相关论文: Physics-constrained neural differential equations …

Many physical and engineering systems require solving direct problems to predict behavior and inverse problems to determine unknown parameters from measurement. In this work, we study both aspects for systems governed by differential…

Modulating ion transport through nanoporous membranes is critical to many important chemical and biological separation processes. The corresponding transport timescales, however, are often too long to capture accurately using conventional…

In this paper, we introduce PDE-LEARN, a novel deep learning algorithm that can identify governing partial differential equations (PDEs) directly from noisy, limited measurements of a physical system of interest. PDE-LEARN uses a Rational…

Whilst the partial differential equations that govern the dynamics of our world have been studied in great depth for centuries, solving them for complex, high-dimensional conditions and domains still presents an incredibly large…

A model of a finite cylindrical ion channel through a phospholipid membrane of width $L$ separating two electrolyte reservoirs is studied. Analytical solution of the Poisson equation is obtained for an arbitrary distribution of ions inside…

Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when…

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…

Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…

Forecasting physical signals in long time range is among the most challenging tasks in Partial Differential Equations (PDEs) research. To circumvent limitations of traditional solvers, many different Deep Learning methods have been…

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…

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 macroscopic model to describe the dynamics of ion transport in ion channels is the Poisson-Nernst-Planck(PNP) equations. In this paper, we develop a finite-difference method for solving PNP equations, which is second-order accurate in…

The challenge of applying learned knowledge from one domain to solve problems in another related but distinct domain, known as transfer learning, is fundamental in operator learning models that solve Partial Differential Equations (PDEs).…

Sodium-ion batteries are a cost-effective and sustainable alternative to lithium-ion systems for large-scale energy storage. Hard carbon (HC) anodes, composed of disordered graphitic and amorphous domains, offer high capacity but exhibit…

Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) using deep learning. However, PINNs face training difficulties for evolutionary PDEs, particularly for dynamical…

We present an end-to-end framework to learn partial differential equations that brings together initial data production, selection of boundary conditions, and the use of physics-informed neural operators to solve partial differential…

Ion transport through nanoscale channels and pores is pivotal to numerous natural processes and industrial applications. Experimental investigation of the kinetics and mechanisms of such processes is, however, hampered by the limited…

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

Cutting edge deep learning techniques allow for image segmentation with great speed and accuracy. However, application to problems in materials science is often difficult since these complex models may have difficultly learning physical…

Porous graphene has high mechanical strength and atomic layer thickness, which make it a promising material for material separation and biomolecule sensing. Electrostatic interactions between charges in aqueous solution are a kind of strong…