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Fourier Neural Operators (FNOs) offer a principled approach for solving complex partial differential equations (PDEs). However, scaling them to handle more complex PDEs requires increasing the number of Fourier modes, which significantly…

Numerical simulation of multiphase flow in porous media is essential for many geoscience applications. Machine learning models trained with numerical simulation data can provide a faster alternative to traditional simulators. Here we…

Neural networks offer high-accuracy solutions to a range of problems, but are costly to run in production systems because of computational and memory requirements during a forward pass. Given a trained network, we propose a techique called…

We study the training process of Deep Neural Networks (DNNs) from the Fourier analysis perspective. We demonstrate a very universal Frequency Principle (F-Principle) -- DNNs often fit target functions from low to high frequencies -- on…

Minimizing PDE-residual losses is a common strategy to promote physical consistency in neural operators. However, standard formulations often lack variational correctness, meaning that small residuals do not guarantee small solution errors…

While Fourier-based neural operators are best suited to learning mappings between functions on periodic domains, several works have introduced techniques for incorporating non trivial boundary conditions. However, all previously introduced…

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…

As artificial intelligence emerges as a transformative enabler for fusion energy commercialization, fast and accurate solvers become increasingly critical. In magnetic confinement nuclear fusion, rapid and accurate solution of the…

This paper introduces for the first time a framework to obtain provable worst-case guarantees for neural network performance, using learning for optimal power flow (OPF) problems as a guiding example. Neural networks have the potential to…

Physics-informed neural operators have emerged as a powerful paradigm for solving parametric partial differential equations (PDEs), particularly in the aerospace field, enabling the learning of solution operators that generalize across…

The commitment to single-precision floating-point arithmetic is widespread in the deep learning community. To evaluate whether this commitment is justified, the influence of computing precision (single and double precision) on the…

Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications. Among them, the Fourier neural operator (FNO) is a popular architecture that…

In this paper, we propose a way to solve partial differential equations (PDEs) by combining machine learning techniques and the finite element method called Phi-FEM. For that, we use the Fourier Neural Operator (FNO), a learning mapping…

Neural network quantization is frequently used to optimize model size, latency and power consumption for on-device deployment of neural networks. In many cases, a target bit-width is set for an entire network, meaning every layer get…

We describe an approach for incorporating prior knowledge into machine learning algorithms. We aim at applications in physics and signal processing in which we know that certain operations must be embedded into the algorithm. Any operation…

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…

In this paper, we evaluate training of deep recurrent neural networks with half-precision floats. We implement a distributed, data-parallel, synchronous training algorithm by integrating TensorFlow and CUDA-aware MPI to enable execution…

Simulating Darcy flows in porous media is fundamental to understand the future flow behavior of fluids in hydrocarbon and carbon storage reservoirs. Geological models of reservoirs are often associated with high uncertainly leading to many…

This paper introduces, for the first time to our knowledge, physics-informed neural networks to accurately estimate the AC-OPF result and delivers rigorous guarantees about their performance. Power system operators, along with several other…

Geological carbon sequestration (GCS) involves injecting CO$_2$ into subsurface geological formations for permanent storage. Numerical simulations could guide decisions in GCS projects by predicting CO$_2$ migration pathways and the…