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We present a method for learning dynamics of complex physical processes described by time-dependent nonlinear partial differential equations (PDEs). Our particular interest lies in extrapolating solutions in time beyond the range of…
A pore network modeling (PNM) framework for the simulation of transport of charged species, such as ions, in porous media is presented. It includes the Nernst-Planck (NP) equations for each charged species in the electrolytic solution in…
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)…
The brain extracellular space (ECS), an irregular, extremely tortuous nanoscale space located between cells or between cells and blood vessels, is crucial for nerve cell survival. It plays a pivotal role in high-level brain functions such…
Physics-informed neural networks (PINNs) are effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data. PINNs employ standard feedforward neural networks (NNs) with the PDEs explicitly…
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…
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…
Physics-informed neural networks (PINNs) have shown remarkable prospects in the solving the forward and inverse problems involving partial differential equations (PDEs). The method embeds PDEs into the neural network by calculating PDE loss…
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…
Parameter estimation for differential equations from measured data is an inverse problem prevalent across quantitative sciences. Physics-Informed Neural Networks (PINNs) have emerged as effective tools for solving such problems, especially…
The structure of a network has a major effect on dynamical processes on that network. Many studies of the interplay between network structure and dynamics have focused on models of phenomena such as disease spread, opinion formation and…
Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. Their ability to seamlessly integrate physical principles into deep learning architectures…
Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time. However, standard space--time PINNs take…
The numerical approximation of partial differential equations (PDEs) poses formidable challenges in high dimensions since classical grid-based methods suffer from the so-called curse of dimensionality. Recent attempts rely on a combination…
Fluid mechanics is a fundamental field in engineering and science. Solving the Navier-Stokes equation (NSE) is critical for understanding the behavior of fluids. However, the NSE is a complex partial differential equation that is difficult…
Transition phenomena between metastable states play an important role in complex systems due to noisy fluctuations. In this paper, the physics informed neural networks (PINNs) are presented to compute the most probable transition pathway.…
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,…
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…
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…
Compared to purely data-driven methods, a key feature of physics-informed neural networks (PINNs) - a proven powerful tool for solving partial differential equations (PDEs) - is the embedding of PDE constraints into the loss function. The…