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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…

Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations (PDEs). However, most existing studies focus only on multi-scale, multi-physics systems within a single…

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…

Neural operators have emerged as powerful surrogates for dynamical systems due to their grid-invariant properties and computational efficiency. However, the Fourier-based neural operator framework inherently truncates high-frequency…

Fourier Neural Operators (FNO) have emerged as promising solutions for efficiently solving partial differential equations (PDEs) by learning infinite-dimensional function mappings through frequency domain transformations. However, the…

Modeling complex systems using standard neural ordinary differential equations (NODEs) often faces some essential challenges, including high computational costs and susceptibility to local optima. To address these challenges, we propose a…

Neural operators generalize classical neural networks to maps between infinite-dimensional spaces, e.g., function spaces. Prior works on neural operators proposed a series of novel methods to learn such maps and demonstrated unprecedented…

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…

Computationally efficient surrogates for parametrized physical models play a crucial role in science and engineering. Operator learning provides data-driven surrogates that map between function spaces. However, instead of full-field…

There has recently been increasing attention towards developing foundational neural Partial Differential Equation (PDE) solvers and neural operators through large-scale pretraining. However, unlike vision and language models that make use…

With the recent rise of neural operators, scientific machine learning offers new solutions to quantify uncertainties associated with high-fidelity numerical simulations. Traditional neural networks, such as Convolutional Neural Networks…

Recently, physics-driven deep learning methods have shown particular promise for the prediction of physical fields, especially to reduce the dependency on large amounts of pre-computed training data. In this work, we target the…

Partial differential equations (PDEs) govern diverse physical phenomena, yet high-fidelity numerical solutions are computationally expensive and Machine Learning approaches lack generalization. While Scientific Foundation Models (SFMs) aim…

Deep neural networks can be powerful tools, but require careful application-specific design to ensure that the most informative relationships in the data are learnable. In this paper, we apply deep neural networks to the nonlinear…

Physics-informed neural networks have gained popularity as a deep-learning based parametric partial differential equation solver. Especially for engineering applications, this approach is promising because a single neural network could…

Self-training techniques have shown remarkable value across many deep learning models and tasks. However, such techniques remain largely unexplored when considered in the context of learning fast solvers for systems of partial differential…

Diffusion models have found widespread adoption in various areas. However, their sampling process is slow because it requires hundreds to thousands of network evaluations to emulate a continuous process defined by differential equations. In…

The uncertainty in human driving behaviors leads to stop-and-go instabilities in freeway traffic. The traffic dynamics are typically modeled by the Aw-Rascle-Zhang (ARZ) Partial Differential Equation (PDE) models, in which the relaxation…

In this paper we investigate the use of Fourier Neural Operators (FNOs) for image classification in comparison to standard Convolutional Neural Networks (CNNs). Neural operators are a discretization-invariant generalization of neural…

Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…