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While many neural networks focus on layers to process information, the GAIN model uses a grid-based structure to improve biological plausibility and the dynamics of the model. The grid structure helps neurons to interact with their closest…

The importance of higher-order relations is widely recognized in a large number of real-world systems. However, annotating them is a tedious and sometimes impossible task. Consequently, current approaches for data modelling either ignore…

In this work, we propose a learning method for solving the linear transport equation under the diffusive scaling. Due to the multiscale nature of our model equation, the model is challenging to solve by using conventional methods. We employ…

An important inference from Neural Tangent Kernel (NTK) theory is the existence of spectral bias (SB), that is, low frequency components of the target function of a fully connected Artificial Neural Network (ANN) being learnt significantly…

One of the main goals of developmental biology is to reveal the gene regulatory networks (GRNs) underlying the robust differentiation of multipotent progenitors into precisely specified cell types. Most existing methods to infer GRNs from…

We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to learning and discovery in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN,…

Taking inspiration from biological evolution, we explore the idea of "Can deep neural networks evolve naturally over successive generations into highly efficient deep neural networks?" by introducing the notion of synthesizing new highly…

Neural machine learning methods, such as deep neural networks (DNN), have achieved remarkable success in a number of complex data processing tasks. These methods have arguably had their strongest impact on tasks such as image and audio…

Emergence of deep neural networks (DNNs) has raised enormous attention towards artificial neural networks (ANNs) once again. They have become the state-of-the-art models and have won different machine learning challenges. Although these…

Data-driven modeling of spatiotemporal physical processes with general deep learning methods is a highly challenging task. It is further exacerbated by the limited availability of data, leading to poor generalizations in standard neural…

Physics-informed neural networks (PINNs) are a class of deep learning models that utilize physics in the form of differential equations to address complex problems, including those with limited data availability. However, solving…

This paper introduces a framework based on physics-informed neural networks (PINNs) for addressing key challenges in nonlinear lattices, including solution approximation, bifurcation diagram construction, and linear stability analysis. We…

Combining machine learning with physics is a trending approach for discovering unknown dynamics, and one of the most intensively studied frameworks is the physics-informed neural network (PINN). However, PINN often fails to optimize the…

Neural Networks (NN) has been used in many areas with great success. When a NN's structure (Model) is given, during the training steps, the parameters of the model are determined using an appropriate criterion and an optimization algorithm…

We introduce MixFunn, a novel neural network architecture designed to solve differential equations with enhanced precision, interpretability, and generalization capability. The architecture comprises two key components: the mixed-function…

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 remarkable success of Deep Neural Networks(DNN) is driven by gradient-based optimization, yet this process is often undermined by its tendency to produce disordered weight structures, which harms feature clarity and degrades learning…

Physics-informed neural networks (PINNs) have been proven as a promising way for solving various partial differential equations, especially high-dimensional ones and those with irregular boundaries. However, their capabilities in real…

Physics-informed neural networks (PINNs) have emerged as a versatile and widely applicable concept across various science and engineering domains over the past decade. This article offers a comprehensive overview of the fundamentals of…

We proposed the boundary-integral type neural networks (BINN) for the boundary value problems in computational mechanics. The boundary integral equations are employed to transfer all the unknowns to the boundary, then the unknowns are…