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We propose an extended Fourier neural operator (FNO) architecture for learning state and linear quadratic additive optimal control of systems governed by partial differential equations. Using the Ehrenpreis-Palamodov fundamental principle,…
Data-driven emulation of nonlinear dynamics is challenging due to long-range skill decay that often produces physically unrealistic outputs. Recent advances in generative modeling aim to address these issues by providing uncertainty…
Real-time thermal-hydraulic simulation is essential for digital twin (DT) technology that supports the safe and efficient operation of small modular reactors (SMRs). Computational fluid dynamics (CFD) provides high-fidelity flow analysis,…
Neural operators extend data-driven models to map between infinite-dimensional functional spaces. While these operators perform effectively in either the time or frequency domain, their performance may be limited when applied to…
Multifunctional metamaterials (MMM) bear promise as next-generation material platforms supporting miniaturization and customization. Despite many proof-of-concept demonstrations and the proliferation of deep learning assisted design, grand…
The physics-informed neural operator (PINO) is a machine learning paradigm that has demonstrated promising results for learning solutions to partial differential equations (PDEs). It leverages the Fourier Neural Operator to learn solution…
Learning accurate and stable time-advancement operators for nonlinear partial differential equations (PDEs) remains challenging, particularly for chaotic, stiff, and long-horizon dynamical systems. While neural operator methods such as the…
Applications that require multi-robot systems to operate independently for extended periods of time in unknown or unstructured environments face a broad set of challenges, such as hardware degradation, changing weather patterns, or…
Modeling three-dimensional (3D) turbulence by neural networks is difficult because 3D turbulence is highly-nonlinear with high degrees of freedom and the corresponding simulation is memory-intensive. Recently, the attention mechanism has…
Two models based on convolutional neural networks are trained to predict the two-dimensional velocity-fluctuation fields at different wall-normal locations in a turbulent open channel flow, using the wall-shear-stress components and the…
In this paper, a multi-scale Fourier neural operator (MscaleFNO) is proposed to reduce the spectral bias of the FNO in learning the mapping between highly oscillatory functions, with application to the nonlinear mapping between the…
Interfacial dynamics underlie a wide range of phenomena, including phase transitions, microstructure coarsening, pattern formation, and thin-film growth, and are typically described by stiff, time-dependent nonlinear partial differential…
This paper proposes a physics-informed neural operator (PINO) framework for solving inverse scattering problems, enabling rapid and accurate reconstructions under diverse measurement conditions. In the proposed approach, the dielectric…
Microstructural evolution, particularly grain growth, plays a critical role in shaping the physical, optical, and electronic properties of materials. Traditional phase-field modeling accurately simulates these phenomena but is…
This paper introduces two novel concepts in data-driven turbulence modeling that enable the simultaneous development of multiple closure models and the training towards multiple objectives. The concepts extend the evolutionary framework by…
Neural operators are becoming the default tools to learn solutions to governing partial differential equations (PDEs) in weather and ocean forecasting applications. Despite early promising achievements, significant challenges remain,…
Simulating massively separated turbulent flows over bodies is one of the major applications for large-eddy simulation (LES). In the current work, we propose a machine-learning-based LES framework for the rapid simulation of turbulent flows…
Synthetic turbulence models are a useful tool that provide realistic representations of turbulence, necessary to test theoretical results, to serve as background fields in some numerical simulations, and to test analysis tools. Models of 1D…
We investigate conditional neural fields (CNFs), mesh-agnostic, coordinate-based decoders conditioned on a low-dimensional latent, for spatial dimensionality reduction of turbulent flows. CNFs are benchmarked against Proper Orthogonal…
Neural Operators (NOs) are machine learning models designed to solve partial differential equations (PDEs) by learning to map between function spaces. Neural Operators such as the Deep Operator Network (DeepONet) and the Fourier Neural…