in explainability, scalability, and architectural complexity. This paper…
Physics-Informed Neural Networks (PINNs) have become a prominent application of deep learning in scientific computation, as they are powerful approximators of solutions to nonlinear partial differential equations (PDEs). There have been…
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 networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems for PDEs. We focus on a particular class of inverse problems, the so-called data assimilation or unique…
Physics-Informed Neural Networks (PINNs) seek to solve partial differential equations (PDEs) with deep learning. Mainstream approaches that deploy fully-connected multi-layer deep learning architectures require prolonged training to achieve…
The modeling and control of single-phase flow systems governed by Partial Differential Equations (PDEs) present challenges, especially under transient conditions. In this work, we extend the Physics-Informed Neural Nets for Control (PINC)…
Physics-informed neural networks (PINNs) provide a promising framework for solving inverse problems governed by partial differential equations (PDEs) by integrating observational data and physical constraints in a unified optimization…
Successfully training Physics Informed Neural Networks (PINNs) for highly nonlinear PDEs on complex 3D domains remains a challenging task. In this paper, PINNs are employed to solve the 3D incompressible Navier-Stokes (NS) equations at…
Iterative methods are widely used for solving partial differential equations (PDEs). However, the difficulty in eliminating global low-frequency errors significantly limits their convergence speed. In recent years, neural networks have…
As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…
Accurate simulation of turbulent flows is fundamental to scientific and engineering applications. Direct numerical simulation (DNS) offers the highest fidelity but is computationally prohibitive, while existing data-driven alternatives…
Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Reynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification,…
Large-scale wave field reconstruction requires precise solutions but faces challenges with computational efficiency and accuracy. The physics-based numerical methods like Finite Element Method (FEM) provide high accuracy but struggle with…