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Ongoing climate change calls for fast and accurate weather and climate modeling. However, when solving large-scale weather prediction simulations, state-of-the-art CPU and GPU implementations suffer from limited performance and high energy…

Computational fluid dynamics (CFD) simulations are broadly applied in engineering and physics. A standard description of fluid dynamics requires solving the Navier-Stokes (N-S) equations in different flow regimes. However, applications of…

Accurate prediction of blast pressure fields is essential for applications in structural safety, defense planning, and hazard mitigation. Traditional methods such as empirical models and computational fluid dynamics (CFD) simulations offer…

Data-driven prediction of fluid flow and temperature distribution in marine and aerospace engineering has received extensive research and demonstrated its potential in real-time prediction recently. However, usually large amounts of…

Natural climate solutions (NCS) offer an approach to mitigating carbon dioxide (CO2) emissions. However, monitoring the carbon drawdown of ecosystems over large geographic areas remains challenging. Eddy-flux covariance towers provide…

Mesoscale simulations of fission gas release (FGR) in nuclear fuel provide a powerful tool for understanding how microstructure evolution impacts FGR, but they are computationally intensive. In this study, we present an alternate,…

Classical sequential models employed in time-series prediction rely on learning the mappings from the past to the future instances by way of a hidden state. The Hidden states characterise the historical information and encode the required…

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…

Combinatorial optimization (CO) is one of the most fundamental mathematical models in real-world applications. Traditional CO solvers, such as Branch-and-Bound (B&B) solvers, heavily rely on expert-designed heuristics, which are reliable…

Data-driven modeling of constrained multibody dynamics remains challenged by (i) the training cost of Neural ODEs, which typically require backpropagation through an ODE solver, and (ii) error accumulation in rollout predictions. We…

Modeling and simulation of High Power Microwave (HPM) breakdown, a multiscale phenomenon, is computationally expensive and requires solving Maxwell's equations (EM solver) coupled with a plasma continuity equation (plasma solver). In this…

Operator learning is a variant of machine learning that is designed to approximate maps between function spaces from data. The Fourier Neural Operator (FNO) is one of the main model architectures used for operator learning. The FNO combines…

We propose a new data-driven method to learn the dynamics of an unknown hyperbolic system of conservation laws using deep neural networks. Inspired by classical methods in numerical conservation laws, we develop a new conservative form…

Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps…

We introduce the Laplace neural operator (LNO), which leverages the Laplace transform to decompose the input space. Unlike the Fourier Neural Operator (FNO), LNO can handle non-periodic signals, account for transient responses, and exhibit…

Implicit neural representations such as Neural Radiance Field (NeRF) have focused mainly on modeling static objects captured under multi-view settings where real-time rendering can be achieved with smart data structures, e.g., PlenOctree.…

We introduce Kolmogorov--Arnold Neural Operator (KANO), a dual-domain neural operator jointly parameterized by both spectral and spatial bases with intrinsic symbolic interpretability. We theoretically demonstrate that KANO overcomes the…

The high cost of high-resolution computational fluid/flame dynamics (CFD) has hindered its application in combustion related design, research and optimization. In this study, we propose a new framework for turbulent combustion simulation…

A plentitude of applications in scientific computing requires the approximation of mappings between Banach spaces. Recently introduced Fourier Neural Operator (FNO) and Deep Operator Network (DeepONet) can provide this functionality. For…

Over the past decades, there has been an explosion in the amount of available Earth Observation (EO) data. The unprecedented coverage of the Earth's surface and atmosphere by satellite imagery has resulted in large volumes of data that must…