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Spatio-temporal process models are often used for modeling dynamic physical and biological phenomena that evolve across space and time. These phenomena may exhibit environmental heterogeneity and complex interactions that are difficult to…

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)…

Convolutional graph networks are used in particle physics for effective event reconstructions and classifications. However, their performances can be limited by the considerable amount of sensors used in modern particle detectors if applied…

We present approximation theories and efficient training methods for derivative-informed Fourier neural operators (DIFNOs) with applications to PDE-constrained optimization. A DIFNO is an FNO trained by minimizing its prediction error…

Next-generation multiple-input multiple-output (MIMO) systems, characterized by extremely large-scale arrays, holographic surfaces, three-dimensional architectures, and flexible antennas, are poised to deliver unprecedented data rates,…

Acquisition of large datasets for three-dimensional (3D) partial differential equations (PDE) is usually very expensive. Physics-informed neural operator (PINO) eliminates the high costs associated with generation of training datasets, and…

In computational physics, a longstanding challenge lies in finding numerical solutions to partial differential equations (PDEs). Recently, research attention has increasingly focused on Neural Operator methods, which are notable for their…

Physics-informed neural operators offer a powerful framework for learning solution operators of partial differential equations (PDEs) by combining data and physics losses. However, these physics losses rely on derivatives. Computing these…

Memory complexity and data scarcity have so far prohibited learning solution operators of partial differential equations (PDEs) at high resolutions. We address these limitations by introducing a new data efficient and highly parallelizable…

Phase-field simulations provide mechanistic descriptions of microstructure evolution, but repeated high-fidelity integration over long horizons and broad parameter spaces remains computationally expensive. We present PFNet, a…

Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…

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,…

Physics-Informed Neural Networks (PINNs) are a useful framework for approximating partial differential equation solutions using deep learning methods. In this paper, we propose a principled redesign of the PINNsformer, a Transformer-based…

High-fidelity direct numerical simulation of turbulent flows for most real-world applications remains an outstanding computational challenge. Several machine learning approaches have recently been proposed to alleviate the computational…

Fourier neural operators (FNOs) provide a mesh-independent way to learn solution operators for partial differential equations, yet their efficacy for magnetized turbulence is largely unexplored. Here we train an FNO surrogate for the 2-D…

Elliptic partial differential equations (PDEs) are a major class of time-independent PDEs that play a key role in many scientific and engineering domains such as fluid dynamics, plasma physics, and solid mechanics. Recently, neural…

Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and…

The UNet-enhanced Fourier Neural Operator (UFNO) extends the Fourier Neural Operator (FNO) by incorporating a parallel UNet pathway, enabling the retention of both high- and low-frequency components. While UFNO improves predictive accuracy…

The numerical approximation of the Boltzmann collision operator presents significant challenges arising from its high dimensionality, nonlinear structure, and nonlocal integral form. In this work, we propose a Fourier Neural Operator (FNO)…

Substitution of well-grounded theoretical models by data-driven predictions is not as simple in engineering and sciences as it is in social and economic fields. Scientific problems suffer most times from paucity of data, while they may…