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A key appeal of the recently proposed Neural Ordinary Differential Equation (ODE) framework is that it seems to provide a continuous-time extension of discrete residual neural networks. As we show herein, though, trained Neural ODE models…

ADCME is a novel computational framework to solve inverse problems involving physical simulations and deep neural networks (DNNs). This paper benchmarks its capability to learn spatially-varying physical fields using DNNs. We demonstrate…

We propose doubly nested network(DNNet) where all neurons represent their own sub-models that solve the same task. Every sub-model is nested both layer-wise and channel-wise. While nesting sub-models layer-wise is straight-forward with…

Deep neural networks (DNNs) have emerged as key enablers of machine learning. Applying larger DNNs to more diverse applications is an important challenge. The computations performed during DNN training and inference are dominated by…

Learning solution operators for differential equations with neural networks has shown great potential in scientific computing, but ensuring their stability under input perturbations remains a critical challenge. This paper presents a robust…

Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs),…

Physics-informed neural networks and Physics-informed DeepONet excel in solving partial differential equations; however, they often fail to converge for singularly perturbed problems. To address this, we propose two novel frameworks,…

Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of…

Atomistic modeling of energetic disorder in organic semiconductors (OSCs) and its effects on the optoelectronic properties of OSCs requires a large number of excited-state electronic-structure calculations, a computationally daunting task…

Neural operators (NO) are discretization invariant deep learning methods with functional output and can approximate any continuous operator. NO have demonstrated the superiority of solving partial differential equations (PDEs) over other…

Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…

Differential algebraic equations (DAEs) describe the temporal evolution of systems that obey both differential and algebraic constraints. Of particular interest are systems that contain implicit relationships between their components, such…

Recent work has introduced a simple numerical method for solving partial differential equations (PDEs) with deep neural networks (DNNs). This paper reviews and extends the method while applying it to analyze one of the most fundamental…

Neural operator learning models have emerged as very effective surrogates in data-driven methods for partial differential equations (PDEs) across different applications from computational science and engineering. Such operator learning…

Nonlinear differential equations are challenging to solve numerically and are important to understanding the dynamics of many physical systems. Deep neural networks have been applied to help alleviate the computational cost that is…

We introduce OS-net (Orbitally Stable neural NETworks), a new family of neural network architectures specifically designed for periodic dynamical data. OS-net is a special case of Neural Ordinary Differential Equations (NODEs) and takes…

Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. Recent advances in deep learning have enabled us to solve them in a higher dimension by addressing the curse of…

Maxwell's equations, a system of linear partial differential equations (PDEs), describe the behavior of electric and magnetic fields in time and space and are essential for many important electromagnetic applications. Although numerical…

Wave propagation problems are typically formulated as partial differential equations (PDEs) on unbounded domains to be solved. The classical approach to solving such problems involves truncating them to problems on bounded domains by…

Neural operators, as a powerful approximation to the non-linear operators between infinite-dimensional function spaces, have proved to be promising in accelerating the solution of partial differential equations (PDE). However, it requires a…